2016-09-01(Chap1a).pdf - General setup of decision problem...

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General setup of decision problem representing the “truth”
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accept 𝐻𝐻 0 reject 𝐻𝐻 0
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LIKELIHOOD SUFFICIENCY (Fisher) Model sample sample sample DECISION RULE DECISION RULE DECISION RULE answer answer answer Evaluate performance of DECISION RULE
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𝒙𝒙 𝑥𝑥 Data 𝑥𝑥 parameter 𝜽𝜽 𝑳𝑳 𝜽𝜽 , 𝒂𝒂 Basis for evaluating performance of DECISION RULE 𝒅𝒅 Action 𝒅𝒅 𝒂𝒂 𝑎𝑎 𝑎𝑎 𝐿𝐿 𝜃𝜃 , 𝑎𝑎 𝐿𝐿 𝜃𝜃 , 𝑎𝑎 Loss
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Total 𝟑𝟑 𝟒𝟒 = 𝟖𝟖𝟖𝟖 rules ~ can evaluate all possible decision rules: Rule 𝒙𝒙 = 𝟎𝟎 𝒙𝒙 = 𝟖𝟖 𝒙𝒙 = 𝟐𝟐 𝒙𝒙 = 𝟑𝟑 𝑑𝑑 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 𝑎𝑎
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