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Chapter 20 - An introduction to decision theory. When you have completed this chapter, you will be able to: Define the terms state of nature, event, decision alternative, and payoff; organize information in a payoff table or a decision tree; find the expected payoff of a decision alternative; compute opportunity loss and expected opportunity loss; assess the expected value of information. | An Introduction to Decision Theory On CD Chapter 20 GOALS Define the terms state of nature, event, decision alternative, and payoff. Organize information in a payoff table or a decision tree. Find the expected payoff of a decision alternative. Compute opportunity loss and expected opportunity loss. Assess the expected value of information. Statistical Decision Theory Classical statistics focuses on estimating a parameter, such as the population mean, constructing confidence intervals, or hypothesis testing. Statistical Decision Theory (Bayesian statistics) is concerned with determining which decision, from a set of possible decisions, is optimal. Three components to any decision-making situation: The available choices (alternatives or acts). The states of nature, which are not under the control of the decision maker - uncontrollable future events. The payoffs - needed for each combination of decision alternative and state of nature. A Payoff Table is a listing of all possible | An Introduction to Decision Theory On CD Chapter 20 GOALS Define the terms state of nature, event, decision alternative, and payoff. Organize information in a payoff table or a decision tree. Find the expected payoff of a decision alternative. Compute opportunity loss and expected opportunity loss. Assess the expected value of information. Statistical Decision Theory Classical statistics focuses on estimating a parameter, such as the population mean, constructing confidence intervals, or hypothesis testing. Statistical Decision Theory (Bayesian statistics) is concerned with determining which decision, from a set of possible decisions, is optimal. Three components to any decision-making situation: The available choices (alternatives or acts). The states of nature, which are not under the control of the decision maker - uncontrollable future events. The payoffs - needed for each combination of decision alternative and state of nature. A Payoff Table is a listing of all possible combinations of decision alternatives and states of nature. The Expected Payoff or the Expected Monetary Value (EMV) is the expected value for each decision. Decision Making Calculating the EMV Let Ai be the ith decision alternative. Let P(Sj) be the probability of the jth state of nature. Let V(Ai, Sj) be the value of the payoff for the combination of decision alternative Ai and state of nature Sj. Let EMV (Ai) be the expected monetary value for the decision alternative Ai. Decision Making Under Conditions of Uncertainty - Example EXAMPLE Bob Hill, a small investor, has $1,100 to invest. He has studied several common stocks and narrowed his choices to three, namely, Kayser Chemicals, Rim Homes, and Texas Electronics. He estimated that, if his $1,100 were invested in Kayser Chemicals and a strong bull market developed by the end of the year (that is, stock prices increased drastically), the value of his Kayser stock would more than double, to $2,400. However, if there were
