Computational Methods in Bayesian Statistics

TL;DR

This paper compares Variational Bayesian and Nested Sampling methods on toy data analysis problems, highlighting speed and accuracy differences in polynomial selection and Gaussian Mixture Models.

Contribution

It demonstrates the application and comparison of two Bayesian computational methods on specific toy problems, emphasizing their performance differences.

Findings

Variational Bayesian is faster than Nested Sampling.

Both methods yield similar accuracy in results.

The study provides insights into method selection for toy problems.

Abstract

This paper focuses on utilizing two different Bayesian methods to deal with a variety of toy problems which occur in data analysis. In particular we implement the Variational Bayesian and Nested Sampling methods to tackle the problems of polynomial selection and Gaussian Mixture Models, comparing the algorithms in terms of processing speed and accuracy. In the problems tackled here it is the Variational Bayesian algorithms which are the faster though both results give similar results.