Ch 15

Expected Value (EV)

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

Branches

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

Sample Information

New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities.

Decision Nodes

Nodes indicating points at which a decision is made.

Chase Nodes

Nodes indicating points at which an uncertain event will occur.

Risk Taker

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

Utility Function for Money

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

Risk-Neutral

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.

Risk Avoider

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

Design Tree

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

Payoff

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 payoff.

Utility

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

Perfect Information

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

Discussion Strategy

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

Payoff table

A tabular representation of the payoffs for a decision problem.

Bayes' Theorem

A theorem that enables the use of sample information to revise prior probabilities.

Expected Value Approach

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.

Optimistic Approach

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.

Conservative Approach

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.

Minimax Regret Approach

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.

Nodes

An intersection or junction point of a decision tree.

Chance Events

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

Decision Alternatives

Options available to the decision maker.

Opportunity Loss

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

Regret

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

Expected value of Perfect Information (EVPI)

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

Expected Vale of Sample Information (EVSI)

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

States of Nature

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

Posterior Probabilities

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

Prior Probability

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

Risk Profile

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

Conditional Probability

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

Outcomes

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

Sensitivity Analysis

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

Risk Analysis

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

Expected Utility (EU)

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