Decision Models and Decision Tree Analysis

• Decision models offer a framework to consider all facets of a decision problem.

Decision Tree

• Decision trees visually represent a sequence of decisions.
• They include a list of feasible alternatives, associated outcomes, probabilities, and utility evaluations.
• They start with a square decision node with several alternatives and outcomes.
• Nature controls the result at a chance node.

Decision Criteria

• Pessimism and optimism can influence utility scores.
• The minimax criterion selects the alternative minimizing the maximum loss.
• The maximax criterion maximizes the possible gain among alternatives.

Prior Analysis vs. Terminal Analysis

• Prior analysis relies solely on available prior information for decision analysis.
• Terminal analysis is updated with additional new information.

Terminal Analysis

• Acquiring additional information costs time, energy, and money, but may improve decision-making.

Value of Information

• Decisions involve determining whether to acquire additional information.
• The value of perfect information is the maximum cost a decision maker should pay for additional information.

Sensitivity of Decision

• Sensitivity of the optimal alternative to calculated probability values is of interest.

Bayes Point Estimator

• The Bayes approach to estimation assumes probability distribution parameters are random variables.
• Uncertainty of a parameter is modeled by corresponding prior or posterior distributions.
• The Bayes point estimator minimizes expected loss associated with prediction error.

Utility Theory

• Utility is a true measure of value to a decision maker.
• The alternative with the highest utility value is preferable.

Axioms of Utility Theory

• Orderability allows preferences between alternatives to be ordered.
• Transitivity dictates if A is preferred over B, and B over C, then A is preferred over C.
• Continuity, Substitutability, Monotonicity, and Decomposability are also key axioms.

Utility Function

• The utility of a lottery equals the expected utility of its prizes.
• Relative utility values remain unchanged after a linear transformation of the utility function.

Determination of Utility Values

• Assign a utility of 1 to the most preferred event and 0 to the least preferred.

Utility Function and Monetary Value

• A decision maker's order of preference may change with varying monetary assignments.
• Other variables include time, settlement, and pollutant level.

Maximized Expected Utility

• It serves as a more general criterion for selecting alternatives.
• The value of information is obtained through trial and error

Utility Functions

• Utility functions are usually convex.
• Risk-averse individuals have convex utility functions.
• Most people are risk-averse.
  • Exponential, Logarithmic, and Quadratic functions are common.
• Risk-affinitive utility functions are concave up but not realistic.

Sensitivity of Expected Utility

• The exact form of the utility function may not be a crucial factor in computing expected utility.

Probability Estimation

• Probability estimation should base entirely on observed information.
• Probabilities of events or distributions of random variables can be estimated solely on subjective judgment.
• Bayesian approach can be used.
• The fractile method applies here.

Weighted Objective Decision Analysis

• Objectives listed in decreasing order of importance using ordinal or cardinal ranking.

Multiattribute Utility Approach

• Statistical independence simplifies the assessment of an n-dimensional function to n one-dimensional functions.
• Preferential independence means trade-offs between two attributes are governed by the unique indifference curve between them, regardless of other attribute values.
• Utility independence means relative utility remains the same regardless of other utility values.

Explore decision models including decision trees, decision criteria like minimax and maximax, and the difference between prior and terminal analysis. Learn how to evaluate the value of information in decision-making.