On August 25 at 14.15 Joonas Sova will defend his doctoral dissertation "Pairwise Markov Models" for obtaining the degree of Doctor of Philosophy (Mathematics).
Professor Jüri Lember, University of Tartu
Professor Pavel Chigansky, The Hebrew University of Jerusalem (Israel)
Professor Evgeny Verbitskiy, Leiden University (Netherlands)
Latent variable Markovian models are a great success story of modern statistics. Nowadays there is increasing prevalence of data where the classic assumptions of statistics, such as independence and equal distribution of observations, cannot be assumed, and so the classic statistical methodologies fail to be effective. In contrast, the latent variable Markovian models offer a wide range of highly adaptable methodologies for analyzing complex inter-dependent data. This thesis investigates a wide class of such models, namely the “pairwise Markov model” (PMM). PMM is simply any model for which the hidden or latent layer and the observed layer both together constitute a Markov chain. As such, the PMM encompasses a wide range of models, but among them the most notable and most frequently applied in practice is certainly the hidden Markov model. This latter model is a special case of the PMM in which case the observations depend on each other only through the hidden layer.
This thesis is an overview of three papers, all of which deal with some aspects of the PMM. Oftentimes the goal of applying a PMM is to estimate the hidden layer based on the observations. Probably the most popular method for this is the famous Viterbi algorithm, which will find with linear time the maximum likelihood estimate for the hidden path. This estimate is known as the “Viterbi path” (also Viterbi alignment). The Viterbi path maximizes the probability that the estimation of the whole hidden path is correct. At the same time the Viterbi path does not generally maximize the average number of the correctly estimated states (this is done by the so-called “pointwise a posteriori estimate”).
Zoom Meeting: https://ut-ee.zoom.us/j/93234060711?pwd=dU94dnVoam9VVC9aOVF6UTVWaER4UT09
Meeting ID: 932 3406 0711