# On the method of likelihood-induced priors

## TL;DR

This paper introduces a method to construct priors directly from the likelihood function using information entropy, especially for exponential family models, linking likelihood properties to conjugate priors.

## Contribution

It presents a four-step algorithm for deriving likelihood-induced priors based on information entropy and likelihood resolution, connecting likelihood form to prior construction.

## Key findings

- Likelihood contains sufficient information for prior construction.
- Likelihood-induced prior coincides with conjugate prior for exponential family models.
- The method leverages coarse-graining and resolving power of likelihood.

## Abstract

We demonstrate that the functional form of the likelihood contains a sufficient amount of information for constructing a prior for the unknown parameters. We develop a four-step algorithm by invoking the information entropy as the measure of uncertainty and show how the information gained from coarse-graining and resolving power of the likelihood can be used to construct the likelihood-induced priors. As a consequence, we show that if the data model density belongs to the exponential family, the likelihood-induced prior is the conjugate prior to the corresponding likelihood.