Title: Nonparametric statistical learning with Markov jump processes 

Speaker: Ioannis Sgouralis, UTK

Abstract:  Markov Jump Processes are an important example of continuous-time dynamical systems that, although simple enough, allow for a faithful representation of many problems in the Sciences and Engineering. Traditionally, mathematical representation with Markov Jump Processes have been used for simulation purposes with profound bearing in the Doob-Gillespie algorithm and chief applications, among others, in the domains of Chemistry and Biotechnology. Recently, statistical models with Markov Jump Processes such as Hidden Markov Jump Process, Markov Modulated Poisson Processes, or Continuous-time Bayesian Networks have also been incorporated for inference purposes and the solution of inverse problems. In this talk, I will present the basics of Markov Jump Processes and investigate the sampling problem from their posterior probability distribution given partial or corrupted data without approximations or simplifying assumptions based on time-discretization. I will use uniformization to develop a Gibbs sampler that may be added as an integral component in larger frameworks for comprehensive Statistical Learning. My talk will focus on students and requires no advanced background in either Statistics or Probability.