西南交通大学：《管理统计学》（双语版） 第15章 应用统计决策

第15章应用统计决策 Statistical decision

第15章 应用统计决策 Statistical Decision

本章概要 .The payoff Table and Decision Trees Opportunity Loss Criteria for Decision Making Expected Monetary value Expected Profit Under Certainty Return to risk ratio .Decision Making with Sample Information Utility

本章概要 •The Payoff Table and Decision Trees •Opportunity Loss •Criteria for Decision Making •Expected Monetary Value •Expected Profit Under Certainty •Return to Risk Ratio •Decision Making with Sample Information •Utility

Features of Decision Making 决策特征 o List Alternative courses of action (Possible Events or Outcomes e Determine Payoffs? (AsSociate a Payoff with Each Event or Outcome) Adopt Decision Criteria (Evaluate Criteria for Selecting the Best Course of Action)

Features of Decision Making 决策特征 •List Alternative Courses of Action (Possible Events or Outcomes) •Determine Payoffs? (Associate a Payoff with Each Event or Outcome) •Adopt Decision Criteria (Evaluate Criteria for Selecting the Best Course of Action)

List possible actions or events 可能行为与事件清单 Two Methods of Listing I Payoff Table Decision Tree

List Possible Actions or Events 可能行为与事件清单 Payoff Table Decision Tree Two Methods of Listing

Payoff Table 盈利表 Consider a food vendor determining whether to sell soft drinks or hot dogs. Course of Action(Ai Event (Ei Sell Soft Drinks(A, Sell Hot Dogs(A2 Cool Weather (Eu 1=S50 12=S100 Warm Weather (E2) x21=200 125 i- payoff(profit) for event i and action j

Event (Ei ) Cool Weather (E1 ) x11 =$50 x12 = $100 Warm Weather (E2 ) x21 = 200 x22 = 125 Payoff Table 盈利表 Consider a food vendor determining whether to sell soft drinks or hot dogs. Course of Action (Aj ) Sell Soft Drinks (A1 ) Sell Hot Dogs (A2 ) xij = payoff (profit) for event i and action j

Decision Tree决策树): Example Food Vendor Profit Tree Diagram ther s50 Weal W D rm Weather 200 ot D 100 wes the 12 Warm Weath X2=125

Decision Tree（决策树）:Example Food Vendor Profit Tree Diagram x11 = $50 x21 = 200 x22 =125 x12 = 100

Opportunity loss(机会损失) Example Highest possible profit for an event E Actual profit obtained for an action A Opportunity Loss(i) Event: Cool Weather Action: Soft Drinks Profit: S50 Alternative Action: Hot Dogs Profit: S100 Opportunity Loss=$100-$50=$50

Opportunity Loss（机会损失）: Example Highest possible profit for an event Ei - Actual profit obtained for an action Aj Opportunity Loss (l ij ) Event: Cool Weather Action: Soft Drinks Profit: $50 Alternative Action: Hot Dogs Profit: $100 Opportunity Loss = $100 - $50 = $50

Opportunity Loss: Table Alternative Course of Action Event Optimal Profit of Sell Soft Drinks Sell Hot Dogs Action Optimal Action Cool Hot 100 100-50=50100-100=0 Weather Dogs Warm Soft 200 200-200=0 200-125=75 Weather Drinks

Opportunity Loss: Table Event Optimal Profit of Sell Soft Drinks Sell Hot Dogs Action Optimal Action Cool Hot 100 100 - 50 = 50 100 - 100 = 0 Weather Dogs Warm Soft 200 200 - 200 = 0 200 - 125 = 75 Weather Drinks Alternative Course of Action

Decision criteria 决策准则 Expected Monetary Value (EMv) The expected profit for taking an action Expected Opportunity Loss (o) The expected loss for not taking action A Expected Value of Perfect Information(EVPI) The expected opportunity loss from the best decision

Decision Criteria 决策准则 Expected Monetary Value (EMV) • The expected profit for taking an action Aj Expected Opportunity Loss (EOL) • The expected loss for not taking action Aj Expected Value of Perfect Information (EVPI) • The expected opportunity loss from the best decision

Decision Criteria -- EMV 期望货币价值 Expected Monetary value (EMV) Sum (monetary payoffs of events)x(probabilities of the events) EMV:-2X EMV=expected monetary value of action j ,payoff for action j and event i Pi= probability of event i occurring

Decision Criteria -- EMV 期望货币价值 Expected Monetary Value (EMV) Sum (monetary payoffs of events)  (probabilities of the events) V Xij Pi j =  N EMVj = expected monetary value of action j xi,j = payoff for action j and event i Pi = probability of event i occurring i = 1