Bayesian econometrics

Bayesian econometrics is a branch of econometrics which applies Bayesian principles to economic modelling. Bayesianism is based on a degree-of-belief interpretation of probability, as opposed to a relative-frequency interpretation.

The Bayesian principle relies on Bayes' theorem which states that the probability 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.

Subjective probabilities have to satisfy the standard axioms of probability theory if one wishes to avoid losing a bet regardless of the outcome. Before the data is observed, the parameter ${\displaystyle \theta }$ is regarded as an unknown quantity and thus random variable, which is assigned a prior distribution ${\displaystyle \pi (\theta )}$ with ${\displaystyle 0\leq \theta \leq 1}$. Bayesian analysis concentrates on the inference of the posterior distribution ${\displaystyle \pi (\theta |y)}$, i.e. the distribution of the random variable ${\displaystyle \theta }$ conditional on the observation of the discrete data ${\displaystyle y}$. The posterior density function ${\displaystyle \pi (\theta |y)}$ can be computed based on Bayes' Theorem:

...
Wikipedia