arkab-ds / mth598a

Confidence Interval for Asymptotic Variance Estimation in Adaptive Markov Chain Monte Carlo

MTH598A

This repo is for the course MTH598A: M.Sc. Project-I during the academic session 2021-2022 (odd semester) at IIT Kanpur.

Project Title:

Understanding Confidence Intervals in Adaptive Markov Chain Monte Carlo [Report]

Project Supervisor:

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

Report Contents:

Section	Topic
1	Introduction
2	Ergodicity 2.1 Sufficient Conditions for Ergodicity in AMCMC
3	Asymptotic Variance Estimation
4	Main Results 4.1 Setup and nontations 4.2 Assumptions 4.3 Theorems
5	Examples 5.1 Univariate Standard Normal 5.2 Multivariate Logistic Regression
6	Conclusion
7	Supplementary Material
8	Acknowledgements

Key References:

1. ADAPTIVE MARKOV CHAIN MONTE CARLO CONFIDENCE INTERVALS - YF Atchade
2. Kernel estimators of asymptotic variance for adaptive Markov chain Monte Carlo - Yves F. Atchade
3. Examples of adaptive MCMC - GO Roberts, JS Rosenthal
4. Coupling and ergodicity of adaptive Markov chain Monte Carlo algorithms - GO Roberts, JS Rosenthal
5. On adaptive markov chain monte carlo algorithms - YF Atchade, JS Rosenthal