Decision Making Under Uncertainty: Strategies and Analysis

Decision Alternatives and States of Nature

Alternatives are options for a decision. Outcomes are influenced by random factors beyond control, known as states of nature. Prior probabilities indicate the likelihood of each state. Each alternative and state combination yields a payoff, often monetary.

Decision-Making Approaches

1. Optimistic Approach

Maximax (Profit)

Choose the alternative with the highest possible payoff.

Minimin (Cost)

Choose the alternative with the lowest possible cost.

2. Conservative Approach

Maximin (Profit)

Choose the alternative with the best worst-case payoff.

Minimax (Cost)

Choose the alternative with the lowest worst-case cost.

3. Minimax Regret

Minimize the maximum regret by constructing a regret table.

4. Expected Value (Bayes' Decision Rule)

Calculate the expected payoff for each alternative using prior probabilities. Choose the alternative with the highest expected payoff for long-term benefits.

Decision Nodes and Event Nodes

• Decision Node (Square): Represents a decision point.
• Event Node (Circle): Represents a random event with possible outcomes.

Expected Value of Perfect Information (EVPI)

EVPI = Expected payoff with perfect information - Expected payoff without perfect information.

• Perfect Information: Best payoff for each state of nature.
• Without Perfect Information: Expected payoff of the best decision using the expected value approach.

Posterior Probabilities and Sample Information

Additional testing can improve probability estimates.

• USS: Unfavorable Seismic Soundings
• FSS: Favorable Seismic Soundings

P(state and finding) = P(state) * P(finding|state)

P(finding) = P(state1 and finding) + P(state2 and finding) + ...

P(state|finding) = P(state and finding) / P(finding)

Expected Value of Sample Information (EVSI) is the maximum amount one would pay for sample information.

EVSI = Expected payoff with sample information - Expected payoff without sample information.