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\u0686\u0644\u0627\u0646\u06d2 \u0633\u06d2 \u067e\u06c1\u0644\u06d2 GitHub \u0633\u06d2 \u067e\u0691\u06be \u0633\u06a9\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<h2 id=\"heading-table-of-contents\">\u0627\u0646\u0688\u06cc\u06a9\u0633<\/h2>\n<h2 id=\"heading-why-global-rollouts-break-naive-measurement\">\u06a9\u06cc\u0648\u06ba \u06af\u0644\u0648\u0628\u0644 \u0644\u0627\u0646\u0686 \u0646\u06d2 \u0628\u0648\u0644\u06cc \u067e\u06cc\u0645\u0627\u0626\u0634 \u06a9\u0648 \u062a\u0648\u0691 \u062f\u06cc\u0627\u06d4<\/h2>\n<p>A\/B \u0679\u06cc\u0633\u0679\u0646\u06af \u06a9\u06cc \u0631\u06cc\u0627\u0636\u06cc \u0627\u06cc\u06a9 \u0645\u0641\u0631\u0648\u0636\u06d2 \u06a9\u06cc \u0648\u062c\u06c1 \u0633\u06d2 \u062e\u0648\u0628\u0635\u0648\u0631\u062a \u06c1\u06d2: \u067e\u0631\u0648\u0633\u06cc\u0633\u0646\u06af \u0645\u062e\u062a\u0635 \u06c1\u0631 \u0686\u06cc\u0632 \u0633\u06d2 \u0622\u0632\u0627\u062f \u06c1\u06d2\u06d4 \u0627\u06cc\u06a9 \u0633\u06a9\u06d2 \u06a9\u0648 \u067e\u0644\u0679\u0627\u0626\u06cc\u06ba: \u0622\u067e \u06a9\u06d2 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u0627 \u0622\u062f\u06be\u0627 \u062d\u0635\u06c1 Claude 4.6 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u0627\u0648\u0631 \u0628\u0627\u0642\u06cc \u0622\u062f\u06be\u0627 4.5 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0631\u06c1\u062a\u0627 \u06c1\u06d2\u06d4 \u0633\u06a9\u06d2 \u06a9\u0648 \u067e\u0644\u0679\u0646\u06d2 \u0633\u06d2 \u062a\u0645\u0627\u0645 \u0645\u0645\u06a9\u0646\u06c1 \u0627\u0644\u062c\u06be\u0646\u06cc\u06ba \u0679\u0648\u0679 \u062c\u0627\u062a\u06cc \u06c1\u06cc\u06ba\u06d4 \u0639\u0627\u0644\u0645\u06cc \u0644\u0627\u0646\u0686 \u06a9\u06cc \u062f\u0646\u06cc\u0627 \u0645\u06cc\u06ba \u06a9\u0648\u0626\u06cc \u0633\u06a9\u06d2 \u0646\u06c1\u06cc\u06ba \u06c1\u06cc\u06ba\u06d4<\/p>\n<p>\u062a\u06cc\u0646 \u0637\u0631\u06cc\u0642\u06c1 \u06a9\u0627\u0631 \u067e\u06c1\u0644\u06d2 \u0627\u0648\u0631 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\u06c1\u0641\u062a\u06c1 \u0648\u0627\u0631 20-\u06c1\u0641\u062a\u0648\u06ba \u06a9\u06d2 \u0648\u0627\u0642\u0639\u0627\u062a \u06a9\u06d2 \u0633\u0628\u0628 \u0627\u062b\u0631\u0627\u062a \u06a9\u0648 \u062c\u0648\u0691 \u062f\u06cc\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<p>\u0627\u0633 \u0679\u06cc\u0648\u0679\u0648\u0631\u06cc\u0644 \u06a9\u06d2 \u0688\u06cc\u0679\u0627 \u0633\u06cc\u0679 \u0645\u06cc\u06ba\u060c Na\u00efve gap +0.0515 \u06c1\u06d2\u060c \u062c\u0648 \u06a9\u06c1 \u0632\u0645\u06cc\u0646\u06cc \u0633\u0686\u0627\u0626\u06cc +0.05 \u06a9\u06d2 \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0628\u0631\u0627\u0628\u0631 \u06c1\u06d2\u06d4 \u06cc\u06c1 \u0627\u062a\u0641\u0627\u0642\u0627\u062a \u0633\u0628 \u0633\u06d2 \u062e\u0648\u0641\u0646\u0627\u06a9 \u0646\u0627\u06a9\u0627\u0645\u06cc \u06a9\u0627 \u0645\u0648\u0688 \u06c1\u06cc\u06ba\u06d4 \u0628\u06d2 \u06c1\u0648\u062f\u06c1 \u0646\u0645\u0628\u0631 \u06a9\u0628\u06be\u06cc \u06a9\u0628\u06be\u06cc 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(\u0633\u0631\u062e) \u06a9\u0648 \u0628\u06c1\u062a\u0631\u06cc\u0646 \u0637\u0631\u06cc\u0642\u06d2 \u0633\u06d2 \u0679\u0631\u06cc\u06a9 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/em><\/p>\n<p><em>\u0639\u0644\u0627\u062c \u06a9\u06cc \u062a\u0627\u0631\u06cc\u062e (\u06c1\u0641\u062a\u06c1 20\u060c \u0688\u06cc\u0634\u0688 \u0639\u0645\u0648\u062f\u06cc \u0644\u06a9\u06cc\u0631) \u06a9\u06d2 \u0628\u0639\u062f\u060c \u0648\u0632\u0646 \u0645\u0642\u0631\u0631 \u0631\u06c1\u062a\u0627 \u06c1\u06d2 \u0627\u0648\u0631 \u0646\u0642\u0637\u06d2 \u0648\u0627\u0644\u0627 \u0645\u0646\u062d\u0646\u06cc \u062e\u0637\u0648\u0637 \u0645\u062a\u0636\u0627\u062f \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u0622\u06af\u06d2 \u0628\u0691\u06be\u062a\u0627 \u06c1\u06d2\u060c \u062c\u0628\u06a9\u06c1 \u0639\u0644\u0627\u062c \u0634\u062f\u06c1 \u06cc\u0648\u0646\u0679 \u0627\u0648\u067e\u0631 \u06a9\u06cc \u0637\u0631\u0641 \u0628\u0691\u06be\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 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\u0627\u0633\u067e\u06cc\u0633 \u0627\u0645\u06cc\u062f\u0648\u0627\u0631 \u0688\u0648\u0646\u0631 \u06c1\u06d2 \u0627\u06af\u0631 \u0648\u06cc\u0648-2 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u0648 \u0648\u06cc\u0648-1 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u06c1\u06cc \u0645\u0627\u0688\u0644 \u0627\u067e \u06af\u0631\u06cc\u0688 \u0646\u06c1\u06cc\u06ba \u0645\u0644\u062a\u0627 \u06c1\u06d2\u06d4 \u0622\u067e\u0679\u0645\u0627\u0626\u0632\u0631 \u0644\u06c1\u0631 2 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u0627 \u0645\u062c\u0645\u0648\u0639\u06c1 \u062a\u0644\u0627\u0634 \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u062c\u0646 \u06a9\u06d2 \u0648\u0632\u0646\u06cc \u067e\u0631\u06cc \u0627\u067e \u06af\u0631\u06cc\u0688 \u0679\u0631\u06cc\u062c\u06cc\u06a9\u0679\u0631\u0632 \u0644\u06c1\u0631 1 \u0633\u06d2 \u0628\u06c1\u062a\u0631\u06cc\u0646 \u0645\u06cc\u0686 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 \u06c1\u0641\u062a\u06c1 20 \u06a9\u06d2 \u0628\u0639\u062f (\u062c\u0628 \u067e\u06c1\u0644\u06cc \u0644\u06c1\u0631 \u06a9\u0648 \u0627\u067e \u06af\u0631\u06cc\u0688 \u06a9\u06cc\u0627 \u062c\u0627\u062a\u0627 \u06c1\u06d2)\u060c \u067e\u06c1\u0644\u06cc \u0644\u06c1\u0631 \u0627\u0648\u0631 \u062c\u0627\u0645\u0639 \u062c\u0691\u0648\u0627\u06ba \u06a9\u06d2 \u062f\u0631\u0645\u06cc\u0627\u0646 \u0648\u0642\u0641\u06c1 \u06a9\u0627\u0631\u0622\u0645\u062f \u0627\u062b\u0631 \u06a9\u0627 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u06c1\u06d2 \u0627\u06af\u0631 \u0645\u0646\u062f\u0631\u062c\u06c1 \u0630\u06cc\u0644 \u062a\u06cc\u0646 \u0634\u0646\u0627\u062e\u062a\u06cc \u0645\u0641\u0631\u0648\u0636\u0648\u06ba \u06a9\u0648 \u0628\u0631\u0642\u0631\u0627\u0631 \u0631\u06a9\u06be\u0627 \u062c\u0627\u0626\u06d2:<\/p>\n<p>\u06cc\u06c1 \u0634\u0646\u0627\u062e\u062a\u06cc \u0645\u0641\u0631\u0648\u0636\u06d2 \u0645\u0644 \u06a9\u0631 \u06a9\u0627\u0645 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<ul>\n<li>\n<p>\u0633\u0628 \u0633\u06d2 \u067e\u06c1\u0644\u06d2 <strong>\u062d\u06cc\u0636 \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0645\u0648\u0632\u0648\u06ba \u06c1\u06d2\u06d4<\/strong> (Convex Hull Condition): \u0639\u0644\u0627\u062c \u0634\u062f\u06c1 \u0688\u06cc\u0648\u0627\u0626\u0633 \u06a9\u06cc \u067e\u06c1\u0644\u06d2 \u0633\u06d2 \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u0631\u0641\u062a\u0627\u0631 \u0639\u0637\u06cc\u06c1 \u06a9\u0646\u0646\u062f\u06c1 \u06a9\u06d2 \u0645\u062d\u062f\u0628 \u06c1\u0648\u0644 \u06a9\u06d2 \u0627\u0646\u062f\u0631 \u06c1\u0648\u0646\u06cc \u0686\u0627\u06c1\u06cc\u06d2\u060c \u063a\u06cc\u0631 \u0645\u0646\u0641\u06cc \u0627\u0648\u0631 \u062c\u0645\u0639 \u0633\u06d2 \u0627\u06cc\u06a9 \u06a9\u06cc \u0631\u06a9\u0627\u0648\u0679\u0648\u06ba \u06a9\u06d2 \u0633\u0627\u062a\u06be\u06d4<\/p>\n<\/li>\n<li>\n<p>\u062f\u0648\u0633\u0631\u0627 <strong>\u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u06a9\u0648\u0626\u06cc \u0645\u062f\u0627\u062e\u0644\u062a \u0646\u06c1\u06cc\u06ba\u06d4<\/strong> (\u0688\u0648\u0646\u0631 \u067e\u0648\u0644 \u06a9\u06d2 \u0644\u06cc\u06d2 SUTVA): \u0639\u0644\u0627\u062c \u0634\u062f\u06c1 \u06cc\u0648\u0646\u0679\u0633 \u06a9\u06d2 \u0639\u0644\u0627\u062c \u0633\u06d2 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u0648 \u0645\u062a\u0627\u062b\u0631 \u0646\u06c1\u06cc\u06ba \u06a9\u0631\u0646\u0627 \u0686\u0627\u06c1\u06cc\u06d2\u06d4 \u0645\u0634\u062a\u0631\u06a9\u06c1 API \u06a9\u06cc \u0634\u0631\u062d \u06a9\u0648 \u0645\u062d\u062f\u0648\u062f \u06a9\u0631\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u067e\u0648\u0644 \u06cc\u0627 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u06d2 \u062f\u0631\u0645\u06cc\u0627\u0646 \u0645\u0646\u062a\u0642\u0644 \u06c1\u0648\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u06a9\u0633\u06cc \u0628\u06be\u06cc \u0635\u0627\u0631\u0641 \u06a9\u0648 \u0627\u0633 \u0645\u0633\u0626\u0644\u06d2 \u06a9\u0627 \u0633\u0627\u0645\u0646\u0627 \u06a9\u0631\u0646\u0627 \u067e\u0691\u06d2 \u06af\u0627\u06d4<\/p>\n<\/li>\n<li>\n<p>\u062a\u06cc\u0633\u0631\u0627 <strong>\u0645\u0633\u062a\u062d\u06a9\u0645 \u0688\u0648\u0646\u0631 \u06a9\u0645\u067e\u0648\u0632\u06cc\u0634\u0646<\/strong>: \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u0648 \u0645\u062f\u062a \u06a9\u06d2 \u0628\u0639\u062f \u0639\u0644\u0627\u062c \u0633\u06d2 \u063a\u06cc\u0631 \u0645\u062a\u0639\u0644\u0642 \u0633\u0627\u062e\u062a\u06cc \u0646\u0642\u0635\u0627\u0646 \u06a9\u0627 \u0633\u0627\u0645\u0646\u0627 \u0646\u06c1\u06cc\u06ba \u06a9\u0631\u0646\u0627 \u0686\u0627\u06c1\u0626\u06d2\u06d4 \u0627\u06af\u0631 \u062f\u0648\u0646\u0648\u06ba \u0645\u06cc\u06ba \u0633\u06d2 \u06a9\u0633\u06cc \u0627\u06cc\u06a9 \u06a9\u06cc \u0628\u06be\u06cc \u062e\u0644\u0627\u0641 \u0648\u0631\u0632\u06cc \u06a9\u06cc \u062c\u0627\u062a\u06cc \u06c1\u06d2\u060c \u062a\u0648 \u0627\u0633 \u0641\u0631\u0642 \u06a9\u0648 \u06cc\u06a9 \u0637\u0631\u0641\u06c1 \u06a9\u0631 \u062f\u06cc\u0627 \u062c\u0627\u0626\u06d2 \u06af\u0627 \u0686\u0627\u06c1\u06d2 \u0645\u0627\u06c1\u0648\u0627\u0631\u06cc \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u06a9\u0627 \u0641\u0679 \u0628\u0627\u0644\u06a9\u0644 \u062f\u0631\u0633\u062a \u0646\u0638\u0631 \u0622\u0626\u06d2\u06d4 \u0646\u0627\u06a9\u0627\u0645\u06cc \u06a9\u06d2 \u0637\u0631\u06cc\u0642\u0648\u06ba \u06a9\u0627 \u0633\u06cc\u06a9\u0634\u0646 \u06c1\u0631 \u0627\u06cc\u06a9 \u06a9\u06d2 \u0628\u0627\u0631\u06d2 \u0645\u06cc\u06ba \u0622\u067e \u06a9\u06cc \u0631\u06c1\u0646\u0645\u0627\u0626\u06cc \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<\/li>\n<\/ul>\n<p>\u0627\u06cc\u06a9 \u06c1\u0646\u062f\u0633\u06cc \u0646\u0648\u0679: T\u2080 \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0639\u0644\u0627\u062c \u06a9\u06cc \u0645\u062f\u062a \u0627\u0648\u0631 J \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u06d2 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06a9\u06d2 \u0646\u062a\u06cc\u062c\u06d2 \u0645\u06cc\u06ba J T\u2080 \u06a9\u06d2 \u0642\u0631\u06cc\u0628 \u0622\u0646\u06d2 \u067e\u0631 \u0634\u062f\u06cc\u062f \u067e\u0631\u06cc \u067e\u06cc\u0631\u06cc\u0688 \u0627\u0648\u0648\u0631 \u0641\u0679\u0646\u06af \u06a9\u0627 \u0646\u062a\u06cc\u062c\u06c1 \u06c1\u0648\u062a\u0627 \u06c1\u06d2\u06d4 \u06cc\u06c1 \u0679\u06cc\u0648\u0679\u0648\u0631\u06cc\u0644 T\u2080 = 20 \u0627\u0648\u0631 J = 25 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0686\u0644\u062a\u0627 \u06c1\u06d2\u060c \u062c\u0648 \u062e\u0637\u0631\u06d2 \u06a9\u06d2 \u0639\u0644\u0627\u0642\u06d2 \u0645\u06cc\u06ba \u06c1\u06d2\u06d4 LOO \u06a9\u06cc \u062d\u0633\u0627\u0633\u06cc\u062a \u06a9\u06d2 \u0628\u0639\u062f \u06a9\u06d2 \u0627\u0642\u062f\u0627\u0645\u0627\u062a \u0627\u0633 \u0628\u0627\u062a \u06a9\u06cc \u0627\u06cc\u06a9 \u0627\u0686\u06be\u06cc \u062a\u0634\u062e\u06cc\u0635 \u06c1\u06cc\u06ba \u06a9\u06c1 \u0622\u06cc\u0627 \u0641\u0679 \u0635\u062d\u06cc\u062d \u0645\u0648\u0627\u0632\u0646\u06c1 \u06a9\u06cc \u0639\u06a9\u0627\u0633\u06cc \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u06cc\u0627 \u0632\u06cc\u0627\u062f\u06c1 \u0641\u0679\u0646\u06af\u06d4<\/p>\n<h2 id=\"heading-prerequisites\">\u0634\u0631\u0627\u0626\u0637<\/h2>\n<p>Python 3.11 \u06cc\u0627 \u0627\u0633 \u0633\u06d2 \u0632\u06cc\u0627\u062f\u06c1\u060c \u067e\u0627\u0646\u0688\u0627 \u0627\u0648\u0631 numpy \u0633\u06d2 \u0648\u0627\u0642\u0641\u06cc\u062a\u060c \u0627\u0648\u0631 \u0628\u0646\u06cc\u0627\u062f\u06cc \u0645\u062d\u062f\u0648\u062f \u0627\u0635\u0644\u0627\u062d \u0633\u06d2 \u0648\u0627\u0642\u0641\u06cc\u062a \u06a9\u06cc \u0636\u0631\u0648\u0631\u062a \u06c1\u06d2\u06d4<\/p>\n<p>\u0627\u0633 \u0679\u06cc\u0648\u0679\u0648\u0631\u06cc\u0644 \u06a9\u06d2 \u0644\u06cc\u06d2 \u067e\u06cc\u06a9\u062c\u0632 \u0627\u0646\u0633\u0679\u0627\u0644 \u06a9\u0631\u06cc\u06ba\u06d4<\/p>\n<pre><code class=\"language-shell\">pip install numpy pandas scipy matplotlib\n<\/code><\/pre>\n<p><strong>\u0645\u0648\u062c\u0648\u062f\u06c1 \u0635\u0648\u0631\u062a\u062d\u0627\u0644 \u06a9\u0686\u06be \u06cc\u0648\u06ba \u06c1\u06d2:<\/strong> \u0686\u0627\u0631 \u067e\u06cc\u06a9\u062c \u067e\u0648\u0631\u06cc \u067e\u0627\u0626\u067e \u0644\u0627\u0626\u0646 \u06a9\u0627 \u0627\u062d\u0627\u0637\u06c1 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 \u067e\u0627\u0646\u0688\u0627\u0633 \u0635\u0627\u0631\u0641 \u06a9\u06cc \u0633\u0637\u062d \u06a9\u06d2 \u0644\u0648\u06af\u0627\u0631\u062a\u06be\u0645\u0632 \u06a9\u0648 \u0644\u0648\u0688 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u060c NumPy \u067e\u06cc\u0646\u0644 \u0631\u06cc\u0627\u0636\u06cc \u06a9\u0648 \u06c1\u06cc\u0646\u0688\u0644 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u060c SciPy \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u06d2 \u0648\u0632\u0646 \u067e\u0631 \u0645\u062d\u062f\u0628 \u0627\u0645\u062a\u0632\u0627\u062c \u06a9\u06cc \u0631\u06a9\u0627\u0648\u0679\u0648\u06ba \u06a9\u0648 \u0646\u0627\u0641\u0630 \u06a9\u0631\u0646\u06d2 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0627\u06cc\u06a9 SLSQP \u062d\u0644 \u0641\u0631\u0627\u06c1\u0645 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u060c \u0627\u0648\u0631 matplotlib \u0679\u0631\u06cc\u06a9\u0679\u0631\u06cc \u067e\u0644\u0627\u0679 \u0627\u0648\u0631 \u067e\u0644\u06cc\u0633\u0628\u0648 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0648 \u067e\u06cc\u0634 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u0645\u0635\u0646\u0648\u0639\u06cc \u0688\u06cc\u0679\u0627\u0633\u06cc\u0679 \u062d\u0627\u0635\u0644 \u06a9\u0631\u0646\u06d2 \u06a9\u06d2 \u0644\u06cc\u06d2\u060c \u0633\u0627\u062a\u06be\u06cc \u0631\u06cc\u067e\u0648\u0632\u0679\u0631\u06cc \u06a9\u0648 \u06a9\u0644\u0648\u0646 \u06a9\u0631\u06cc\u06ba\u06d4<\/p>\n<pre><code class=\"language-shell\">git clone https:\/\/github.com\/RudrenduPaul\/product-experimentation-causal-inference-genai-llm.git\ncd product-experimentation-causal-inference-genai-llm\npython data\/generate_data.py --seed 42 --n-users 50000 --out data\/synthetic_llm_logs.csv\n<\/code><\/pre>\n<p><strong>\u0645\u0648\u062c\u0648\u062f\u06c1 \u0635\u0648\u0631\u062a\u062d\u0627\u0644 \u06a9\u0686\u06be \u06cc\u0648\u06ba \u06c1\u06d2:<\/strong> \u06a9\u0644\u0648\u0646 \u0633\u0627\u062a\u06be\u06cc \u0630\u062e\u06cc\u0631\u06c1 \u062f\u0631\u0622\u0645\u062f \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u0627\u0648\u0631 <code>generate_data.py<\/code> \u0627\u06cc\u06a9 \u0645\u0634\u062a\u0631\u06a9\u06c1 \u0645\u0635\u0646\u0648\u0639\u06cc \u0688\u06cc\u0679\u0627\u0633\u06cc\u0679 \u062a\u062e\u0644\u06cc\u0642 \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u062c\u0648 \u067e\u0648\u0631\u06cc \u0633\u06cc\u0631\u06cc\u0632 \u0645\u06cc\u06ba \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06c1\u0648\u062a\u0627 \u06c1\u06d2\u06d4 \u0633\u06cc\u0688 42 \u0688\u06cc\u0679\u0627\u0633\u06cc\u0679 \u06a9\u0648 \u062f\u0648\u0628\u0627\u0631\u06c1 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u0646\u06d2 \u06a9\u06d2 \u0642\u0627\u0628\u0644 \u0631\u06a9\u06be\u062a\u0627 \u06c1\u06d2 \u0627\u0648\u0631 50,000 \u0635\u0627\u0631\u0641\u06cc\u0646 \u0627\u0633 \u0679\u06cc\u0648\u0679\u0648\u0631\u06cc\u0644 \u0645\u06cc\u06ba \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0644\u06af\u0627\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0648\u0627\u0636\u062d \u0627\u0634\u0627\u0631\u06c1 \u0641\u0631\u0627\u06c1\u0645 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 \u0622\u0624\u0679 \u067e\u0679 CSV \u0627\u0633 \u067e\u0631 \u067e\u06c1\u0646\u0686\u06d2 \u06af\u0627: <code>data\/synthetic_llm_logs.csv<\/code>.<\/p>\n<h2 id=\"heading-setting-up-the-working-example\">\u0648\u0631\u06a9\u0646\u06af \u0645\u062b\u0627\u0644 \u0633\u06cc\u0679 \u0627\u067e<\/h2>\n<p>\u0645\u0635\u0646\u0648\u0639\u06cc \u0688\u06cc\u0679\u0627\u0633\u06cc\u0679 50 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u0645\u06cc\u06ba \u062a\u0642\u0633\u06cc\u0645 \u06a9\u06cc\u06d2 \u06af\u0626\u06d2 50,000 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u06d2 \u0633\u0627\u062a\u06be SaaS \u067e\u0631\u0648\u0688\u06a9\u0679 \u06a9\u06cc \u0646\u0642\u0644 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633\u0632 0-24 \u0648\u06cc\u0648 1 \u0645\u06cc\u06ba \u06c1\u06cc\u06ba\u060c \u062c\u0633 \u0646\u06d2 \u06c1\u0641\u062a\u06c1 20 \u0645\u06cc\u06ba \u0645\u0627\u0688\u0644 \u0627\u067e \u06af\u0631\u06cc\u0688 \u06a9\u06cc\u0627 \u06c1\u06d2\u06d4 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633\u0632 25 \u0633\u06d2 49 \u0648\u06cc\u0648 2 \u0645\u06cc\u06ba \u06c1\u06cc\u06ba\u060c \u067e\u0686\u06be\u0644\u06d2 \u0645\u0627\u0688\u0644 \u06a9\u0648 \u06c1\u0641\u062a\u06c1 29 \u062a\u06a9 \u0628\u0631\u0642\u0631\u0627\u0631 \u0631\u06a9\u06be\u0627 \u06c1\u0648\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u0688\u06cc\u0679\u0627 \u062c\u0646\u0631\u06cc\u0679\u0631 \u0645\u06cc\u06ba \u0638\u0627\u06c1\u0631 \u06c1\u0648\u0646\u06d2 \u0648\u0627\u0644\u0627 \u0627\u0635\u0644 \u06a9\u0627\u0632\u0644 \u0627\u062b\u0631 \u0639\u0644\u0627\u062c \u06a9\u06d2 \u0628\u0639\u062f \u06a9\u06cc \u0645\u062f\u062a \u0645\u06cc\u06ba Wave-1 \u06a9\u06d2 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u06d2 \u0644\u06cc\u06d2 \u06a9\u0627\u0645 \u06a9\u06cc \u062a\u06a9\u0645\u06cc\u0644 \u06a9\u06cc \u0634\u0631\u062d \u0645\u06cc\u06ba +5 \u0641\u06cc\u0635\u062f \u067e\u0648\u0627\u0626\u0646\u0679 \u0627\u0636\u0627\u0641\u06c1 \u062a\u06be\u0627\u06d4 \u0686\u0648\u0646\u06a9\u06c1 \u0622\u067e \u0633\u0686 \u062c\u0627\u0646\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u0622\u067e \u062f\u06cc\u06a9\u06be \u0633\u06a9\u062a\u06d2 \u06c1\u06cc\u06ba \u06a9\u06c1 \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644 \u06a9\u06cc\u0627 \u0628\u062d\u0627\u0644 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<p>\u0688\u06cc\u0679\u0627 \u0644\u0648\u0688 \u06a9\u0631\u06cc\u06ba \u0627\u0648\u0631 \u0627\u0633\u06d2 \u06c1\u0641\u062a\u06c1 \u0648\u0627\u0631 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u067e\u06cc\u0646\u0644 \u0645\u06cc\u06ba \u062c\u0645\u0639 \u06a9\u0631\u06cc\u06ba\u06d4<\/p>\n<pre><code class=\"language-python\">import numpy as np\nimport pandas as pd\n\ndf = pd.read_csv(\"data\/synthetic_llm_logs.csv\")\n\nPRE = 20         # weeks 0-19 are pre-treatment\nWINDOW = 30      # analysis window weeks 0-29\n\ndf_window = df[df.signup_week < WINDOW].copy()\n\npanel = (\n    df_window.groupby([\"workspace_id\", \"signup_week\"])\n    [\"task_completed\"].mean().reset_index()\n)\npanel.columns = [\"workspace_id\", \"week\", \"task_completed\"]\n\npivot = panel.pivot(\n    index=\"week\", columns=\"workspace_id\", values=\"task_completed\"\n)\npivot = pivot.interpolate(method=\"linear\", axis=0).ffill().bfill()\n\nws_wave = df.groupby(\"workspace_id\").wave.first()\nwave1_ws = sorted(ws_wave[ws_wave == 1].index.tolist())\nwave2_ws = sorted(ws_wave[ws_wave == 2].index.tolist())\n\ntreated_series = pivot[wave1_ws].mean(axis=1).values\ndonor_matrix = pivot[wave2_ws].values\n\nprint(f\"Treated series shape: {treated_series.shape}\")\nprint(f\"Donor matrix shape:   {donor_matrix.shape}\")\nprint(f\"Users per workspace-week: ~{len(df_window) \/ (50 * WINDOW):.1f}\")\nprint(f\"Pre-period treated mean  (weeks 0-19):  {treated_series[:PRE].mean():.4f}\")\nprint(f\"Post-period treated mean (weeks 20-29): {treated_series[PRE:].mean():.4f}\")\n<\/code><\/pre>\n<p><strong>\u0645\u062a\u0648\u0642\u0639 \u067e\u06cc\u062f\u0627\u0648\u0627\u0631:<\/strong><\/p>\n<pre><code class=\"language-python\">Treated series shape: (30,)\nDonor matrix shape:   (30, 25)\nUsers per workspace-week: ~19.2\nPre-period treated mean  (weeks 0-19):  0.5927\nPost-period treated mean (weeks 20-29): 0.6421\n<\/code><\/pre>\n<p><strong>\u0645\u0648\u062c\u0648\u062f\u06c1 \u0635\u0648\u0631\u062a\u062d\u0627\u0644 \u06a9\u0686\u06be \u06cc\u0648\u06ba \u06c1\u06d2:<\/strong> \u0627\u0633\u06d2 30 \u06c1\u0641\u062a\u06c1 \u06a9\u06cc \u0645\u062f\u062a \u062a\u06a9 \u0645\u062d\u062f\u0648\u062f \u06a9\u0631\u06cc\u06ba\u060c \u0635\u0627\u0631\u0641 \u06a9\u06cc \u0642\u0637\u0627\u0631\u0648\u06ba \u06a9\u0648 \u06c1\u0641\u062a\u06c1 \u0648\u0627\u0631 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u067e\u06cc\u0646\u0644 \u0645\u06cc\u06ba \u062c\u0645\u0639 \u06a9\u0631\u06cc\u06ba\u060c \u0627\u0648\u0631 \u0627\u0633 \u06a9\u06cc \u0646\u0626\u06cc \u0634\u06a9\u0644 \u062f\u06cc\u06ba \u062a\u0627\u06a9\u06c1 \u0642\u0637\u0627\u0631\u06cc\u06ba \u06c1\u0641\u062a\u06d2 \u06c1\u0648\u06ba \u0627\u0648\u0631 \u06a9\u0627\u0644\u0645 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06c1\u0648\u06ba\u06d4 \u0627\u0646\u0679\u0631\u067e\u0648\u0644\u06cc\u0634\u0646 \u063a\u0627\u0626\u0628 \u062e\u0644\u06cc\u0648\u06ba \u0645\u06cc\u06ba \u0628\u06be\u0631\u062a\u0627 \u06c1\u06d2 (\u06c1\u0631 \u0633\u06cc\u0644 \u0645\u06cc\u06ba \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u06cc \u0627\u0648\u0633\u0637 \u062a\u0639\u062f\u0627\u062f \u062a\u0642\u0631\u06cc\u0628\u0627\u064b 19 \u06c1\u06d2)\u06d4 \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u0633\u06cc\u0631\u06cc\u0632 25 Wave-1 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u0645\u06cc\u06ba \u0627\u0648\u0633\u0637 \u06c1\u06d2\u060c \u062c\u0648 \u0633\u06cc\u0644 \u06a9\u06cc \u0633\u0637\u062d \u06a9\u06d2 \u0634\u0648\u0631 \u06a9\u0648 \u06a9\u0645 \u06a9\u0631\u0646\u06d2 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0641\u06cc \u06c1\u0641\u062a\u06c1 \u062a\u0642\u0631\u06cc\u0628\u0627\u064b 480 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u0648 \u062c\u0645\u0639 \u06a9\u0631\u062a\u06cc \u06c1\u06d2\u06d4<\/p>\n<p>\u0688\u0648\u0646\u0631 \u0645\u06cc\u0679\u0631\u06a9\u0633 \u06c1\u0631 \u0644\u06c1\u0631 2 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u0648 \u0627\u0644\u06af \u06a9\u0627\u0644\u0645 \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u0628\u0631\u0642\u0631\u0627\u0631 \u0631\u06a9\u06be\u062a\u0627 \u06c1\u06d2\u06d4 \u06c1\u0631 \u06a9\u0627\u0644\u0645 0 \u0633\u06d2 29 \u06c1\u0641\u062a\u0648\u06ba \u067e\u0631 \u0645\u062d\u06cc\u0637 25 \u0679\u0627\u0626\u0645 \u0633\u06cc\u0631\u06cc\u0632 \u06c1\u06d2\u06d4 \u067e\u0631\u06cc \u067e\u06cc\u0631\u06cc\u0688 \u0679\u0631\u06cc\u0679\u0645\u0646\u0679 \u06a9\u0627 \u0645\u0637\u0644\u0628 0.5927 \u0627\u0648\u0631 \u067e\u0648\u0633\u0679 \u067e\u06cc\u0631\u06cc\u0688 \u0679\u0631\u06cc\u0679\u0645\u0646\u0679 \u06a9\u0627 \u0645\u0637\u0644\u0628 0.6421 +5.15 \u200b\u200b\u067e\u06cc \u067e\u06cc \u06a9\u0627 \u062e\u0627\u0645 \u067e\u0631\u06cc \u067e\u0648\u0633\u0679 \u0648\u0642\u0641\u06c1 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4 \u06cc\u06c1 \u0627\u0635\u0644 +5pp \u06a9\u06d2 \u0642\u0631\u06cc\u0628 \u06c1\u0648\u062a\u0627 \u06c1\u06d2 \u0627\u0648\u0631 20-29 \u06c1\u0641\u062a\u0648\u06ba \u0645\u06cc\u06ba \u0645\u0646\u062a\u0642\u0644 \u06c1\u0648\u0646\u06d2 \u0648\u0627\u0644\u06cc \u06c1\u0631 \u0686\u06cc\u0632 \u0633\u06d2 \u0622\u0644\u0648\u062f\u06c1 \u06c1\u0648\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/umang.pk\/wp-content\/uploads\/2026\/05\/1778590037_593_\u0645\u0635\u0646\u0648\u0639\u06cc-\u06a9\u0646\u0679\u0631\u0648\u0644-\u06a9\u06d2-\u0633\u0627\u062a\u06be-\u067e\u0631\u0648\u0688\u06a9\u0679-\u06a9\u0627-\u062a\u062c\u0631\u0628\u06c1-\u0627\u0632\u06af\u0631-\u0645\u06cc\u06ba-\u0639\u0627\u0644\u0645\u06cc.png\" alt=\"9b5d9711-9632-41ec-9c38-5ad531ca676f\" style=\"display:block;margin:0 auto\" width=\"600\" height=\"400\" loading=\"lazy\" title=\"\"><\/p>\n<p><em>\u0634\u06a9\u0644 2: \u062d\u0642\u06cc\u0642\u06cc 50,000 \u0635\u0627\u0631\u0641 \u0688\u06cc\u0679\u0627\u0633\u06cc\u0679 \u067e\u0631 \u062a\u0634\u062e\u06cc\u0635\u06d4 \u0679\u0627\u067e \u067e\u06cc\u0646\u0644: \u0646\u06cc\u0648\u06cc \u0688\u06cc\u0634\u0688 \u0644\u0627\u0626\u0646 \u0645\u06cc\u06ba \u062f\u06a9\u06be\u0627\u06cc\u0627 \u06af\u06cc\u0627 \u0633\u0631\u062e \u0627\u0648\u0631 \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644 \u0645\u06cc\u06ba \u0644\u06c1\u0631 1 \u06a9\u06cc \u0631\u0641\u062a\u0627\u0631\u060c \u0645\u062f\u062a \u0633\u06d2 \u067e\u06c1\u0644\u06d2 RMSE 3.74pp \u0627\u0648\u0631 \u0628\u0639\u062f \u0627\u0632 \u0639\u0644\u0627\u062c \u0648\u0642\u0641\u06c1 \u0627\u0648\u0633\u0637 +8.29pp \u06c1\u06d2\u06d4 \u0646\u06cc\u0686\u06d2 \u06a9\u0627 \u067e\u06cc\u0646\u0644: \u067e\u0644\u06cc\u0633\u0628\u0648 \u06a9\u06cc \u062a\u0642\u0633\u06cc\u0645 25 \u0688\u0648\u0646\u0631 \u0648\u0631\u06a9 \u0633\u0679\u06cc\u0634\u0646\u0648\u06ba \u0645\u06cc\u06ba \u0633\u06d2 \u06c1\u0631 \u0627\u06cc\u06a9 \u0645\u06cc\u06ba \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644 \u06a9\u0648 \u062f\u0648\u0628\u0627\u0631\u06c1 \u062a\u0631\u062a\u06cc\u0628 \u062f\u06d2 \u06a9\u0631 \u0628\u0646\u0627\u0626\u06cc \u06af\u0626\u06cc \u06c1\u06d2 \u062c\u0648 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0679\u0631\u06cc\u0679\u0645\u0646\u0679 \u06cc\u0648\u0646\u0679 \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u06a9\u06be\u0691\u06d2 \u06c1\u06cc\u06ba\u06d4 \u0645\u0634\u0627\u06c1\u062f\u06c1 \u06a9\u06cc\u0627 \u06af\u06cc\u0627 \u062e\u0644\u0627 \u0645\u06a9\u0645\u0644 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0631\u06cc\u0646\u062c \u0633\u06d2 \u0628\u0627\u06c1\u0631 \u06c1\u06d2\u060c \u062c\u0648 \u0645\u0631\u062d\u0644\u06c1 3 \u0645\u06cc\u06ba \u0627\u06cc\u06a9 \u062c\u0639\u0644\u06cc p-\u0648\u06cc\u0644\u06cc\u0648 \u06a9\u06cc \u0637\u0631\u0641 \u0644\u06d2 \u062c\u0627\u062a\u0627 \u06c1\u06d2\u06d4<\/em><\/p>\n<p><em>\u0634\u06a9\u0644 1 \u0645\u0646\u0635\u0648\u0628\u06c1 \u0628\u0646\u062f\u06cc \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u0637\u0631\u06cc\u0642\u06c1 \u06a9\u0648 \u0638\u0627\u06c1\u0631 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u060c \u0644\u06cc\u06a9\u0646 \u0627\u0639\u062f\u0627\u062f \u0648 \u0634\u0645\u0627\u0631 \u0633\u06d2 \u067e\u062a\u06c1 \u0686\u0644\u062a\u0627 \u06c1\u06d2 \u06a9\u06c1 \u06cc\u06c1 \u0627\u06cc\u06a9 \u067e\u0644\u06cc\u0633\u0628\u0648 \u062a\u0642\u0633\u06cc\u0645 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u062c\u0648 \u0645\u0634\u0627\u06c1\u062f\u06c1 \u0634\u062f\u06c1 \u0627\u062b\u0631 \u06a9\u0648 \u067e\u0631\u06cc \u067e\u06cc\u0631\u06cc\u0688 \u0641\u0679 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0634\u0648\u0631 \u0633\u06d2 \u0645\u0645\u062a\u0627\u0632 \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u062c\u0648 \u0628\u0639\u062f \u06a9\u06d2 \u0648\u0642\u0641\u0648\u06ba \u06a9\u06cc \u062a\u0634\u0631\u06cc\u062d \u06a9\u06cc \u0627\u062c\u0627\u0632\u062a \u062f\u06cc\u0646\u06d2 \u06a9\u06d2 \u0644\u06cc\u06d2 \u06a9\u0627\u0641\u06cc \u0642\u0631\u06cc\u0628 \u06c1\u06d2\u06d4<\/em><\/p>\n<h2 id=\"heading-step-1-fit-donor-weights-with-slsqp\">\u0645\u0631\u062d\u0644\u06c1 1: \u0688\u0648\u0646\u0631 \u06a9\u06d2 \u0648\u0632\u0646 \u06a9\u0648 SLSQP \u06a9\u06d2 \u0633\u0627\u062a\u06be \u062c\u0648\u0691\u06cc\u06ba\u06d4<\/h2>\n<p>\u062c\u0627\u0645\u0639 \u06a9\u0646\u0679\u0631\u0648\u0644 \u0648\u0632\u0646 \u0648\u06cc\u06a9\u0679\u0631 <code>w<\/code> \u0627\u06cc\u06a9 \u0645\u062d\u062f\u0648\u062f \u0627\u0635\u0644\u0627\u062d\u06cc \u0645\u0633\u0626\u0644\u06c1 \u06a9\u0627 \u062d\u0644\u06d4 \u0639\u0644\u0627\u062c \u0634\u062f\u06c1 \u0627\u0648\u0631 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u06cc \u0633\u06cc\u0631\u06cc\u0632 \u06a9\u06d2 \u0648\u0632\u0646\u06cc \u0627\u0645\u062a\u0632\u0627\u062c \u06a9\u06d2 \u062f\u0631\u0645\u06cc\u0627\u0646 \u067e\u0631\u06cc \u067e\u06cc\u0631\u06cc\u0688 \u06cc\u0639\u0646\u06cc \u0645\u0631\u0628\u0639 \u063a\u0644\u0637\u06cc \u06a9\u0648 \u06a9\u0645 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4 [0, 1] \u062a\u0645\u0627\u0645 \u0648\u0632\u0646\u0648\u06ba \u06a9\u0627 \u0645\u062c\u0645\u0648\u0639\u06c1 1 \u06c1\u06d2\u06d4 \u063a\u06cc\u0631 \u0645\u0646\u0641\u06cc \u062d\u0627\u0644\u062a \u0627\u0648\u0631 sum-1 \u0631\u06a9\u0627\u0648\u0679 \u0627\u06cc\u06a9 \u0633\u0627\u062a\u06be \u0645\u0644 \u06a9\u0631 \u0645\u062d\u062f\u0628 \u0645\u062c\u0645\u0648\u0639\u06c1 \u06a9\u06cc \u0648\u0636\u0627\u062d\u062a \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 \u06cc\u06c1 \u0688\u0648\u0646\u0631 \u067e\u0648\u0644 \u06a9\u06d2 \u062a\u0639\u0627\u0648\u0646 \u0633\u06d2 \u0628\u0627\u06c1\u0631 \u0627\u06cc\u06a9\u0633\u0679\u0631\u067e\u0648\u0644\u06cc\u0634\u0646 \u06a9\u0648 \u0631\u0648\u06a9\u0646\u06d2 \u06a9\u06d2 \u0644\u0626\u06d2 \u06c1\u06d2\u06d4<\/p>\n<pre><code class=\"language-python\">from scipy.optimize import minimize\n\nn_donors = len(wave2_ws)\nY_pre = treated_series[:PRE]\nD_pre = donor_matrix[:PRE, :]\n\ndef objective(w):\n    return np.mean((Y_pre - D_pre @ w) ** 2)\n\nw0 = np.ones(n_donors) \/ n_donors\nbounds = [(0, 1)] * n_donors\nconstraints = [{\"type\": \"eq\", \"fun\": lambda w: w.sum() - 1}]\n\nresult = minimize(\n    objective, w0, method=\"SLSQP\", bounds=bounds,\n    constraints=constraints,\n    options={\"ftol\": 1e-12, \"maxiter\": 5000},\n)\nw_opt = result.x\n\npre_mse = float(np.mean((Y_pre - D_pre @ w_opt) ** 2))\npre_rmse = float(np.sqrt(pre_mse))\nnz = int((w_opt > 0.001).sum())\n\nprint(f\"Optimization converged: {result.success}\")\nprint(f\"Non-zero donor weights (|w| > 0.001): {nz}\")\nprint(f\"Pre-period MSE:  {pre_mse:.6f}\")\nprint(f\"Pre-period RMSE: {pre_rmse:.4f}  \"\n      f\"({pre_rmse * 100:.2f} percentage points)\")\n\nsynth_full = donor_matrix @ w_opt\ngap = float((treated_series[PRE:] - synth_full[PRE:]).mean())\nprint(f\"nObserved post-period gap: {gap:+.4f}  (ground truth = +0.0500)\")\n\nnz_pairs = sorted(\n    [(ws, w_opt[i]) for i, ws in enumerate(wave2_ws) if w_opt[i] > 0.001],\n    key=lambda x: -x[1]\n)\nprint(\"nTop 5 donor weights:\")\nfor ws_id, weight in nz_pairs[:5]:\n    print(f\"  workspace {ws_id}: w = {weight:.4f}\")\n<\/code><\/pre>\n<p><strong>\u0645\u062a\u0648\u0642\u0639 \u067e\u06cc\u062f\u0627\u0648\u0627\u0631:<\/strong><\/p>\n<pre><code class=\"language-python\">Optimization converged: True\nNon-zero donor weights (|w| > 0.001): 12\nPre-period MSE:  0.001400\nPre-period RMSE: 0.0374  (3.74 percentage points)\n\nObserved post-period gap: +0.0829  (ground truth = +0.0500)\n\nTop 5 donor weights:\n  workspace 35: w = 0.2016\n  workspace 40: w = 0.1900\n  workspace 25: w = 0.1638\n  workspace 32: w = 0.0872\n  workspace 36: w = 0.0784\n<\/code><\/pre>\n<p><strong>\u0645\u0648\u062c\u0648\u062f\u06c1 \u0635\u0648\u0631\u062a\u062d\u0627\u0644 \u06a9\u0686\u06be \u06cc\u0648\u06ba \u06c1\u06d2:<\/strong> \u06a9\u06c1 <code>objective<\/code> \u0641\u0646\u06a9\u0634\u0646 \u0648\u0632\u0646 \u06a9\u06d2 \u0648\u06cc\u06a9\u0679\u0631 \u06a9\u0627 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06a9\u0631\u062a\u06d2 \u06c1\u0648\u0626\u06d2 \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u0645\u062f\u062a \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0633\u06cc\u0631\u06cc\u0632 \u0627\u0648\u0631 \u0688\u0648\u0646\u0631 \u0645\u06cc\u0679\u0631\u06a9\u0633 \u06a9\u06d2 \u0688\u0627\u0679 \u067e\u0631\u0648\u0688\u06a9\u0679 \u06a9\u06d2 \u062f\u0631\u0645\u06cc\u0627\u0646 \u0627\u0648\u0633\u0637 \u0645\u0631\u0628\u0639 \u063a\u0644\u0637\u06cc \u06a9\u0627 \u062d\u0633\u0627\u0628 \u0644\u06af\u0627\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>SLSQP \u0628\u06cc\u06a9 \u0648\u0642\u062a \u063a\u06cc\u0631 \u0645\u0646\u0641\u06cc \u0631\u06cc\u0646\u062c \u0627\u0648\u0631 \u0633\u0645 \u0679\u0648 \u0648\u0646 \u0628\u0631\u0627\u0628\u0631\u06cc \u06a9\u06cc \u0631\u06a9\u0627\u0648\u0679\u0648\u06ba \u06a9\u0648 \u06c1\u06cc\u0646\u0688\u0644 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4 \u06a9\u06c1 <code>w > 0.001<\/code> \u062d\u062f 12 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u0648 \u063a\u06cc\u0631 \u0635\u0641\u0631 \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u062f\u0631\u062c\u06c1 \u0628\u0646\u062f\u06cc \u06a9\u0631\u062a\u06cc \u06c1\u06d2\u06d4 SLSQP \u063a\u06cc\u0631\u0641\u0639\u0627\u0644\u06cc\u062a \u06a9\u06cc \u0631\u06a9\u0627\u0648\u0679\u0648\u06ba \u0645\u06cc\u06ba \u0642\u0637\u0639\u06cc \u0635\u0641\u0631 \u06a9\u06cc \u0636\u0645\u0627\u0646\u062a \u0646\u06c1\u06cc\u06ba \u062f\u06cc\u062a\u0627\u060c \u0644\u06c1\u0630\u0627 \u062d\u062f \u0627\u06cc\u06a9 \u0646\u0634\u0627\u0646 \u0632\u062f \u0627\u0635\u0648\u0644 \u06c1\u06d2\u06d4 3.74 \u067e\u06cc \u067e\u06cc \u06a9\u0627 \u067e\u0631\u06cc \u067e\u06cc\u0631\u06cc\u0688 RMSE \u067e\u06cc\u0645\u0627\u0626\u0634 \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u06a9\u06c1 \u0648\u0632\u0646 \u0648\u0627\u0644\u06d2 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u0646\u06d2 \u0627\u067e \u06af\u0631\u06cc\u0688 \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u06cc\u0648\u0646\u0679\u0633 \u06a9\u0648 \u06a9\u062a\u0646\u06cc \u0628\u0627\u0631\u06cc\u06a9 \u0628\u06cc\u0646\u06cc \u0633\u06d2 \u0679\u0631\u06cc\u06a9 \u06a9\u06cc\u0627\u06d4 \u0645\u0634\u0627\u06c1\u062f\u06c1 \u0634\u062f\u06c1 \u0645\u062f\u062a \u06a9\u06d2 \u0628\u0639\u062f \u0648\u0642\u0641\u06c1 +0.0829 \u06c1\u06cc\u0688 \u0644\u0627\u0626\u0646 \u06a9\u0627 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u06c1\u06d2\u060c \u062c\u0648 \u06a9\u06c1 \u0645\u0631\u062d\u0644\u06c1 5 \u0645\u06cc\u06ba \u0627\u0639\u062a\u0645\u0627\u062f \u06a9\u06d2 \u0648\u0642\u0641\u06c1 \u06a9\u06d2 \u0630\u0631\u06cc\u0639\u06c1 \u0645\u0642\u062f\u0627\u0631 \u06a9\u06d2 \u0645\u0637\u0627\u0628\u0642 \u0627\u0635\u0644 +5pp \u0633\u06d2 \u0632\u06cc\u0627\u062f\u06c1 \u06c1\u06d2\u06d4<\/p>\n<p>\u0648\u0632\u0646 \u067e\u06c1\u0644\u06d2 \u06a9\u06cc \u0645\u062f\u062a \u06a9\u06d2 \u0627\u062e\u062a\u062a\u0627\u0645 \u067e\u0631 \u0637\u06d2 \u06a9\u06cc\u0627 \u062c\u0627\u062a\u0627 \u06c1\u06d2 \u0627\u0648\u0631 \u067e\u0648\u0633\u0679 \u067e\u0631\u0648\u0633\u06cc\u0633\u0646\u06af \u0688\u06cc\u0679\u0627 \u06a9\u0627 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06a9\u0631\u062a\u06d2 \u06c1\u0648\u0626\u06d2 \u062f\u0648\u0628\u0627\u0631\u06c1 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0646\u06c1\u06cc\u06ba \u0644\u06af\u0627\u06cc\u0627 \u062c\u0627\u062a\u0627 \u06c1\u06d2\u06d4 \u06c1\u0641\u062a\u06c1 20 \u06a9\u06d2 \u0628\u0639\u062f \u06a9\u0648\u0626\u06cc \u0628\u06be\u06cc \u0641\u0631\u0642 \u0627\u0646 \u062d\u0631\u06a9\u0627\u062a \u06a9\u06cc \u0639\u06a9\u0627\u0633\u06cc \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u06a9\u06c1 \u0627\u0635\u0644\u0627\u062d \u06a9\u0627\u0631 \u06a9\u06d2 \u067e\u0627\u0633 \u0641\u0679 \u06c1\u0648\u0646\u06d2 \u06a9\u0627 \u0645\u0648\u0642\u0639 \u0646\u06c1\u06cc\u06ba \u062a\u06be\u0627\u06d4<\/p>\n<h2 id=\"heading-step-2-plot-treated-vs-synthetic-control-trajectories\">\u0645\u0631\u062d\u0644\u06c1 2: \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u067e\u0644\u0627\u0679\u0648\u06ba \u06a9\u0627 \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644 \u0679\u0631\u06cc\u062c\u06cc\u06a9\u0679\u0631\u06cc\u0632 \u0633\u06d2 \u0645\u0648\u0627\u0632\u0646\u06c1 \u06a9\u0631\u06cc\u06ba\u06d4<\/h2>\n<p>\u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0628\u0646\u06cc\u0627\u062f\u06cc \u0628\u0635\u0631\u06cc \u062a\u0634\u062e\u06cc\u0635\u06cc \u0679\u0631\u06cc\u062c\u06cc\u06a9\u0679\u0631\u06cc \u0627\u0648\u0648\u0631\u0644\u06d2 \u06c1\u06d2\u06d4 \u062f\u0648\u0646\u0648\u06ba \u0633\u06cc\u0631\u06cc\u0632 \u06a9\u0648 \u0627\u06cc\u06a9 \u0633\u0627\u062a\u06be \u067e\u0644\u0627\u0679 \u06a9\u0631\u06cc\u06ba\u060c \u0639\u0644\u0627\u062c \u06a9\u06cc \u062a\u0627\u0631\u06cc\u062e\u0648\u06ba \u06a9\u0648 \u067e\u0644\u0627\u0679 \u06a9\u0631\u06cc\u06ba\u060c \u0627\u0648\u0631 \u0627\u0633 \u0628\u0627\u062a \u06a9\u0648 \u06cc\u0642\u06cc\u0646\u06cc \u0628\u0646\u0627\u0626\u06cc\u06ba \u06a9\u06c1 \u06a9\u0645\u067e\u0648\u0632\u0679 \u06a9\u0646\u0679\u0631\u0648\u0644 \u0679\u0631\u06cc\u06a9\u0633 \u06cc\u0648\u0646\u0679\u0633 \u062c\u0646 \u06a9\u0627 \u0639\u0644\u0627\u062c \u067e\u0631\u06cc \u067e\u06cc\u0631\u06cc\u0688 \u0645\u06cc\u06ba \u06a9\u06cc\u0627 \u06af\u06cc\u0627 \u062a\u06be\u0627 \u0627\u0648\u0631 \u0628\u0639\u062f \u06a9\u06cc \u0645\u062f\u062a \u0645\u06cc\u06ba \u062e\u0644\u0627 \u06a9\u0648 \u06a9\u06be\u0648\u0644\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u0645\u062f\u062a \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0633\u062e\u062a \u0641\u0679 \u06c1\u0648\u0646\u0627 \u0627\u06cc\u06a9 \u0648\u0627\u0636\u062d \u0639\u0644\u0627\u0645\u062a \u06c1\u06d2 \u062c\u0648 \u0634\u0646\u0627\u062e\u062a \u06a9\u06cc \u0634\u0631\u0627\u0626\u0637 \u06a9\u0648 \u0628\u0631\u0642\u0631\u0627\u0631 \u0631\u06a9\u06be\u062a\u06cc \u06c1\u06d2\u06d4 \u0628\u06d2 \u0642\u0627\u0639\u062f\u06c1 \u0641\u0679 \u06c1\u0648\u0646\u06d2 \u06a9\u0627 \u0645\u0637\u0644\u0628 \u06c1\u06d2 \u06a9\u06c1 \u0639\u0644\u0627\u062c \u0634\u062f\u06c1 \u0622\u0644\u06c1 \u0639\u0637\u06cc\u06c1 \u06a9\u0646\u0646\u062f\u06c1 \u06a9\u06d2 \u0645\u062d\u062f\u0628 \u06c1\u0648\u0644 \u0633\u06d2 \u0628\u0627\u06c1\u0631 \u06c1\u06d2 \u0627\u0648\u0631 \u0627\u0633 \u06a9\u06cc \u0645\u062c\u0645\u0648\u0639\u06cc \u062d\u0631\u06a9\u062a \u0642\u0627\u0628\u0644 \u0627\u0639\u062a\u0631\u0627\u0636 \u06c1\u06d2\u06d4<\/p>\n<pre><code class=\"language-python\">import matplotlib.pyplot as plt\n\nweeks = np.arange(WINDOW)\n\nfig, ax = plt.subplots(figsize=(9, 4.5))\nax.plot(weeks, treated_series, marker=\"o\", linewidth=1.8,\n        color=\"#C44E52\", label=\"Wave 1 (treated)\")\nax.plot(weeks, synth_full, marker=\"s\", linestyle=\"--\",\n        linewidth=1.8, color=\"#4C72B0\", label=\"Synthetic control\")\nax.axvline(PRE, color=\"#555555\", linestyle=\":\", linewidth=1.4,\n           label=\"Model upgrade (week 20)\")\nax.set_xlabel(\"Signup week\")\nax.set_ylabel(\"Mean task completion rate\")\nax.set_title(\"Treated unit vs synthetic control\")\nax.legend(frameon=False)\nplt.tight_layout()\nplt.show()\n\npost_gap = treated_series[PRE:] - synth_full[PRE:]\nprint(\"Post-period weekly gaps (treated minus synthetic):\")\nfor wk, g in zip(range(PRE, WINDOW), post_gap):\n    print(f\"  week {wk}: {g:+.4f}\")\nprint(f\"nMean gap: {post_gap.mean():+.4f}\")\n<\/code><\/pre>\n<p><strong>\u0645\u062a\u0648\u0642\u0639 \u067e\u06cc\u062f\u0627\u0648\u0627\u0631:<\/strong><\/p>\n<pre><code class=\"language-python\">Post-period weekly gaps (treated minus synthetic):\n  week 20: +0.0398\n  week 21: +0.1663\n  week 22: +0.1019\n  week 23: +0.1535\n  week 24: +0.1071\n  week 25: +0.1047\n  week 26: +0.0424\n  week 27: +0.0326\n  week 28: +0.0327\n  week 29: +0.0479\n\nMean gap: +0.0829\n<\/code><\/pre>\n<p><strong>\u0645\u0648\u062c\u0648\u062f\u06c1 \u0635\u0648\u0631\u062a\u062d\u0627\u0644 \u06a9\u0686\u06be \u06cc\u0648\u06ba \u06c1\u06d2:<\/strong> \u0641\u0679 \u0645\u0641\u0631\u0648\u0636\u0648\u06ba \u06a9\u0648 \u062c\u0627\u0646\u0686\u0646\u06d2 \u06a9\u06d2 \u0644\u06cc\u06d2 \u062f\u0648\u0646\u0648\u06ba \u0644\u0627\u0626\u0646\u06cc\u06ba \u067e\u06c1\u0644\u06d2 \u06a9\u06cc \u0645\u062f\u062a \u0645\u06cc\u06ba \u0627\u06cc\u06a9 \u062f\u0648\u0633\u0631\u06d2 \u06a9\u0648 \u0679\u0631\u06cc\u06a9 \u06a9\u0631\u062a\u06cc \u06c1\u06cc\u06ba\u06d4 \u06c1\u0641\u062a\u06c1 20 \u06a9\u06d2 \u0628\u0639\u062f\u060c \u0639\u0644\u0627\u062c \u0634\u062f\u06c1 \u0644\u0627\u0626\u0646\u06cc\u06ba \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644 \u0633\u06d2 \u0632\u06cc\u0627\u062f\u06c1 \u0628\u0691\u06be \u062c\u0627\u062a\u06cc \u06c1\u06cc\u06ba \u0627\u0648\u0631 \u06c1\u0641\u062a\u06c1 \u0648\u0627\u0631 \u0648\u0642\u0641\u06d2 \u062a\u0645\u0627\u0645 \u0645\u062b\u0628\u062a \u06c1\u0648\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u0627\u0648\u0633\u0637\u0627\u064b +8.29 pp\u06d4<\/p>\n<p>\u06c1\u0641\u062a\u06c1 \u0648\u0627\u0631 \u067e\u06be\u06cc\u0644\u0627\u0624 (+3.26pp \u0633\u06d2 +16.63pp \u062a\u06a9) \u06c1\u0641\u062a\u06c1 \u0648\u0627\u0631 \u0634\u0648\u0631 \u06a9\u06cc \u0645\u0642\u062f\u0627\u0631 \u06c1\u06d2 \u062c\u0633\u06d2 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0644\u06af\u0627\u0646\u06d2 \u0648\u0627\u0644\u0627 \u062c\u0630\u0628 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4 \u0635\u0631\u0641 \u0627\u06cc\u06a9 \u0628\u0631\u0627 \u06c1\u0641\u062a\u06c1 \u0627\u0648\u0633\u0637 \u06a9\u0648 \u0627\u06cc\u06a9 \u0641\u06cc\u0635\u062f \u067e\u0648\u0627\u0626\u0646\u0679 \u062a\u06a9 \u0628\u062f\u0644 \u0633\u06a9\u062a\u0627 \u06c1\u06d2\u06d4 \u06cc\u06c1\u06cc \u0648\u062c\u06c1 \u06c1\u06d2 \u06a9\u06c1 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0627\u0648\u0631 \u0641\u0627\u0644\u0648 \u0627\u067e \u0627\u0642\u062f\u0627\u0645\u0627\u062a \u0633\u0646\u06af\u0644 \u067e\u0648\u0627\u0626\u0646\u0679 \u06a9\u06d2 \u062a\u062e\u0645\u06cc\u0646\u06d2 \u0633\u06d2 \u0632\u06cc\u0627\u062f\u06c1 \u0627\u06c1\u0645 \u06c1\u06cc\u06ba\u06d4<\/p>\n<h2 id=\"heading-step-3-in-space-placebo-permutation-test\">\u0645\u0631\u062d\u0644\u06c1 3: \u062e\u0644\u0627 \u0645\u06cc\u06ba \u067e\u0644\u06cc\u0633\u0628\u0648 \u067e\u0631\u0645\u0648\u0679\u06cc\u0634\u0646 \u0679\u06cc\u0633\u0679<\/h2>\n<p>\u0627\u06cc\u06a9 \u0645\u0639\u06cc\u0627\u0631\u06cc \u0679\u06cc \u0679\u06cc\u0633\u0679 \u0627\u06cc\u06a9 \u0648\u0627\u062d\u062f \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u06cc\u0648\u0646\u0679 \u067e\u0631 \u0646\u06c1\u06cc\u06ba \u0686\u0644\u0627\u06cc\u0627 \u062c\u0627 \u0633\u06a9\u062a\u0627\u06d4 \u062c\u0627\u0645\u0639 \u06a9\u0646\u0679\u0631\u0648\u0644 \u0645\u06cc\u06ba \u0627\u06cc\u06a9 \u0639\u0644\u0627\u062c \u0634\u062f\u06c1 \u0645\u0634\u0627\u06c1\u062f\u06c1 (\u0644\u06c1\u0631 1) \u0627\u0648\u0631 25 \u0688\u0648\u0646\u0631 \u0645\u0634\u0627\u06c1\u062f\u0627\u062a \u06c1\u06cc\u06ba\u060c \u062c\u0648 \u06a9\u06c1 \u0627\u06cc\u0633\u06cc \u062a\u0631\u062a\u06cc\u0628 \u0646\u06c1\u06cc\u06ba \u06c1\u06d2 \u062c\u0633 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0631\u0648\u0627\u06cc\u062a\u06cc p-values \u200b\u200b\u06a9\u0627 \u0627\u0637\u0644\u0627\u0642 \u06c1\u0648\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u0645\u0639\u06cc\u0627\u0631\u06cc \u062a\u0648\u062b\u06cc\u0642 \u062e\u0644\u0627 \u0645\u06cc\u06ba \u067e\u0644\u06cc\u0633\u0628\u0648 \u067e\u0631\u0645\u0648\u0679\u06cc\u0634\u0646 \u0679\u06cc\u0633\u0679 \u06c1\u06d2\u06d4 \u06c1\u0631 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06c1 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0628\u062f\u0644\u06d2 \u0645\u06cc\u06ba \u0627\u06cc\u0633\u0627 \u0633\u0644\u0648\u06a9 \u06a9\u0631\u06cc\u06ba \u062c\u06cc\u0633\u06d2 \u06cc\u06c1 \u0627\u06cc\u06a9 \"\u0639\u0644\u0627\u062c \u0634\u062f\u06c1\" \u06cc\u0648\u0646\u0679 \u06c1\u0648\u060c \u0628\u0642\u06cc\u06c1 24 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u0648 \u067e\u0644\u06cc\u0633\u0628\u0648 \u067e\u0648\u0644 \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06a9\u0631\u062a\u06d2 \u06c1\u0648\u0626\u06d2 \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644 \u06af\u0631\u0648\u067e \u06a9\u0648 \u0631\u06cc\u0641\u0679 \u06a9\u0631\u06cc\u06ba\u060c \u067e\u0644\u06cc\u0633\u0628\u0648 \u0645\u062f\u062a \u06a9\u06d2 \u0628\u0639\u062f \u0648\u0642\u0641\u0648\u06ba \u06a9\u0648 \u0631\u06cc\u06a9\u0627\u0631\u0688 \u06a9\u0631\u06cc\u06ba\u060c \u0627\u0648\u0631 \u0645\u0634\u0627\u06c1\u062f\u06c1 \u0634\u062f\u06c1 \u0648\u0642\u0641\u0648\u06ba \u06a9\u0627 \u067e\u0644\u06cc\u0633\u0628\u0648 \u062a\u0642\u0633\u06cc\u0645 \u0633\u06d2 \u0645\u0648\u0627\u0632\u0646\u06c1 \u06a9\u0631\u06cc\u06ba\u06d4<\/p>\n<pre><code class=\"language-python\">placebo_gaps = []\n\nfor j in range(n_donors):\n    placebo_treated = donor_matrix[:, j]\n    placebo_pool = np.delete(donor_matrix, j, axis=1)\n    n_p = placebo_pool.shape[1]\n\n    def obj_p(w):\n        return np.mean((placebo_treated[:PRE] - placebo_pool[:PRE] @ w) ** 2)\n\n    res_p = minimize(\n        obj_p, np.ones(n_p) \/ n_p, method=\"SLSQP\",\n        bounds=[(0, 1)] * n_p,\n        constraints=[{\"type\": \"eq\", \"fun\": lambda w: w.sum() - 1}],\n        options={\"ftol\": 1e-12, \"maxiter\": 5000},\n    )\n    synth_p = placebo_pool @ res_p.x\n    placebo_gaps.append((placebo_treated[PRE:] - synth_p[PRE:]).mean())\n\nplacebo_gaps = np.array(placebo_gaps)\nobserved_gap = gap\n\nrank = int((np.abs(placebo_gaps) >= abs(observed_gap)).sum())\npseudo_p = (rank + 1) \/ (len(placebo_gaps) + 1)\n\nprint(f\"Observed gap:      {observed_gap:+.4f}\")\nprint(f\"Placebo mean gap:  {placebo_gaps.mean():+.4f}\")\nprint(f\"Placebo std gap:   {placebo_gaps.std():.4f}\")\nprint(f\"Placebo gap range: [{placebo_gaps.min():+.4f}, \"\n      f\"{placebo_gaps.max():+.4f}]\")\nprint(f\"|placebo| >= |observed|: {rank} of {len(placebo_gaps)}\")\nprint(f\"Pseudo p-value: {pseudo_p:.4f}\")\n<\/code><\/pre>\n<p><strong>\u0645\u062a\u0648\u0642\u0639 \u067e\u06cc\u062f\u0627\u0648\u0627\u0631:<\/strong><\/p>\n<pre><code class=\"language-python\">Observed gap:      +0.0829\nPlacebo mean gap:  -0.0008\nPlacebo std gap:   0.0380\nPlacebo gap range: [-0.0748, +0.0707]\n|placebo| >= |observed|: 0 of 25\nPseudo p-value: 0.0385\n<\/code><\/pre>\n<p><strong>\u0645\u0648\u062c\u0648\u062f\u06c1 \u0635\u0648\u0631\u062a\u062d\u0627\u0644 \u06a9\u0686\u06be \u06cc\u0648\u06ba \u06c1\u06d2:<\/strong> \u0644\u0648\u067e \u062a\u0645\u0627\u0645 25 Wave-2 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u06d2 \u0630\u0631\u06cc\u0639\u06d2 \u0627\u0639\u0627\u062f\u06c1 \u06c1\u0648\u062a\u0627 \u06c1\u06d2\u06d4 \u06c1\u0631 \u0627\u06cc\u06a9 \u06a9\u06d2 \u0644\u06cc\u06d2\u060c \u06c1\u0645 \u0627\u0646\u06c1\u06cc\u06ba \u0688\u0648\u0646\u0631 \u067e\u0648\u0644 \u0633\u06d2 \u06c1\u0679\u0627\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u0627\u0646 \u06a9\u0648 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0679\u0631\u06cc\u0679\u0645\u0646\u0679 \u06cc\u0648\u0646\u0679 \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u062f\u06cc\u06a9\u06be\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u0627\u0648\u0631 \u067e\u06be\u0631 SLSQP \u0622\u067e\u0679\u06cc\u0645\u0627\u0626\u0632\u06cc\u0634\u0646 \u06a9\u0648 \u062f\u0648\u0628\u0627\u0631\u06c1 \u0686\u0644\u0627\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 25 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0631\u0646 \u06a9\u06d2 \u0628\u0639\u062f\u060c \u06c1\u0645 \u062d\u0633\u0627\u0628 \u0644\u06af\u0627\u062a\u06d2 \u06c1\u06cc\u06ba \u06a9\u06c1 \u06a9\u062a\u0646\u06d2 \u067e\u0644\u06cc\u0633\u0628\u0648 \u06af\u06cc\u067e\u0633 \u0645\u0637\u0644\u0642 \u0642\u062f\u0631 \u0645\u06cc\u06ba \u0645\u0634\u0627\u06c1\u062f\u06c1 \u0634\u062f\u06c1 \u062e\u0644\u0627 \u06a9\u0648 \u067e\u0648\u0631\u0627 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba \u06cc\u0627 \u0627\u0633 \u0633\u06d2 \u0632\u06cc\u0627\u062f\u06c1 \u06c1\u0648\u062a\u06d2 \u06c1\u06cc\u06ba \u0627\u0648\u0631 \u0627\u06cc\u06a9 \u0642\u062f\u0627\u0645\u062a \u067e\u0633\u0646\u062f (\u0646\u0645\u0628\u0631 + 1) \/ (N + 1) \u0627\u0635\u0644\u0627\u062d \u06a9\u0627 \u0627\u0637\u0644\u0627\u0642 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<p>25 \u067e\u0644\u06cc\u0633\u0628\u0648\u0633 \u0645\u06cc\u06ba \u0633\u06d2 \u06a9\u0633\u06cc \u0646\u06d2 \u0628\u06be\u06cc \u0627\u062a\u0646\u0627 \u0632\u06cc\u0627\u062f\u06c1 \u0641\u0631\u0642 \u0646\u06c1\u06cc\u06ba \u062f\u06a9\u06be\u0627\u06cc\u0627 \u062c\u062a\u0646\u0627 \u06a9\u06c1 \u0645\u0634\u0627\u06c1\u062f\u06c1 \u06a9\u06cc\u0627 \u06af\u06cc\u0627 +0.0829 \u06c1\u06d2\u060c \u062c\u0633 \u0633\u06d2 0.0385 \u06a9\u06cc \u0633\u06cc\u0648\u0688\u0648 \u067e\u06cc \u0648\u06cc\u0644\u06cc\u0648 \u062d\u0627\u0635\u0644 \u06c1\u0648\u062a\u06cc \u06c1\u06d2\u06d4 \u06cc\u06c1 \u0645\u0633\u062a\u0631\u062f \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u06a9\u06c1 5% \u06a9\u06cc \u0633\u0637\u062d \u067e\u0631 \u06a9\u0648\u0626\u06cc \u0627\u062b\u0631 \u0646\u06c1\u06cc\u06ba \u06c1\u06d2\u06d4 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0688\u0633\u0679\u0631\u06cc \u0628\u06cc\u0648\u0634\u0646 0 \u06a9\u06d2 \u0642\u0631\u06cc\u0628 \u0645\u0631\u06a9\u0648\u0632 \u06c1\u06d2 (\u0645\u0637\u0644\u0628 -0.0008\u060c \u0645\u0639\u06cc\u0627\u0631\u06cc 3.80pp)\u060c \u062c\u0648 \u0634\u0648\u0631 \u06a9\u0627 \u0641\u0644\u0648\u0631 \u06c1\u06d2 \u062c\u0633 \u06a9\u06d2 \u062e\u0644\u0627\u0641 \u0645\u0634\u0627\u06c1\u062f\u06c1 \u0634\u062f\u06c1 \u062e\u0644\u0627 \u06a9\u0627 \u0645\u0648\u0627\u0632\u0646\u06c1 \u06a9\u06cc\u0627 \u062c\u0627\u0626\u06d2 \u06af\u0627\u06d4<\/p>\n<p>\u062f\u0631\u0633\u062a \u0627\u0639\u062f\u0627\u062f\u0648\u0634\u0645\u0627\u0631 \u06a9\u06cc \u062a\u0641\u0635\u06cc\u0644 \u06a9\u0686\u06be \u06cc\u0648\u06ba \u06c1\u06d2: \u0645\u0634\u0627\u06c1\u062f\u06c1 \u0634\u062f\u06c1 \u0641\u0631\u0642 5% \u06a9\u06cc \u0633\u0637\u062d \u067e\u0631 \u0639\u0644\u0627\u062c \u0646\u06c1 \u06a9\u06cc\u06d2 \u062c\u0627\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u0633\u06d2 \u062d\u0627\u0635\u0644 \u06a9\u0631\u062f\u06c1 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0633\u06d2 \u0632\u06cc\u0627\u062f\u06c1 \u06c1\u06d2\u06d4 \u067e\u0631\u0645\u0648\u0679\u06cc\u0634\u0646 \u0679\u06cc\u0633\u0679 \u06a9\u06cc \u0637\u0627\u0642\u062a \u06a9\u0627 \u0627\u0646\u062d\u0635\u0627\u0631 \u0688\u0648\u0646\u0631 \u067e\u0648\u0644 \u06a9\u06d2 \u0633\u0627\u0626\u0632 \u067e\u0631 \u06c1\u0648\u062a\u0627 \u06c1\u06d2\u06d4 25 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u06d2 \u0633\u0627\u062a\u06be\u060c \u0633\u0628 \u0633\u06d2 \u0686\u06be\u0648\u0679\u0627 \u0645\u0645\u06a9\u0646\u06c1 pseudo-p 1\/26 = 0.0385 \u06c1\u06d2\u060c \u0644\u06c1\u0630\u0627 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u06cc \u0627\u0633 \u062a\u0639\u062f\u0627\u062f \u0633\u06d2 \u0686\u06be\u0648\u0679\u06cc p-value \u062d\u0627\u0635\u0644 \u0646\u06c1\u06cc\u06ba \u06a9\u06cc \u062c\u0627 \u0633\u06a9\u062a\u06cc\u06d4 \u0648\u0633\u06cc\u0639 \u067e\u0644\u06cc\u0633\u0628\u0648 \u062a\u0642\u0633\u06cc\u0645 \u06cc\u0627 \u0686\u06be\u0648\u0679\u06d2 \u0645\u0634\u0627\u06c1\u062f\u06d2 \u06a9\u06d2 \u0648\u0642\u0641\u06d2 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0628\u0644\u06a9 \u06a9\u06d2 \u0627\u0646\u062f\u0631 \u0645\u0634\u0627\u06c1\u062f\u0627\u062a \u06a9\u06cc \u062f\u0631\u062c\u06c1 \u0628\u0646\u062f\u06cc \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba \u0627\u0648\u0631 \u0633\u06cc\u0648\u0688\u0627\u067e \u06a9\u0648 \u0645\u0641\u06cc\u062f \u062d\u062f \u0633\u06d2 \u0622\u06af\u06d2 \u0628\u0691\u06be\u0627\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<h2 id=\"heading-step-4-leave-one-out-donor-sensitivity\">\u0645\u0631\u062d\u0644\u06c1 4: \u0627\u06cc\u06a9 \u0628\u0627\u0631 \u0688\u0648\u0646\u0631 \u06a9\u06cc \u062d\u0633\u0627\u0633\u06cc\u062a<\/h2>\n<p>\u0627\u06af\u0631 \u0635\u0631\u0641 \u0627\u06cc\u06a9 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06c1 \u062a\u06a9 \u0645\u062d\u062f\u0648\u062f \u06c1\u0648 \u062a\u0648 \u0633\u062e\u062a \u0646\u06a9\u062a\u06c1 \u06a9\u0627 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0627\u0628 \u0628\u06be\u06cc \u06a9\u0645\u0632\u0648\u0631 \u06c1\u0648 \u0633\u06a9\u062a\u0627 \u06c1\u06d2\u06d4 \u0627\u06cc\u06a9 \u0644\u06cc\u0648 \u0648\u0646 \u0622\u0624\u0679 (LOO) \u062d\u0633\u0627\u0633\u06cc\u062a \u06a9\u0627 \u0679\u06cc\u0633\u0679 \u0628\u062f\u0644\u06d2 \u0645\u06cc\u06ba \u06c1\u0631 \u0627\u06cc\u06a9 \u063a\u06cc\u0631 \u0635\u0641\u0631 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06c1 \u06a9\u0648 \u062d\u0630\u0641 \u06a9\u0631 \u062f\u06cc\u062a\u0627 \u06c1\u06d2\u060c \u0628\u0627\u0642\u06cc \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u06d2 \u0644\u06cc\u06d2 \u062c\u0627\u0645\u0639 \u06a9\u0646\u0679\u0631\u0648\u0644 \u06a9\u0648 \u0631\u06cc\u0641\u0679 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u060c \u0627\u0648\u0631 \u0646\u0626\u06d2 \u0648\u0642\u0641\u0648\u06ba \u06a9\u0648 \u0631\u06cc\u06a9\u0627\u0631\u0688 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>Abadi (2021) \u0627\u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0622\u0631\u0688\u0631 \u06a9\u06cc \u0645\u0636\u0628\u0648\u0637\u06cc \u06a9\u06cc \u062c\u0627\u0646\u0686 \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u062a\u062c\u0648\u06cc\u0632 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4 \u0627\u06af\u0631 \u06a9\u0633\u06cc \u0627\u06cc\u06a9 \u0688\u0648\u0646\u0631 \u06a9\u0648 \u06c1\u0679\u0627\u0646\u06d2 \u067e\u0631 \u0641\u0631\u0642 \u0646\u0645\u0627\u06cc\u0627\u06ba \u0637\u0648\u0631 \u067e\u0631 \u0627\u062a\u0627\u0631 \u0686\u0691\u06be\u0627\u0624 \u0622\u062a\u0627 \u06c1\u06d2 \u062a\u0648 \u06a9\u0648\u0626\u06cc \u062c\u0627\u0645\u0639 \u062a\u0636\u0627\u062f \u0646\u06c1\u06cc\u06ba \u06c1\u06d2\u06d4 \u0627\u0636\u0627\u0641\u06cc \u0648\u0632\u0646 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0627\u06cc\u06a9 \u0648\u0627\u062d\u062f \u0688\u0648\u0646\u0631 \u06a9\u0627 \u0645\u0648\u0627\u0632\u0646\u06c1 \u06c1\u06d2\u06d4<\/p>\n<pre><code class=\"language-python\">def fit_and_gap(treated, donors, pre=PRE):\n    n = donors.shape[1]\n    def obj(w):\n        return np.mean((treated[:pre] - donors[:pre] @ w) ** 2)\n    res = minimize(\n        obj, np.ones(n) \/ n, method=\"SLSQP\",\n        bounds=[(0, 1)] * n,\n        constraints=[{\"type\": \"eq\", \"fun\": lambda w: w.sum() - 1}],\n        options={\"ftol\": 1e-12, \"maxiter\": 5000},\n    )\n    synth = donors @ res.x\n    return float((treated[pre:] - synth[pre:]).mean())\n\n\nnz_idx = np.where(w_opt > 0.001)[0]\nloo_rows = []\nfor j in nz_idx:\n    kept = np.delete(donor_matrix, j, axis=1)\n    gap_new = fit_and_gap(treated_series, kept)\n    loo_rows.append({\n        \"dropped_workspace\": int(wave2_ws[j]),\n        \"dropped_weight\": float(w_opt[j]),\n        \"new_gap\": gap_new,\n    })\nloo_df = pd.DataFrame(loo_rows).sort_values(\"dropped_weight\", ascending=False)\nprint(loo_df.round(4).to_string(index=False))\nprint(f\"nLOO gap range: [{loo_df.new_gap.min():+.4f}, \"\n      f\"{loo_df.new_gap.max():+.4f}]\")\nprint(f\"Original gap:  {gap:+.4f}\")\n<\/code><\/pre>\n<p><strong>\u0645\u062a\u0648\u0642\u0639 \u067e\u06cc\u062f\u0627\u0648\u0627\u0631:<\/strong><\/p>\n<pre><code class=\"language-python\"> dropped_workspace  dropped_weight  new_gap\n                35          0.2016   0.0945\n                40          0.1900   0.0756\n                25          0.1638   0.0932\n                32          0.0872   0.0868\n                36          0.0784   0.0739\n                31          0.0718   0.0858\n                29          0.0648   0.0782\n                26          0.0439   0.0786\n                27          0.0364   0.0867\n                46          0.0350   0.0794\n                39          0.0192   0.0848\n                42          0.0078   0.0839\n\nLOO gap range: [+0.0739, +0.0945]\nOriginal gap:  +0.0829\n<\/code><\/pre>\n<p><strong>\u0645\u0648\u062c\u0648\u062f\u06c1 \u0635\u0648\u0631\u062a\u062d\u0627\u0644 \u06a9\u0686\u06be \u06cc\u0648\u06ba \u06c1\u06d2:<\/strong> \u0644\u0648\u067e \u0627\u06cc\u06a9 \u0648\u0642\u062a \u0645\u06cc\u06ba \u063a\u06cc\u0631 \u0635\u0641\u0631 \u0648\u0632\u0646 \u0648\u0627\u0644\u06d2 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u0648 \u062d\u0630\u0641 \u0627\u0648\u0631 \u0631\u06cc\u0641\u0679 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4 LOO \u06a9\u06d2 \u062a\u0645\u0627\u0645 12 \u062a\u062e\u0645\u06cc\u0646\u06d2 \u0645\u062b\u0628\u062a \u0631\u06c1\u06d2\u06d4 [+7.39 pp, +9.45 pp] \u0627\u0635\u0644 +8.29 \u067e\u06cc \u067e\u06cc \u06a9\u0648 \u06a9\u0633\u06cc \u0628\u06be\u06cc \u0633\u0645\u062a \u0645\u06cc\u06ba \u062a\u0642\u0631\u06cc\u0628\u0627\u064b 1 \u0641\u06cc\u0635\u062f \u067e\u0648\u0627\u0626\u0646\u0679 \u06a9\u06be\u0648\u0644\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u06a9\u0648\u0626\u06cc \u0627\u06cc\u06a9 \u0688\u0648\u0646\u0631 \u0646\u062a\u0627\u0626\u062c \u0646\u06c1\u06cc\u06ba \u0686\u0644\u0627\u062a\u0627\u06d4 \u06cc\u06c1\u0627\u06ba \u062a\u06a9 \u06a9\u06c1 \u0627\u06af\u0631 \u06c1\u0645 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 35 \u06a9\u0648 \u062d\u0630\u0641 \u06a9\u0631 \u062f\u06cc\u062a\u06d2 \u06c1\u06cc\u06ba (0.2016 \u067e\u0631 \u0633\u0628 \u0633\u06d2 \u0628\u0691\u0627 \u0648\u0632\u0646)\u060c \u0641\u0631\u0642 +9.45pp \u062a\u06a9 \u0628\u0691\u06be \u062c\u0627\u062a\u0627 \u06c1\u06d2 \u06a9\u06cc\u0648\u0646\u06a9\u06c1 \u0622\u067e\u0679\u0645\u0627\u0626\u0632\u0631 \u0648\u0632\u0646 \u06a9\u0648 \u0628\u0627\u0642\u06cc \u0688\u0648\u0646\u0631\u0632 \u0645\u06cc\u06ba \u062f\u0648\u0628\u0627\u0631\u06c1 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u06cc\u06c1 \u062f\u0648\u0628\u0627\u0631\u06c1 \u062a\u0642\u0633\u06cc\u0645 \u0645\u062d\u062f\u0628 \u0645\u062c\u0645\u0648\u0639\u06c1 \u0648\u0632\u0646 \u06a9\u06cc \u06a9\u0644\u06cc\u062f \u06c1\u06d2\u06d4 \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0627\u06cc\u06a9 \u062c\u06cc\u0633\u06d2 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u0627 \u0645\u0631\u06a9\u0628 \u0627\u0633\u06cc \u0637\u0631\u062d \u06a9\u06d2 \u0645\u062a\u0636\u0627\u062f \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<h2 id=\"heading-step-5-cluster-bootstrap-95-confidence-intervals\">\u0645\u0631\u062d\u0644\u06c1 5: \u06a9\u0644\u0633\u0679\u0631 \u0628\u0648\u0679\u0633\u0679\u0631\u06cc\u067e 95% \u0627\u0639\u062a\u0645\u0627\u062f \u06a9\u0627 \u0648\u0642\u0641\u06c1<\/h2>\n<p>\u0646\u0642\u0637\u06c1 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0635\u0631\u0641 \u0622\u062f\u06be\u06cc \u06a9\u06c1\u0627\u0646\u06cc \u06c1\u06d2\u06d4 \u0627\u0633\u0679\u06cc\u06a9 \u06c1\u0648\u0644\u0688\u0631\u0632 \u062c\u0648 \u067e\u0648\u0686\u06be\u062a\u06d2 \u06c1\u06cc\u06ba \"\u0622\u067e \u06a9\u062a\u0646\u06d2 \u06cc\u0642\u06cc\u0646\u06cc \u06c1\u06cc\u06ba\u061f\" \u0641\u0627\u0635\u0644\u06c1 \u0686\u0627\u06c1\u062a\u06d2 \u06c1\u06cc\u06ba\u061f \u0631\u0648\u0627\u06cc\u062a\u06cc \u0646\u0627\u0646 \u067e\u06cc\u0631\u0627\u0645\u06cc\u0679\u0631\u06a9 \u0628\u0648\u0679\u0633\u0679\u0631\u06cc\u067e\u0646\u06af \u0648\u0627\u062d\u062f \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u06cc\u0648\u0646\u0679\u0633 \u06a9\u06d2 \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644 \u067e\u0631 \u0635\u0627\u0641 \u0637\u0648\u0631 \u067e\u0631 \u0644\u0627\u06af\u0648 \u0646\u06c1\u06cc\u06ba \u06c1\u0648\u062a\u06cc \u06c1\u06d2\u06d4 \u0627\u0633 \u06a9\u06cc \u0648\u062c\u06c1 \u06cc\u06c1 \u06c1\u06d2 \u06a9\u06c1 \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u0679\u0627\u0626\u0645 \u0633\u06cc\u0631\u06cc\u0632 \u06a9\u0648 \u0645\u062a\u0628\u0627\u062f\u0644 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u062f\u0648\u0628\u0627\u0631\u06c1 \u0646\u0645\u0648\u0646\u06c1 \u06a9\u0631\u0646\u06d2 \u0633\u06d2 \u0648\u0642\u062a \u06a9\u06cc \u062a\u0631\u062a\u06cc\u0628 \u06a9\u0648 \u062e\u062a\u0645 \u06a9\u0631 \u062f\u06cc\u0627 \u062c\u0627\u062a\u0627 \u06c1\u06d2 \u062c\u0633 \u067e\u0631 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0644\u06af\u0627\u0646\u06d2 \u0648\u0627\u0644\u0627 \u0627\u0646\u062d\u0635\u0627\u0631 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u0627\u06cc\u06a9 \u062f\u0631\u0633\u062a \u0645\u062a\u0628\u0627\u062f\u0644 \u0635\u0627\u0631\u0641 \u06a9\u06cc \u0633\u0637\u062d \u06a9\u06cc \u06a9\u0644\u0633\u0679\u0631 \u0628\u0648\u0679\u0633\u0679\u0631\u06cc\u067e\u0646\u06af \u06c1\u06d2\u06d4 \u0645\u062a\u0628\u0627\u062f\u0644 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06a9\u0646\u0646\u062f\u06af\u0627\u0646 \u06a9\u0648 \u062f\u0648\u0628\u0627\u0631\u06c1 \u0646\u0645\u0648\u0646\u06c1 \u0628\u0646\u0627\u0626\u06cc\u06ba\u060c \u062f\u0648\u0628\u0627\u0631\u06c1 \u0646\u0645\u0648\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u0635\u0627\u0631\u0641 \u0644\u0627\u06af\u0632 \u0633\u06d2 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0645\u062e\u0635\u0648\u0635 \u067e\u06cc\u0646\u0644 \u062f\u0648\u0628\u0627\u0631\u06c1 \u0628\u0646\u0627\u0626\u06cc\u06ba\u060c \u0645\u062f\u062a \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0688\u0648\u0646\u0631 \u06a9\u06d2 \u0648\u0632\u0646 \u06a9\u0648 \u062f\u0631\u0633\u062a \u06a9\u0631\u06cc\u06ba\u060c \u0627\u0648\u0631 \u0645\u062f\u062a \u06a9\u06d2 \u0628\u0639\u062f \u0648\u0642\u0641\u06c1 \u0631\u06cc\u06a9\u0627\u0631\u0688 \u06a9\u0631\u06cc\u06ba\u06d4<\/p>\n<p>500 \u0628\u0627\u0631 \u062f\u06c1\u0631\u0627\u0626\u06cc\u06ba\u06d4 \u0646\u062a\u06cc\u062c\u06c1 \u062e\u06cc\u0632 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0627 2.5 \u0648\u0627\u06ba \u0627\u0648\u0631 97.5 \u0641\u06cc\u0635\u062f \u0641\u06cc\u0635\u062f 95% CI \u06c1\u06d2\u06d4<\/p>\n<pre><code class=\"language-python\">def build_panel(df_inner):\n    dfw = df_inner[df_inner.signup_week < WINDOW].copy()\n    panel = (dfw.groupby([\"workspace_id\", \"signup_week\"])\n             [\"task_completed\"].mean().reset_index())\n    panel.columns = [\"workspace_id\", \"week\", \"task_completed\"]\n    piv = panel.pivot(index=\"week\", columns=\"workspace_id\",\n                      values=\"task_completed\")\n    piv = piv.interpolate(method=\"linear\", axis=0).ffill().bfill()\n    ws_wave_b = df_inner.groupby(\"workspace_id\").wave.first()\n    w1 = sorted(ws_wave_b[ws_wave_b == 1].index.tolist())\n    w2 = sorted(ws_wave_b[ws_wave_b == 2].index.tolist())\n    return piv[w1].mean(axis=1).values, piv[w2].values\n\n\nrng = np.random.default_rng(7)\nn = len(df)\nn_reps = 500\ngaps_boot = np.empty(n_reps)\nfor i in range(n_reps):\n    sample = df.iloc[rng.integers(0, n, size=n)]\n    t_b, d_b = build_panel(sample)\n    gaps_boot[i] = fit_and_gap(t_b, d_b)\n\nlo = float(np.percentile(gaps_boot, 2.5))\nhi = float(np.percentile(gaps_boot, 97.5))\nprint(f\"Post-period gap 95% CI: [{lo:+.4f}, {hi:+.4f}]\")\nprint(f\"Observed point estimate: {gap:+.4f}\")\nprint(f\"Ground truth +0.0500 inside CI: \"\n      f\"{'YES' if lo <= 0.05 <= hi else 'NO'}\")\nprint(f\"Zero inside CI: {'YES' if lo <= 0 <= hi else 'NO'}\")\n<\/code><\/pre>\n<p><strong>\u0645\u062a\u0648\u0642\u0639 \u067e\u06cc\u062f\u0627\u0648\u0627\u0631:<\/strong><\/p>\n<pre><code class=\"language-text\">Post-period gap 95% CI: [+0.0511, +0.1215]\nObserved point estimate: +0.0829\nGround truth +0.0500 inside CI: NO\nZero inside CI: NO\n<\/code><\/pre>\n<p><strong>\u0645\u0648\u062c\u0648\u062f\u06c1 \u0635\u0648\u0631\u062a\u062d\u0627\u0644 \u06a9\u0686\u06be \u06cc\u0648\u06ba \u06c1\u06d2:<\/strong> \u06c1\u0645 \u0635\u0627\u0631\u0641 \u0644\u0627\u06af \u06a9\u0648 500 \u0628\u0627\u0631 \u062f\u0648\u0628\u0627\u0631\u06c1 \u0646\u0645\u0648\u0646\u06c1 \u0628\u0646\u0627\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u06c1\u0631 \u0627\u06cc\u06a9 \u0646\u0645\u0648\u0646\u06d2 \u067e\u0631 \u067e\u06cc\u0646\u0644\u0632 \u06a9\u0648 \u062f\u0648\u0628\u0627\u0631\u06c1 \u0628\u0646\u0627\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u0633\u0627\u0628\u0642\u06c1 \u200b\u200b\u0645\u062f\u062a \u06a9\u0648 \u062f\u0648\u0628\u0627\u0631\u06c1 \u0648\u0632\u0646 \u062f\u06cc\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u0627\u0648\u0631 500 \u06a9\u06d2 \u0646\u062a\u06cc\u062c\u06d2 \u0645\u06cc\u06ba \u0622\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u0648\u0642\u0641\u0648\u06ba \u06a9\u06d2 2.5\u0648\u06cc\u06ba \u0627\u0648\u0631 97.5\u0648\u06cc\u06ba \u067e\u0631\u0633\u0646\u0679\u0627\u0626\u0644 \u0644\u06cc\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 95% CI \u06c1\u06d2\u06d4 [+5.11 pp, +12.15 pp]. \u0686\u0648\u0646\u06a9\u06c1 0 \u06a9\u06d2 \u0639\u0644\u0627\u0648\u06c1 \u06a9\u0633\u06cc \u0628\u06be\u06cc \u0686\u06cc\u0632 \u06a9\u06cc \u06af\u0646\u062c\u0627\u0626\u0634 \u06c1\u06d2\u060c \u0627\u0633 \u0644\u06cc\u06d2 \u0627\u062b\u0631 \u0634\u0645\u0627\u0631\u06cc\u0627\u062a\u06cc \u0644\u062d\u0627\u0638 \u0633\u06d2 \u0627\u06c1\u0645 \u06c1\u06d2\u06d4<\/p>\n<p>\u0646\u0686\u0644\u06cc \u062d\u062f +5pp \u0632\u0645\u06cc\u0646\u06cc \u0633\u0686\u0627\u0626\u06cc \u06a9\u06d2 \u0628\u0627\u0644\u06a9\u0644 \u0627\u0648\u067e\u0631 \u0648\u0627\u0642\u0639 \u06c1\u06d2\u06d4 \u06cc\u0639\u0646\u06cc\u060c \u0686\u06be\u0648\u0679\u06d2 \u0688\u0648\u0646\u0631 \u067e\u06cc\u0646\u0644\u0632 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644 \u06a9\u0627 \u0645\u062d\u062f\u0648\u062f \u0646\u0645\u0648\u0646\u06c1 \u0627\u0648\u067e\u0631 \u06a9\u06cc \u0637\u0631\u0641 \u062a\u0639\u0635\u0628\u060c \u062c\u06c1\u0627\u06ba \u06c1\u0631 \u0688\u0648\u0646\u0631 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 (\u062a\u0642\u0631\u06cc\u0628\u0627\u064b 19 \u0635\u0627\u0631\u0641\u06cc\u0646 \u0641\u06cc \u06c1\u0641\u062a\u06c1) 25 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u067e\u0631\u0648\u0633\u06cc\u0633\u0646\u06af \u0627\u0648\u0633\u0637 \u0633\u06d2 \u0632\u06cc\u0627\u062f\u06c1 \u0634\u0648\u0631 \u0627\u0679\u06be\u0627\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u067e\u0644\u06cc\u0633\u0628\u0648\u060c \u0627\u06cc\u0644 \u0627\u0648 \u0627\u0648\u060c \u0627\u0648\u0631 \u0628\u0648\u0679\u0633\u0679\u0631\u06cc\u067e\u0646\u06af \u0627\u06cc\u06a9 \u0633\u0627\u062a\u06be \u062f\u0631\u0627\u0635\u0644 \u0645\u062b\u0628\u062a \u0627\u062b\u0631\u0627\u062a \u062f\u06cc\u06a9\u06be\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 \u0627\u06cc\u06a9 \u0648\u0627\u062d\u062f \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u0688\u0648\u0646\u0631 \u06a9\u0627 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06a9\u0631\u062a\u06d2 \u0648\u0642\u062a \u067e\u0648\u0627\u0626\u0646\u0679 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u062a\u0639\u0635\u0628 \u0627\u06cc\u06a9 \u062a\u062c\u0627\u0631\u062a\u06cc \u0628\u0646\u062f \u06c1\u06d2\u06d4<\/p>\n<p>\u0627\u0633\u0679\u06cc\u06a9 \u06c1\u0648\u0644\u0688\u0631 \u06a9\u06cc \u0631\u067e\u0648\u0631\u0679\u0633 \u06a9\u06d2 \u0644\u06cc\u06d2\u060c \u067e\u0648\u0627\u0626\u0646\u0679 \u06a9\u06d2 \u062a\u062e\u0645\u06cc\u0646\u06d2 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0648\u0642\u0641\u0648\u06ba \u06a9\u0627 \u062d\u0648\u0627\u0644\u06c1 \u062f\u06cc\u06ba \u0627\u0648\u0631 \u062a\u0639\u0635\u0628 \u06a9\u06cc \u0633\u0645\u062a \u06a9\u0648 \u0646\u0648\u0679 \u06a9\u0631\u06cc\u06ba \u062a\u0627\u06a9\u06c1 \u0679\u06cc\u0645 \u0635\u062d\u06cc\u062d \u06a9\u06cc\u0644\u06cc\u0628\u0631\u06cc\u0634\u0646 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0646\u0645\u0628\u0631\u0648\u06ba \u06a9\u0648 \u067e\u0691\u06be \u0633\u06a9\u06d2\u06d4<\/p>\n<h2 id=\"heading-when-synthetic-control-fails\">\u062c\u0628 \u062c\u0627\u0645\u0639 \u06a9\u0646\u0679\u0631\u0648\u0644 \u0646\u0627\u06a9\u0627\u0645 \u06c1\u0648\u062c\u0627\u062a\u0627 \u06c1\u06d2\u06d4<\/h2>\n<p>\u0679\u0648\u0679\u0644 \u06a9\u0646\u0679\u0631\u0648\u0644 \u062a\u0646\u06af \u0646\u0627\u06a9\u0627\u0645\u06cc \u06a9\u06d2 \u0637\u0631\u06cc\u0642\u0648\u06ba \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0627\u06cc\u06a9 \u062f\u0631\u0633\u062a \u0679\u0648\u0644 \u06c1\u06d2\u06d4 \u0686\u0627\u0631 \u0633\u0628 \u0633\u06d2 \u0632\u06cc\u0627\u062f\u06c1 \u0639\u0627\u0645 \u0634\u0646\u0627\u062e\u062a \u06a9\u0631\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u062a\u06cc\u0646 \u0645\u0641\u0631\u0648\u0636\u0648\u06ba \u0633\u06d2 \u0628\u0631\u0627\u06c1 \u0631\u0627\u0633\u062a \u062c\u0691\u06d2 \u06c1\u0648\u0626\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<h3 id=\"heading-1-donor-pool-contamination-violates-no-interference\">1. \u0688\u0648\u0646\u0631 \u067e\u0648\u0644 \u06a9\u06cc \u0622\u0644\u0648\u062f\u06af\u06cc (\u0639\u062f\u0645 \u0645\u062f\u0627\u062e\u0644\u062a \u06a9\u06cc \u062e\u0644\u0627\u0641 \u0648\u0631\u0632\u06cc)<\/h3>\n<p>\u0627\u06af\u0631 \u0644\u06c1\u0631 1 \u0645\u06cc\u06ba \u0641\u0631\u0627\u06c1\u0645 \u06a9\u0631\u062f\u06c1 \u0627\u067e \u06af\u0631\u06cc\u0688 \u0644\u06c1\u0631 2 \u062a\u06a9 \u067e\u06be\u06cc\u0644 \u062c\u0627\u062a\u06d2 \u06c1\u06cc\u06ba (\u0645\u0634\u062a\u0631\u06a9\u06c1 API \u06a9\u06cc \u0634\u0631\u062d \u06a9\u0648 \u0645\u062d\u062f\u0648\u062f \u06a9\u0631\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u067e\u0648\u0644\u0632\u060c \u0645\u0634\u062a\u0631\u06a9\u06c1 \u067e\u0631\u0627\u0645\u067e\u0679 \u06a9\u06cc\u0634\u060c \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u06d2 \u062f\u0631\u0645\u06cc\u0627\u0646 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u06cc \u0645\u0646\u062a\u0642\u0644\u06cc)\u060c \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u0622\u0644\u0648\u062f\u06c1 \u06c1\u0648\u062a\u06d2 \u06c1\u06cc\u06ba \u0627\u0648\u0631 \u0641\u0631\u0642 \u062d\u0642\u06cc\u0642\u06cc \u0627\u062b\u0631 \u06a9\u0648 \u06a9\u0645 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u062f\u0641\u0627\u0639 \u0627\u062f\u0627\u0631\u06c1 \u062c\u0627\u062a\u06cc \u06c1\u06d2\u06d4 \u06c1\u0645 \u0648\u0627\u0636\u062d \u0637\u0648\u0631 \u067e\u0631 \u0645\u0627\u0688\u0644 \u0633\u0637\u062d \u06a9\u06d2 \u0686\u06cc\u0646\u0644\u0632 \u06a9\u0648 \u0634\u0627\u0645\u0644 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba \u062c\u06cc\u0633\u06d2 \u0645\u0634\u062a\u0631\u06a9\u06c1 \u0631\u0648\u0679\u0646\u06af\u060c \u0645\u0634\u062a\u0631\u06a9\u06c1 \u06a9\u06cc\u0634\u0646\u06af\u060c \u0627\u0648\u0631 \u0645\u0634\u062a\u0631\u06a9\u06c1 \u0646\u06af\u0631\u0627\u0646\u06cc \u062a\u0627\u06a9\u06c1 \u0639\u0644\u0627\u062c \u06a9\u06cc \u062a\u0627\u0631\u06cc\u062e\u0648\u06ba \u06a9\u06d2 \u0627\u0631\u062f \u06af\u0631\u062f \u0688\u0648\u0646\u0631 \u06cc\u0648\u0646\u0679\u0633 \u0645\u06cc\u06ba \u062a\u0628\u062f\u06cc\u0644\u06cc\u0648\u06ba \u06a9\u0627 \u0622\u0688\u0679 \u06a9\u06cc\u0627 \u062c\u0627 \u0633\u06a9\u06d2\u06d4<\/p>\n<h3 id=\"heading-2-fundamentally-different-units-violates-pre-period-fit\">2. \u0628\u0646\u06cc\u0627\u062f\u06cc \u0637\u0648\u0631 \u067e\u0631 \u0645\u062e\u062a\u0644\u0641 \u0627\u06a9\u0627\u0626\u06cc\u0627\u06ba (\u0645\u062f\u062a \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0645\u0637\u0627\u0628\u0642\u062a \u06a9\u06cc \u062e\u0644\u0627\u0641 \u0648\u0631\u0632\u06cc)<\/h3>\n<p>\u0645\u062d\u062f\u0628 \u06c1\u0644 \u06a9\u06cc \u062d\u0627\u0644\u062a \u0627\u0633 \u0628\u0627\u062a \u06a9\u06cc \u0646\u0634\u0627\u0646\u062f\u06c1\u06cc \u06a9\u0631\u062a\u06cc \u06c1\u06d2 \u06a9\u06c1 \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u0622\u0644\u06c1 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06c1 \u06a9\u06cc \u0645\u062f\u062f \u06a9\u06d2 \u0627\u0646\u062f\u0631 \u06c1\u0648\u0646\u0627 \u0686\u0627\u06c1\u06cc\u06d2\u06d4 \u0627\u06af\u0631 \u0639\u0644\u0627\u062c \u06a9\u06cc \u062c\u0627\u0646\u06d2 \u0648\u0627\u0644\u06cc \u0627\u06a9\u0627\u0626\u06cc\u0627\u06ba \u0633\u0627\u062e\u062a\u06cc \u0637\u0648\u0631 \u067e\u0631 \u0645\u062e\u062a\u0644\u0641 \u06c1\u06cc\u06ba (\u0645\u062b\u0627\u0644 \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631\u060c \u06a9\u0627\u0631\u067e\u0648\u0631\u06cc\u0679 \u0635\u0627\u0631\u0641\u06cc\u0646 \u062c\u06c1\u0627\u06ba \u062a\u0645\u0627\u0645 \u0634\u0631\u0627\u06a9\u062a \u06a9\u0646\u0646\u062f\u06af\u0627\u0646 SMBs \u06c1\u06cc\u06ba)\u060c \u06a9\u0648\u0626\u06cc \u0628\u06be\u06cc \u0648\u0632\u0646 \u06a9\u06cc \u0627\u0633\u06a9\u06cc\u0645 \u0642\u0627\u0628\u0644 \u0628\u06be\u0631\u0648\u0633\u06c1 \u062c\u0648\u0627\u0628\u06cc \u062d\u0642\u06cc\u0642\u062a \u067e\u06cc\u062f\u0627 \u0646\u06c1\u06cc\u06ba \u06a9\u0631\u06d2 \u06af\u06cc\u060c \u0627\u0633 \u0633\u06d2 \u06a9\u0648\u0626\u06cc \u0641\u0631\u0642 \u0646\u06c1\u06cc\u06ba \u067e\u0691\u062a\u0627 \u06c1\u06d2 \u06a9\u06c1 \u067e\u0631\u06cc \u067e\u06cc\u0631\u06cc\u0688 \u0641\u0679 \u06a9\u062a\u0646\u0627 \u06c1\u06cc \u0642\u0631\u06cc\u0628 \u0646\u0638\u0631 \u0622\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u0648\u0632\u0646 \u0686\u06cc\u06a9 \u06a9\u0631\u06cc\u06ba\u06d4 \u0627\u06af\u0631 \u0622\u067e\u0679\u06cc\u0645\u0627\u0626\u0632\u0631 \u06a9\u0633\u06cc \u0627\u06cc\u06a9 \u0688\u0648\u0646\u0631 \u06a9\u0648 80% \u0645\u062e\u062a\u0635 \u06a9\u0631 \u0631\u06c1\u0627 \u06c1\u06d2\u060c \u062a\u0648 \u0622\u067e \u06a9\u0648 \u06cc\u06c1 \u067e\u0648\u0686\u06be\u0646\u0627 \u06c1\u0648\u06af\u0627 \u06a9\u06c1 \u06a9\u06cc\u0627 \u0648\u06c1 \u0688\u0648\u0646\u0631 \u0627\u0635\u0644 \u0645\u06cc\u06ba \u067e\u0648\u0631\u0627 \u06a9\u0627\u0645 \u06a9\u0631 \u0631\u06c1\u0627 \u06c1\u06d2\u060c \u062a\u0648 \u0648\u06c1 \u0648\u0627\u0642\u0639\u06cc \u0645\u0648\u0627\u0632\u0646\u06c1 \u06a9\u0631 \u0633\u06a9\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<h3 id=\"heading-3-post-treatment-shocks-to-donors-violate-stable-donor-composition\">3. \u0639\u0644\u0627\u062c \u06a9\u06d2 \u0628\u0639\u062f \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06c1 \u06a9\u0648 \u062c\u06be\u0679\u06a9\u0627 (\u0645\u0633\u062a\u0642\u0644 \u0688\u0648\u0646\u0631 \u06a9\u06cc \u0633\u0627\u062e\u062a \u06a9\u06cc \u062e\u0644\u0627\u0641 \u0648\u0631\u0632\u06cc)<\/h3>\n<p>\u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0627\u0633\u0679 \u067e\u0631\u06cc \u067e\u06cc\u0631\u06cc\u0688 \u0648\u0632\u0646 \u0633\u06d2 \u0688\u0648\u0646\u0631 \u06a9\u06d2 \u0631\u0648\u06cc\u06d2 \u06a9\u06cc \u067e\u06cc\u0634 \u06af\u0648\u0626\u06cc \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4 \u0627\u06af\u0631 \u06a9\u0633\u06cc \u0628\u0691\u06d2 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06c1 \u06a9\u0648 \u0639\u0644\u0627\u062c \u06a9\u06d2 \u0628\u0639\u062f \u0627\u06cc\u06a9 \u0628\u0691\u0627 \u062c\u06be\u0679\u06a9\u0627 \u0644\u06af\u062a\u0627 \u06c1\u06d2 (\u06a9\u0633\u0679\u0645\u0631 \u0645\u0646\u062a\u06be\u0646\u060c \u0645\u0646\u0642\u0637\u0639 \u06c1\u0648\u0646\u0627\u060c \u0645\u0633\u0627\u0628\u0642\u062a\u06cc \u0622\u063a\u0627\u0632)\u060c \u0639\u0644\u0627\u062c \u06a9\u06d2 \u0628\u0639\u062f \u06a9\u06cc \u0631\u0641\u062a\u0627\u0631 \u0627\u0628 \u0645\u06a9\u0645\u0644 \u0637\u0648\u0631 \u067e\u0631 \u0645\u062a\u0636\u0627\u062f \u0646\u06c1\u06cc\u06ba \u06c1\u06d2\u06d4 \u0632\u06cc\u0627\u062f\u06c1 \u0648\u0632\u0646 \u0648\u0627\u0644\u06d2 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u06cc \u0679\u0627\u0626\u0645 \u0633\u06cc\u0631\u06cc\u0632 \u06a9\u0648 \u063a\u06cc\u0631 \u0645\u0639\u0645\u0648\u0644\u06cc \u067e\u0648\u0633\u0679 \u067e\u0631\u0648\u0633\u06cc\u0633\u0646\u06af \u067e\u06cc\u0679\u0631\u0646 \u06a9\u06d2 \u0644\u06cc\u06d2 \u062c\u0627\u0646\u0686\u0627 \u062c\u0627\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<h3 id=\"heading-4-overfitting-risk-when-j-approaches-t-degrades-pre-period-fit-in-practice\">4. J T\u2080 \u06a9\u06d2 \u0642\u0631\u06cc\u0628 \u0622\u062a\u06d2 \u06c1\u06cc \u0627\u0648\u0648\u0631 \u0641\u0679\u0646\u06af \u06a9\u0627 \u062e\u0637\u0631\u06c1 (\u062f\u0631\u0627\u0635\u0644 \u0645\u062f\u062a \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0641\u0679 \u06a9\u0627 \u0628\u06af\u0691 \u062c\u0627\u0646\u0627)<\/h3>\n<p>\u0627\u0635\u0644\u0627\u062d \u06a9\u0627\u0631 \u0635\u0631\u0641 \u0634\u0648\u0631 \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u06a9\u06cc \u0645\u062f\u062a \u0645\u06cc\u06ba \u0641\u0679 \u06c1\u0648 \u0633\u06a9\u062a\u0627 \u06c1\u06d2 \u062c\u0628 J \u2265 T\u2080\u060c \u0645\u0648\u0627\u0632\u0646\u06c1 \u06a9\u0627 \u0628\u06be\u0631\u0645 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4 \u06cc\u06c1 \u0679\u06cc\u0648\u0679\u0648\u0631\u06cc\u0644 \u0627\u06c1\u0645 \u0632\u0648\u0646 \u0645\u06cc\u06ba T\u2080\/J = 20\/25 = 0.8 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0686\u0644\u062a\u0627 \u06c1\u06d2\u06d4 LOO \u062d\u0633\u0627\u0633\u06cc\u062a \u06a9\u06cc \u062c\u0627\u0646\u0686 \u0627\u06cc\u06a9 \u0639\u0645\u0644\u06cc \u062f\u0641\u0627\u0639 \u06c1\u06d2\u06d4 \u0627\u06af\u0631 \u0639\u0637\u06cc\u06c1 \u062f\u06c1\u0646\u062f\u06af\u0627\u0646 \u06a9\u06d2 \u0642\u0637\u0631\u0648\u06ba \u0645\u06cc\u06ba \u0641\u0631\u0642 \u06a9\u0648 \u0628\u0631\u0642\u0631\u0627\u0631 \u0631\u06a9\u06be\u0627 \u062c\u0627\u062a\u0627 \u06c1\u06d2\u060c \u062a\u0648 \u0641\u0679 \u062d\u0642\u06cc\u0642\u06cc \u0645\u0648\u0627\u0632\u0646\u06c1 \u06a9\u06cc \u0639\u06a9\u0627\u0633\u06cc \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u06cc\u06c1 \u0646\u0627\u06a9\u0627\u0645\u06cc \u06a9\u06d2 \u0637\u0631\u06cc\u0642\u06d2 \u067e\u0648\u0627\u0626\u0646\u0679 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0645\u06cc\u06ba \u067e\u0648\u0634\u06cc\u062f\u06c1 \u0631\u06c1\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 \u06cc\u06c1 \u0627\u06cc\u06a9 \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644 \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u0638\u0627\u06c1\u0631 \u06c1\u0648\u062a\u0627 \u06c1\u06d2 \u062c\u0648 \u06a9\u0627\u063a\u0630 \u067e\u0631 \u0627\u0686\u06be\u06cc \u0637\u0631\u062d \u0641\u0679 \u06c1\u0648\u062a\u0627 \u06c1\u06d2 \u0627\u0648\u0631 \u0627\u06cc\u0633\u06d2 \u062e\u0644\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u062c\u0648 \u0627\u06af\u0644\u06d2 \u0645\u0631\u062d\u0644\u06d2 \u062a\u06a9 \u067e\u0631\u0648\u0633\u06cc\u0633\u0646\u06af \u06a9\u06d2 \u062f\u0648\u0631\u0627\u0646 \u0628\u0631\u0642\u0631\u0627\u0631 \u0646\u06c1\u06cc\u06ba \u0631\u06c1\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0679\u06cc\u0633\u0679\u0646\u06af\u060c LOO \u062d\u0633\u0627\u0633\u06cc\u062a\u060c \u0627\u0648\u0631 \u0628\u0648\u0679\u0633\u0679\u0631\u06cc\u067e\u0646\u06af \u06a9\u0627 \u0645\u062c\u0645\u0648\u0639\u06c1 \u062a\u062d\u0641\u0638 \u0641\u0631\u0627\u06c1\u0645 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<h2 id=\"heading-what-to-do-next\">\u0622\u06af\u06d2 \u06a9\u06cc\u0627 \u06a9\u0631\u0646\u0627 \u06c1\u06d2\u06d4<\/h2>\n<p>\u062c\u0627\u0645\u0639 \u06a9\u0646\u0679\u0631\u0648\u0644 \u0627\u06cc\u06a9 \u0645\u0646\u0627\u0633\u0628 \u0679\u0648\u0644 \u06c1\u06d2 \u062c\u0628 \u0641\u06cc\u0686\u0631 \u0639\u0627\u0644\u0645\u06cc \u0633\u0637\u062d \u067e\u0631 \u062c\u0627\u0631\u06cc \u06a9\u06cc\u0627 \u062c\u0627 \u0631\u06c1\u0627 \u06c1\u0648 \u0627\u0648\u0631 \u063a\u06cc\u0631 \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u0627\u06a9\u0627\u0626\u06cc\u0648\u06ba \u06a9\u0627 \u0627\u06cc\u06a9 \u067e\u0648\u0644 \u0645\u0648\u062c\u0648\u062f \u06c1\u0648 \u062c\u0648 \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u06cc\u0648\u0646\u0679\u0648\u06ba \u0633\u06d2 \u0645\u0644\u062a\u0627 \u062c\u0644\u062a\u0627 \u06c1\u0648\u06d4<\/p>\n<p>\u0627\u06af\u0631 \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u06cc\u0648\u0646\u0679 \u0627\u0648\u0631 \u0688\u0648\u0646\u0631 \u06cc\u0648\u0646\u0679 \u0645\u062e\u062a\u0644\u0641 \u067e\u06cc\u0645\u0627\u0646\u06d2 \u067e\u0631 \u06a9\u0627\u0645 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u061b <strong>\u0628\u0691\u06be\u0627 \u06c1\u0648\u0627 \u062a\u0631\u06a9\u06cc\u0628 \u06a9\u0646\u0679\u0631\u0648\u0644<\/strong> \u0644\u06a9\u06cc\u0631\u06cc \u0646\u062a\u0627\u0626\u062c \u06a9\u06d2 \u0645\u0627\u0688\u0644 \u0645\u06cc\u06ba \u062a\u0639\u0635\u0628 \u06a9\u06cc \u0627\u0635\u0644\u0627\u062d \u06a9\u06cc \u0627\u0635\u0637\u0644\u0627\u062d \u0634\u0627\u0645\u0644 \u06a9\u0631\u06cc\u06ba\u06d4 \u0627\u06af\u0631 \u0645\u062e\u062a\u0644\u0641 \u0627\u0648\u0642\u0627\u062a \u0645\u06cc\u06ba \u06a9\u0626\u06cc \u0627\u06a9\u0627\u0626\u06cc\u0627\u06ba \u0627\u062e\u062a\u06cc\u0627\u0631 \u06a9\u06cc \u06af\u0626\u06cc \u06c1\u06cc\u06ba\u060c <strong>\u0639\u0627\u0645 \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644<\/strong> (\u0648\u06c1 <code>gsynth<\/code> R \u067e\u06cc\u06a9\u062c\u0632) \u0641\u0631\u06cc\u0645 \u0648\u0631\u06a9 \u06a9\u0648 \u0628\u0691\u06be\u0627\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<p>\u067e\u0631\u0648\u0688\u06a9\u0634\u0646 \u0627\u0632\u06af\u0631 \u06a9\u06d2 \u06a9\u0627\u0645\u0648\u06ba \u06a9\u06d2 \u0644\u06cc\u06d2: <code>pysyncon<\/code> \u06c1\u0645 \u0645\u06a9\u0645\u0644 Abadi-Diamond-Hainmueller \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0644\u06af\u0627\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u06a9\u0648 V-matrix \u0628\u06cc\u0631\u0648\u0646\u06cc \u0644\u0648\u067e \u06a9\u06d2 \u0630\u0631\u06cc\u0639\u06d2 \u067e\u06cc\u0634\u06cc\u0646 \u06af\u0648\u0626\u06cc \u06a9\u06d2 \u0648\u0632\u0646 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0644\u0627\u06af\u0648 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u0627\u0648\u0631 \u0627\u0646 \u0679\u0627\u0626\u0645 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0679\u06cc\u0633\u0679\u0646\u06af \u0634\u0627\u0645\u0644 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba (\u067e\u06cc\u0631\u06cc\u0688 \u0633\u06d2 \u06a9\u0686\u06be \u062f\u0646 \u067e\u06c1\u0644\u06d2 \u0639\u0644\u0627\u062c \u062a\u0641\u0648\u06cc\u0636 \u06a9\u0631\u0646\u0627 \u0627\u0648\u0631 \u062c\u0639\u0644\u06cc \u0648\u0642\u0641\u0648\u06ba \u06a9\u06cc \u062c\u0627\u0646\u0686 \u06a9\u0631\u0646\u0627)\u060c \u062c\u0633 \u06a9\u0627 \u0627\u0633 \u0679\u06cc\u0648\u0679\u0648\u0631\u06cc\u0644 \u0645\u06cc\u06ba \u0627\u062d\u0627\u0637\u06c1 \u0646\u06c1\u06cc\u06ba \u06a9\u06cc\u0627 \u06af\u06cc\u0627 \u06c1\u06d2\u06d4 \u0627\u06af\u0631 \u06c1\u0645 \u0627\u0633\u06d2 \u062f\u0648\u0628\u0627\u0631\u06c1 \u0634\u0631\u0648\u0639 \u0633\u06d2 \u06cc\u06c1\u0627\u06ba \u0646\u0627\u0641\u0630 \u06a9\u0631\u06cc\u06ba \u062a\u0648 \u062d\u0631\u06a9\u06cc\u0627\u062a \u0627\u0633 \u0637\u0631\u062d \u0646\u0638\u0631 \u0622\u0626\u06cc\u06ba \u06af\u06cc: <code>pysyncon<\/code> \u06cc\u06c1 \u062c\u0627\u0626\u0632\u06c1 \u0644\u06cc\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u06a9\u0648 \u0628\u06be\u06cc\u062c\u0627 \u062c\u0627\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u0627\u0633 \u0679\u06cc\u0648\u0679\u0648\u0631\u06cc\u0644 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0633\u0627\u062a\u06be\u06cc \u0646\u0648\u0679 \u0628\u06a9 github.com\/RudrenduPaul\/product-experimentation-causal-inference-genai-llm\/tree\/main\/04_synthetic_control \u067e\u0631 \u06c1\u06d2\u06d4 \u0631\u06cc\u067e\u0648\u0632\u0679\u0631\u06cc \u06a9\u0648 \u06a9\u0644\u0648\u0646 \u06a9\u0631\u06cc\u06ba\u060c \u0627\u06cc\u06a9 \u0645\u0635\u0646\u0648\u0639\u06cc \u0688\u06cc\u0679\u0627\u0633\u06cc\u0679 \u0628\u0646\u0627\u0626\u06cc\u06ba\u060c \u0627\u0648\u0631 \u0627\u0633\u06d2 \u0686\u0644\u0627\u0626\u06cc\u06ba\u06d4 <code>synthetic_control_demo.ipynb<\/code> (\u06cc\u0627 <code>synthetic_control_demo.py<\/code>) \u0627\u0633 \u0679\u06cc\u0648\u0679\u0648\u0631\u06cc\u0644 \u0645\u06cc\u06ba \u06c1\u0631 \u06a9\u0648\u0688 \u0628\u0644\u0627\u06a9\u060c \u06c1\u0631 \u0646\u0645\u0628\u0631\u060c \u0627\u0648\u0631 \u06c1\u0631 \u062a\u0635\u0648\u06cc\u0631 \u06a9\u0648 \u062f\u0648\u0628\u0627\u0631\u06c1 \u067e\u06cc\u0634 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u0627\u06af\u0631 \u0645\u0627\u0688\u0644 \u0627\u067e \u06af\u0631\u06cc\u0688 \u062a\u0645\u0627\u0645 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u0648 \u0628\u06cc\u06a9 \u0648\u0642\u062a \u067e\u06cc\u0634 \u06a9\u06cc\u0627 \u062c\u0627\u062a\u0627 \u06c1\u06d2\u060c \u062a\u0648 \u0639\u0627\u0645 \u0637\u0648\u0631 \u067e\u0631 \u063a\u0644\u0637 \u0646\u0645\u0628\u0631 \u0633\u06d2 \u067e\u06c1\u0644\u06d2\/\u0628\u0639\u062f \u0645\u06cc\u06ba \u0628\u0648\u0644\u06cc \u06c1\u0648\u062a\u06cc \u06c1\u06d2\u06d4 \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644\u0632 \u0622\u067e \u06a9\u06d2 \u067e\u0627\u0633 \u067e\u06c1\u0644\u06d2 \u0633\u06d2 \u0645\u0648\u062c\u0648\u062f \u0688\u06cc\u0679\u0627 \u0633\u06d2 \"\u063a\u06cc\u0631 \u0627\u067e \u06af\u0631\u06cc\u0688 \u0634\u062f\u06c1 \u0635\u0627\u0631\u0641\u06cc\u0646\" \u0628\u0646\u0627\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u0639\u0644\u0627\u062c \u06a9\u06d2 \u06c1\u0641\u062a\u06d2 \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0648\u0632\u0646 \u0679\u06be\u06cc\u06a9 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u0627\u0648\u0631 \u0627\u06cc\u06a9 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0688\u0633\u0679\u0631\u06cc \u0628\u06cc\u0648\u0634\u0646 \u0627\u0648\u0631 \u0628\u0648\u0679\u0633\u0679\u0631\u06cc\u067e \u0648\u0642\u0641\u06c1 \u0641\u0631\u0627\u06c1\u0645 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba \u062c\u0633 \u06a9\u06d2 \u062e\u0644\u0627\u0641 \u0622\u067e \u062f\u0641\u0627\u0639 \u06a9\u0631 \u0633\u06a9\u062a\u06d2 \u06c1\u06cc\u06ba \u062c\u0628 \u0627\u0633\u0679\u06cc\u06a9 \u06c1\u0648\u0644\u0688\u0631\u0632 \u067e\u0648\u0686\u06be\u06cc\u06ba \u06a9\u06c1 \u0622\u067e \u06a9\u062a\u0646\u06d2 \u067e\u0631 \u0627\u0639\u062a\u0645\u0627\u062f \u06c1\u06cc\u06ba\u06d4<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"<p>LLM \u067e\u0631 \u0645\u0628\u0646\u06cc \u062e\u0635\u0648\u0635\u06cc\u0627\u062a \u067e\u0631 \u06a9\u0627\u0631\u0622\u0645\u062f \u0627\u0646\u062f\u0627\u0632\u06c1 \u0644\u06af\u0627\u0646\u06d2 \u0648\u0627\u0644\u06cc \u06a9\u0648\u0626\u06cc \u0628\u06be\u06cc \u0645\u0635\u0646\u0648\u0639\u0627\u062a \u06a9\u06cc \u062a\u062c\u0631\u0628\u06c1 \u06a9\u0627\u0631 \u0679\u06cc\u0645 \u0628\u0627\u0644\u0622\u062e\u0631 \u0627\u0633\u06cc \u062f\u06cc\u0648\u0627\u0631 \u0633\u06d2 \u0679\u06a9\u0631\u0627\u0626\u06d2 \u06af\u06cc\u06d4 \u0627\u0633 \u06a9\u0627 \u0645\u0637\u0644\u0628 \u06cc\u06c1 \u06c1\u06d2 \u06a9\u06c1 \u062c\u0628 \u06a9\u0648\u0626\u06cc \u0633\u067e\u0644\u0627\u0626\u0631 \u0646\u06cc\u0627 \u0645\u0627\u0688\u0644 \u0648\u0631\u0698\u0646 \u062c\u0627\u0631\u06cc \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u060c \u062a\u0648 \u0645\u0632\u0627\u062d\u0645\u062a \u06a9\u06cc \u06a9\u0648\u0626\u06cc \u06af\u0646\u062c\u0627\u0626\u0634 \u0646\u06c1\u06cc\u06ba \u06c1\u0648\u062a\u06cc\u06d4 \u0627\u0646\u0641\u0631\u0627\u0633\u0679\u0631\u06a9\u0686\u0631 \u0679\u06cc\u0645 \u0631\u0627\u062a\u0648\u06ba \u0631\u0627\u062a \u06a9\u0644\u0627\u0688 4.5 \u0633\u06d2 \u06a9\u0644\u0627\u0688 4.6 \u062a\u06a9 \u062a\u0645\u0627\u0645 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