Adaptive-MCMC

This repository is for a group project for the course MTH707A: Markov Chain Monte Carlo during the academic session 2021-2022 (even semester) at IIT Kanpur.

Group Memebers :

1. Aritra Majumdar
2. Arkajyoti Bhattacharjee
3. Sanket Agrawal

Title :

Adaptive Markov chain Monte Carlo: A Review [Report]

Guide :

Prof. Dootika Vats, Department of Mathematics and Statistics, IIT Kanpur

Abstract:

We briefly review the adaptive Markov chain Monte Carlo techniques using some examples. We also talk about the theoretical properties like stationarity and ergodicity of such algorithms.

Report Outline :

Section	Topic
1	Introduction
2	Setup and Notation
3	Examples Adaptive Metropolis algorithm A banana-shaped distribution Adaptive Metropolis within Gibbs algorithm
4	Ergodicity
5	Conclusions

Directory :

• Code : Contains relevant code for generating plots in the report
• Plots : Contains plots

Key References:

• Examples of Adaptive MCMC - Gareth O. Roberts, Jeffrey S. Rosenthal
• Coupling and Ergodicity of Adaptive MCMC algorithms - Gareth O. Roberts, Jeffrey S. Rosenthal
• Optimal Proposal Distributions and Adaptive MCMC - Jeffrey Rosenthal
• Adaptive Markov chain Monte Carlo: Theory and Methods - Yves Atchade, Gersende Fort and Eric Moulines, Pierre Priouret
• An Adaptive Metropolis Algorithm - Harrio et al.

Other useful resources

• Optimal Scaling and Adaptive Markov Chain Monte Carlo - Krzysztof Latuszynski (Slides)
• Adaptive MCMC for Everyone - Jeffrey J. Rosenthal