**Bayesian decision theory** refers to a decision theory which is informed by Bayesian probability. It is a statistical system that tries to quantify the tradeoff between various decisions, making use of probabilities and costs. An agent operating under such a decision theory uses the concepts of Bayesian statistics to estimate the expected value of its actions, and update its expectations based on new information. These agents can and are usually referred to as estimators.

Bayesian decision theory is another name for Evidential Decision Theory (EDT).

From the perspective of Bayesian decision theory, any kind of probability distribution - such as the distribution for tomorrow's weather - represents a prior distribution. That is, it represents how we expect *today* the weather is going to be *tomorrow.* This contrasts with frequentist inference, the classical probability interpretation, where conclusions about an experiment are drawn from a set of repetitions of such experience, each producing statistically independent results. For a frequentist, a probability function would be a simple distribution function with no special meaning....