Tata Institute of Fundamental Research
Diffusion Approximation to Adaptive MCMC
Seminar
Speaker:
Gopal Basak (Indian Statistical Institute
Department of Statistics and Mathematics
203, Barrackpore Trunk Road
Kolkata 700108)
Organiser:
Sandeep K Juneja
Date:
Tuesday, 4 Mar 2014, 11:30 to 12:30
Venue:
AG-80
(Scan to add to calendar)
Abstract:
Abstract: Adaptive MCMC algorithms are designed to tune the chain properly to decrease the time to convergence to stationary. However since the transition kernel is changed at each step of iteration proper ergodicity conditions has to be ensured. Here we define a discrete time Adaptive MCMC algorithm and study its convergence properties. We apply the diffusion approximation method to a discrete time Adaptive MCMC procedure to obtain the limiting stochastic differential equation governing the dynamics of the adaptation parameter $\theta$ and the state space variable $X$. The solution to the coupled equation will give the stationary distribution of the chain. Comparison of rates of convergence between the standard and the adaptive method will be of interest.
| Speaker: | Gopal Basak (Indian Statistical Institute Department of Statistics and Mathematics 203, Barrackpore Trunk Road Kolkata 700108) |
| Organiser: | Sandeep K Juneja |
| Date: | Tuesday, 4 Mar 2014, 11:30 to 12:30 |
| Venue: | AG-80 |
(Scan to add to calendar)
Abstract:
Abstract: Adaptive MCMC algorithms are designed to tune the chain properly to decrease the time to convergence to stationary. However since the transition kernel is changed at each step of iteration proper ergodicity conditions has to be ensured. Here we define a discrete time Adaptive MCMC algorithm and study its convergence properties. We apply the diffusion approximation method to a discrete time Adaptive MCMC procedure to obtain the limiting stochastic differential equation governing the dynamics of the adaptation parameter $\theta$ and the state space variable $X$. The solution to the coupled equation will give the stationary distribution of the chain. Comparison of rates of convergence between the standard and the adaptive method will be of interest.