Chapter 13

Decision Alternatives

These are the various options or strategies available to a decision-maker when faced with a problem or choice. Each alternative presents a different course of action that can potentially lead to a distinct outcome.

States of Nature

These refer to the various future scenarios or events outside the control of the decision-maker that can influence the results of the decision alternatives. They are typically uncertain and may have different probabilities associated with them.

Payoff Table

A structured table that outlines the results (payoffs) of each decision alternative against different states of nature. The table helps in visualizing the potential outcomes and expected benefits of the decisions.

Influence Diagram

A visual representation that illustrates the relationships among decisions, uncertain events (chance nodes), and their corresponding consequences. It helps analyze how different factors influence one another.

Decision Trees

A diagrammatic tool used to represent a decision-making problem chronologically. It consists of decision nodes (represented by squares) where choices are made and chance nodes (represented by circles) indicating uncertain outcomes. This structure helps in visualizing complex decision paths.

Optimistic Approach (Maximax Criterion)

A decision-making strategy that focuses on maximizing the best possible outcome (i.e., the maximum payoff) for a given decision alternative, assuming that the most favorable state will occur.

Conservative Approach (Maximin Criterion)

This strategy seeks to maximize the minimum possible payoff. It is used by decision-makers who prefer to ensure the least favorable outcome is as high as possible, thereby adopting a more cautious stance.

Minimax Regret Approach

A decision-making approach that aims to minimize the maximum possible regret or opportunity loss. Here, the decision-maker assesses the potential regret associated with each alternative and chooses the one attached to the least loss.

Laplace (Equal Likelihood) Criterion

An approach that considers all future states of nature to be equally likely. The decision-maker calculates the average payoff for each alternative and selects the one with the highest average, assuming no bias in probabilities.

Expected Value (EV)

A statistical measure calculated as a weighted sum of all possible payoffs, where each payoff is multiplied by its associated probability of occurrence. Expected Value gives a comprehensive overview of the likely worth of each decision.

Expected Opportunity Loss (EOL)

This is a measure that represents the expected value of regret for each decision alternative. It quantifies the potential missed opportunities if the optimal decision is not chosen.

Expected Value of Perfect Information (EVPI)

The estimated increase in expected profit that a decision-maker would obtain if they had complete knowledge about future states of nature, thus eliminating all uncertainty.

Expected Value of Sample Information (EVSI)

This measures the additional expected value gained from acquiring sample data that informs decision-making, compared to making decisions without that data.

Efficiency of Sample Information

The ratio that compares the Expected Value of Sample Information (EVSI) to the Expected Value of Perfect Information (EVPI). It assesses how beneficial the sample information is relative to having complete future knowledge.

Risk Analysis

The systematic evaluation of the impact and implications of uncertain variables on decision-making processes. This analysis helps decision-makers understand and manage potential risks.

Sensitivity Analysis

A method used to determine how sensitive the outcomes of a decision are to changes in input variables. This analysis helps in identifying which variables significantly influence results and informs decision flexibility.

Bayes’ Theorem

A mathematical formula used for updating the probabilities of hypotheses as more information becomes available. It combines prior probabilities with new evidence to calculate posterior probabilities.

Sequential Decision Trees

A type of decision tree that involves making a series of interdependent decisions over time, accounting for the outcomes of previous choices and their effects on future decisions.

Branch Probabilities

These are the probabilities assigned to different paths in a decision tree, representing the likelihood of each outcome occurring at a chance node.

Dominant Decision

An alternative decision option that is preferred over another across all potential states of nature, meaning it yields better outcomes regardless of the circumstances.