---
title: "Bayes minimax criterion"
source: "https://systems-analysis.info/eng/Bayes_minimax_criterion"
wiki: "systems-analysis.info/eng"
article: "Bayes_minimax_criterion"
language: "en"
categories:
  - "Category:Decision theory"
  - "Category:Decision-making"
  - "Category:English"
  - "Category:Science"
revision_id: 78
wiki_created_at: 2026-09-06T22:17:08Z
wiki_modified_at: 2026-09-06T22:17:08Z
downloaded_at: 2026-09-07T22:20:50Z
---

# 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:

1.  A set of permissible probability distributions for the outcomes is formed (if the exact probabilities are unknown).
2.  For each strategy, the maximum expected risk is determined, considering all possible permissible distributions.
3.  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.

## External links

- <a href="https://en.wikipedia.org/wiki/Minimax_estimator" class="external text" rel="nofollow">Minimax estimator — Wikipedia</a>

## See also

- [Bayes criterion](https://systems-analysis.info/eng/Bayes_criterion "Bayes criterion")
- [Minimax regret criterion (Savage criterion)](https://systems-analysis.info/eng/Minimax_regret_criterion_(Savage_criterion) "Minimax regret criterion (Savage criterion)")
- [Criterion](https://systems-analysis.info/eng/Criterion "Criterion")
- [Hodges-Lehmann criterion](https://systems-analysis.info/eng/Hodges-Lehmann_criterion "Hodges-Lehmann criterion")