Lecture Series on Branching Processes and Markov Chain Monte Carlo (MCMC).

Speaker: Prof. Krishna B. Athreya  

Date: 15 to 19 July 2019 

Time: 4:00 to 5:00 PM (Everyday) 

Abstract: There will be three talks on Branching processes(BP) and two talks on MCMC.
Talk 1 (BP) : Definition of (Bienyeme- Galton- Watson)BGW processes Single type case, extinction probability,
subcritical, critical and supercritical cases with Yaglom, Kolmogorov, Kesten -Stigum theorems.
 
Talk 2 (BP) : Definition of BGW processes multitype case, extinction probability Application of Perron Frobenius theorem for nonnegative matrices to the sub-critical, critical and super-critical cases with Yaglom, Kolmogorov and Kesten and Stigum theorems.
Talk 3 (BP) : Definition of Continuous time BGW processes age-dependent branching processes, the embedding of Polya Urn scheme using finite type BGW processes with exponential lifetimes.
Talk 4 (MCMC) : The Metropolis, Rosenblath, etc paper leading to MCMC. The IID case, The case of a target probability measure, the Bayesian case. The infinite measure case via regenerative stochastic processes.
Talk 5 (MCMC) : The Metropolis-Hastings algorithm, the independent case and the random walk case. The Gibbs sampler.
 
About the Speaker: 
Prof. Krishna B. Athreya has been working as a Professor Emeritus at the Iowa State University since 2014 and a Distinguished Professor at the College of Liberal Arts and Sciences, Iowa State University since 1997. He worked as a Professor in the Department of Mathematics and Statistics, Iowa State University, Ames, Iowa, USA between 1980 and 2014 and the Department of Mathematics, Indian Institute of Science (IISc), Bangalore, India between 1971 and 1979. Before this, he worked as a Lecturer in the Department of Mathematics, Stanford University from 1967 to 1968 and as an Assistant Professor in the Department of Mathematics, University of Wisconsin, Madison from 1968 to 1971. In his long academic life, he has published more than 200 research papers in respectable mathematics and statistics international journals. He has written two books both by Springer-Verlag, Germany namely Branching Processes (jointly with Peter Ney, 1971) and Measure Theory and Probability Theory (jointly with Soumen Lahiri, 2006). He completed his PhD degree (Math) from Stanford University in 1967, his two year advanced statistical course from Indian Statistical Institute (ISI) Calcutta in 1961 and his BA (Hons) in Mathematics from Loyola College, Madras University in 1959. He has supervised more than 25 research students-five of them at IISc and more than 20 at Iowa State University. He is an internationally renowned researcher in the fields of Branching processes and MCMC.