BayesProj

This repo contains the codes, images, report and slides for the project of the course - MTH535A: An Introduction To Bayesian Analysis at IIT Kanpur during the academic year 2022-2023.

Project Members

• Arkajyoti Bhattacharjee
• Devyanshi Singh
• Dhruvil Sangani
• Nitin Garg
• Rishabh Gupta

Project Title

Bernoulli factory based Portkey and Flipped Portkey MCMC Algorithms: Theory and Examples [Slides] [Report]

Abstract

In this report, we present two stable Bernoulli factories that generate events within those class of acceptance probabilities which do not involve the ratio of intractable target (posterior) distribution evaluated at two points. The efficiency of the methods rely on obtaining a reasonable lower and upper bound on the target density and we present examples were such bounds are viable. The report is primarily based on [1].

Table of Contents

Section	Topic
1	Introduction
2	Barker's method and the 2-coin algorithm
3	Portkey Barker's Method
4	Flipped portkey two-coin algorithm
5	Examples 5.1 Gamma mixture of Weibulls 5.2 MCMC on constrained spaces 5.3 Bayesian inference for the Wright-Fisher diffusion

Repo Directories

1. Data: Contains the saved data files.
2. R Codes: Contains the R codes to replicate the figures in the report and slides.
3. figures: Contains the figures present in our report adn slides.

Primary Reference

[1]. Vats, D., Gonçalves, F. B., Łatuszyński, K., & Roberts, G. O. (2021). Efficient Bernoulli factory Markov chain Monte Carlo for intractable posteriors. Biometrika.