Expected Value Decision Analysis
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| Decision alternatives | Options available to the decision maker.
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| Chance event | An uncertain future event affecting the consequence, or payoff, associated with a decision.
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| 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.
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| States of nature | The possible outcomes for chance events that affect the payoff associated with a decision alternative.
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| Influence diagram | A graphical device that shows the relationship among decisions, chance events, and consequences for a decision problem.
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| Node | An intersection or junction point of an influence diagram or a decision tree.
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| Decision nodes | Nodes indicating points where a decision is made.
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| Chance nodes | Nodes indicating points where an uncertain event will occur.
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| Consequence nodes | Nodes of an influence diagram indicating points where a payoff will occur.
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| 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).
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| Payoff table | A tabular representation of the payoffs for a decision problem.
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| Decision tree | A graphical representation of the decision problem that shows the sequential nature of the decision-making process.
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| Branch | Lines showing the alternatives from decision nodes and the outcomes from chance nodes.
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| Optimistic approach | An approach to choosing a decision alt. w/o using probabilities. For a max.problem, it leads to choosing the decision alt.corresponding to the largest payoff; for a min. problem, it leads to choosing the decision alt. corresponding to the smallest payoff.
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| Conservative approach | An approach to choosing a decision alt. w/o using probabilities. For a max.problem, it leads to choosing the decision alt.that max. the min. payoff; for a min. problem, it leads to choosing the decision alternative that minimizes the maximum payoff.
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| 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.
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| Opportunity loss, or regret | The amount of loss (lower profit or higher cost) from not making the best decision for each state of nature.
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| 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.
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| Expected value (EV) | For a chance node, it is the weighted average of the payoffs. The weights are the state-of-nature probabilities.
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| 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).
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| Risk analysis | The study of the possible payoffs and probabilities associated with a decision alternative or a decision strategy.
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| 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.
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| Risk profile | The probability distribution of the possible payoffs associated with a decision alternative or decision strategy.
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| Prior probabilities | The probabilities of the states of nature prior to obtaining sample information.
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| Sample information | New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities.
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| Posterior (revised) | probabilities The probabilities of the states of nature after revising the prior probabilities based on sample information.
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| Decision strategy | A strategy involving a sequence of decisions and chance outcomes to provide the optimal solution to a decision problem.
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| 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.
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| Efficiency | The ratio of EVSI to EVPI as a percentage; perfect information is 100% efficient.
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| Bayes’ theorem | A theorem that enables the use of sample information to revise prior probabilities.
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| Conditional probabilities | The probability of one event given the known outcome of a (possibly) related event.
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| Joint probabilities | The probabilities of both sample information and a particular state of nature occurring simultaneously.
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