Bayes minimax criterion
Bayes Minimax Criterion is a decision-making method under conditions of risk and partial uncertainty, aimed at minimizing the maximum expected risk. It is applied when the probabilities of outcomes are known imprecisely or are represented by a set of permissible distributions.
Essence of the Criterion
The Bayes minimax criterion assumes that the decision-maker does not fully trust the available probability estimates. Instead of choosing a strategy that maximizes expected payoff (as in the classic Bayes criterion), a strategy is adopted that minimizes the worst-case expected risk.
In other words, the Bayes minimax criterion combines:
- the probabilistic nature of the Bayesian approach,
- the caution characteristic of minimax strategies.
The strategy is chosen such that for the most unfavorable probability distribution, the expected loss is as low as possible.
Application of the Criterion
The application process includes the following steps:
- A set of permissible probability distributions for the outcomes is formed (if the exact probabilities are unknown).
- For each strategy, the maximum expected risk is determined, considering all possible permissible distributions.
- The strategy that minimizes this maximum risk is chosen.
This approach ensures the robustness of decisions in the presence of uncertainty regarding probabilities.
Advantages and Disadvantages
Advantages:
- Robustness of decisions against errors in probability estimation.
- Provides protection against worst-case scenarios even with incomplete information.
Disadvantages:
- Can be overly conservative when probabilities are known accurately.
- Requires complex work with sets of probability distributions, which complicates calculations.