QAT1 Chapter 4 Decision Analysis

expected value (EV)

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

branch

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 where a decision is made.

chance nodes

Nodes indicating points where an uncertain event will occur.

consequence nodes

Nodes of an influence diagram indicating points where a payoff will occur.

influence diagram

A graphical device that shows the relationship among decisions, chance events, and consequences for a decision problem.

decision tree

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

payoff

A measure of the consequence of a decision such as profit, cost, or time. Each combination of a decision alternative and a state of nature has an associated payoff (consequence).

decision 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.

node

An intersection or junction point of an influence diagram or a decision tree.

chance event

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

decision alternatives

Options available to the decision maker.

opportunity loss, or regret

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

expected value 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.

expected value of perfect information (EVPI)

The expected value of information that would tell the decision maker exactly which state of nature is going to occur (i.e., perfect information).

states of nature

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

joint probabilities

The probabilities of both sample information and a particular state of nature occurring simultaneously.

posterior (revised) probabilities

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

prior probabilities

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 probabilities

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

efficiency

The ratio of EVSI to EVPI as a percentage; perfect information is 100% efficient.

consequence

The result obtained when a decision alternative is chosen and a chance event occurs. A measure of the consequence is often called a payoff.

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.