Exam 25: Decision Analysis

A payoff table, the prior probabilities for three states of nature and the likelihood probabilities are shown below. Payoff Table: Alternative State of Nature 80 120 90 60 130 170 200 140 100 Prior Probabilities: P( $s _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.5, P( $S _ { 3 }$ ) = 0.1. Likelihood Probabilities: 0.5 0.3 0.2 0.2 0.6 0.2 0.1 0.2 0.7 a. Determine the EMV decision. b. Set up the opportunity loss table. c. Determine the EOL decision. d. What is the expected payoff with perfect information? e. What is the expected value of perfect information?

Define the expected monetary value (EMV) of a decision alternative.

The expected value of sample information (EVSI) is the difference between the expected monetary value with additional information (EMV´)and the expected monetary value without additional information (EMV*). That is, EVSI = EMV´ - EMV*.

Incentive programs for sales staff would be considered a state of nature for a business firm.

The expected payoff with perfect information (EPPI) represents the maximum amount a decision maker would be willing to pay for perfect information.

The expected monetary value (EMV) decision is always the same as the expected opportunity loss (EOL) decision, simply because the opportunity loss table is produced directly from the payoff table.

A payoff table, the prior probabilities for two states of nature, and the likelihood probabilities are shown below. Payoff Table: Alternative State of Nature 0.95 0.05 33 0.08 0.92 25 Prior Probabilities: P( $s _ { 1 }$ ) = 0.4, P( $S _ { 2 }$ ) = 0.6. Likelihood Probabilities: 0.95 0.05 0.08 0.92 A) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 1 }$ . B) Use the posterior probabilities from a. to recalculate the expected monetary value of each act, then determine the optimal act and the EMV*. C) Use the prior and likelihood probabilities to calculate the posterior probabilities for the experimental outcome $I _ { 2 }$ . D) Use the posterior probabilities from c. to recalculate the expected monetary value of each act, then determine the optimal act and the $\text { EMV } ^ { * }$ . E) Use your answers to parts a. to d. to calculate the expected monetary value with additional information. F) Calculate the expected value of sample information.

If EMV( $a _ { 1 }$ ) = $50 000, EMV( $a _ { 2 }$ ) = $65 000, and EMV( $a _ { 3 }$ ) = $45 000, then EMV* = $160 000.

In making decisions, we choose the decision with the smallest expected monetary value, or the largest expected opportunity loss.

We can use the payoff table to calculate the expected monetary value (EMV) and the expected opportunity loss (EOL) of each act (alternative).

In decision analysis, the alternatives are referred to as events and the states of nature are referred to as acts.

The payoff table is a table in which the rows are states of nature, the columns are decision alternatives, and the entry at each intersection of a row and column is a numerical payoff such as a profit or loss.

Which of the following would not be considered a state of nature for a business firm?

In general, the branches of a decision tree represent stages of events.

An opportunity loss is the difference between what the decision maker's profit for an act (alternative) is and what the profit could have been had the best decision been made.

The expected value of perfect information (EVPI) equals the largest expected opportunity loss (EOL*).

Define the term payoff table.

Which of the following statements is correct?

The objective of a preposterior analysis is to determine whether the value of the prediction is greater or less than the cost of the information.

The following table displays the payoffs (in thousands of dollars) for five different decision alternatives under three possible states of nature: Alternative(Decision) State of Nature \1 00 \8 0 \3 5 \2 0 \0 \7 0 \7 5 \5 5 \5 0 \1 5 - \3 0 \0 \3 5 \5 5 \6 0 The prior probabilities of the states of nature are: P( $s _ { 1 }$ ) = 0.2, P( $S _ { 2 }$ ) = 0.3, P( $S _ { 3 }$ ) = 0.5 a. Calculate the expected monetary value for each alternative with present information. What decision should be made using the EMV criterion? b. Calculate the expected payoff with perfect information. c. Calculate the expected value of perfect information. d. Convert the payoff table to an opportunity loss table. e. Calculate the expected opportunity loss for each act with present information. What decision should be made using the EOL criterion?