A Random Weighting Approach for Posterior Distributions

TL;DR

This paper introduces a novel random weighting method for approximating posterior distributions in Bayesian analysis, providing theoretical guarantees on convergence speed to improve numerical simulation accuracy.

Contribution

It proposes an alternative to asymptotic expansions, offering a new approach with proven convergence properties for scaled posterior distributions.

Findings

The method achieves ideal convergence speed.

It provides a theoretical guarantee for numerical simulations.

Applicable to scaled posterior distributions.

Abstract

In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic expansions for posterior distributions. In this paper, we propose an alternative method, named random weighting method, for scaled posterior distributions, and give an ideal convergence speed, which serves as the theoretical guarantee for methods of numerical simulations.