Bayesian econometrics is a branch of econometrics

Econometrics

Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...

 which applies Bayesian principles to economic modelling. Bayesianism is based on a degree-of-belief interpretation of probability

Probability interpretations

The word probability has been used in a variety of ways since it was first coined in relation to games of chance. Does probability measure the real, physical tendency of something to occur, or is it just a measure of how strongly one believes it will occur? In answering such questions, we...

, as opposed to a relative-frequency interpretation.

The Bayesian principle relies on Bayes' theorem

Bayes' theorem

In probability theory and applications, Bayes' theorem relates the conditional probabilities P and P. It is commonly used in science and engineering. The theorem is named for Thomas Bayes ....

 which states that the probability

Bayesian probability

Bayesian probability is one of the different interpretations of the concept of probability and belongs to the category of evidential probabilities. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with propositions, whose truth or falsity is...

 of B conditional on A is the ratio of joint probability of A and B divided by probability of B. Bayesian econometricians assume that coefficients in the model have prior distributions.

This approach was first propagated by Arnold Zellner

Arnold Zellner

Arnold Zellner was an American economist and statistician specializing in the fields of Bayesian probability and econometrics...

.