Course Description: Review of various results about Markov chains on general (non-countable) state spaces and Markov chain Monte Carlo (MCMC) algorithms.
References:
- Probability Surveys Vol. 1 (2004) 20–71 ISSN: 1549-5787 DOI: 10.1214/154957804100000024
- General state space Markov chains and MCMC algorithms by Gareth Roberts and Jeffery Rosenthal
Course Outcome:
- Sufficient conditions for geometric and uniform ergodicity are presented, along with quantitative bounds on the rate of convergence to stationarity.
- Necessary and sufficient conditions for Central Limit Theorems (CLTs) proved via the Poisson Equation or direct regeneration constructions.
- Optimal scaling and weak convergence results for Metropolis-Hastings algorithms
- Teacher: Siva Athreya
Credit Score: 4