Decision Analysis

Question 1

Bayes’ Theorem

Answer 1

P(A|B) = P(B|A)P(A)/P(B); posterior equals likelihood times prior over marginal

Question 2

Branch

Answer 2

Lines showing the alternatives from decision nodes and the outcomes from chance nodes.

Question 3

Chance event

Answer 3

An uncertain future event affecting the consequence, or payoff, associated with a decision.

Question 4

Chance nodes

Answer 4

Nodes indicating points at which an uncertain event will occur.

Question 5

Conditional Probability

Answer 5

The probability of one event, given the known outcome of a (possibly) related event.

Question 6

Conservative approach

Answer 6

An approach to choosing a decision alternative without using probabilities. For a maximization problem, it leads to choosing the decision alternative that maximizes the minimum payoff; for a minimization problem, it leads to choosing the decision alternative that minimizes the maximum payoff.

Question 7

Decision alternatives

Answer 7

Options available to the decision maker.

Question 8

Decision nodes

Answer 8

Nodes indicating points at which a decision is made.

Question 9

Decision strategy

Answer 9

A strategy involving a sequence of decisions and chance outcomes to provide the optimal solution to a decision problem.

Question 10

Decision tree

Answer 10

A graphical representation of the decision problem that shows the sequential nature of the decision-making process.

Question 11

Expected utility

Answer 11

The weighted average of the utilities associated with a decision alternative. The weights are the state-of-nature probabilities.

Question 12

Expected value

Answer 12

For a chance node, the weighted average of the payoffs. The weights are the state-of-nature probabilities.

Question 13

Expected value approach

Answer 13

An approach to choosing a decision alternative based on the expected value of each decision alternative. The recommended decision alternative is the one that provides the best expected value.

Question 14

Expected value of perfect information

Answer 14

The difference between the expected value of an optimal strategy based on perfect information and the “best” expected value without any sample information.

Question 15

Expected value of sample information

Answer 15

The difference between the expected value of an optimal strategy based on sample information and the “best” expected value without any sample information.

Question 16

minimax regret approach

Answer 16

An approach to choosing a decision alternative without using probabilities. For each alternative, the maximum regret is computed, which leads to choosing the decision alternative that minimizes the maximum regret.

Question 17

Node

Answer 17

An intersection or junction point of a decision tree.

Question 18

Optimistic approach

Answer 18

An approach to choosing a decision alternative without using probabilities. For a maximization problem, it leads to choosing the decision alternative corresponding to the largest payoff; for a minimization problem, it leads to choosing the decision alternative corresponding to the smallest payoff.

Question 19

Outcome

Answer 19

The result obtained when a decision alternative is chosen and a chance event occurs.

Question 20

Payoff

Answer 20

A measure of the outcome of a decision such as profit, cost, or time. Each combination of a decision alternative and a state of nature has an associated value.

Question 21

Payoff table

Answer 21

A tabular representation of the outcomes for a decision problem.

Question 22

Perfect information

Answer 22

A special case of sample information in which the information tells the decision maker exactly which state of nature is going to occur.

Question 23

Posterior probability

Answer 23

The probabilities of the states of nature after revising the prior probabilities based on sample information.

Question 24

Prior probability

Answer 24

The probabilities of the states of nature prior to obtaining sample information.

Question 25

Regret (opportunity loss)

Answer 25

The amount of loss (lower profit or higher cost) from not making the best decision for each state of nature.

Question 26

Risk analysis

Answer 26

The study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy in the face of uncertainty.

Question 27

Risk avoider

Answer 27

A decision maker who would choose a guaranteed payoff over a lottery with a better expected payoff.

Question 28

Risk neutral

Answer 28

A decision maker who is neutral to risk. For this decision maker, the decision alternative with the best expected value is identical to the alternative with the highest expected utility.

Question 29

Risk profile

Answer 29

The probability distribution of the possible payoffs associated with a decision alternative or decision strategy.

Question 30

Risk taker

Answer 30

A decision maker who would choose a lottery over a better guaranteed payoff.

Question 31

Sample information

Answer 31

New information obtained through research or experimentation thatenables updating or revising the state-of-nature probabilities.

Question 32

Sensitivity analysis

Answer 32

The study of how changes in the probability assessments for the states of nature or changes in the payoffs affect the recommended decision alternative.

Question 33

States of nature

Answer 33

The possible outcomes for chance events that affect the payoff associated with a decision alternative.

Question 34

Utility

Answer 34

A measure of the total worth of a consequence reflecting a decision maker’s attitude toward considerations such as profit, loss, and risk.

Question 35

Utility function for money

Answer 35

A curve that depicts the relationship between monetary value and utility.