Κατεύθυνση Στατιστική και Επιχειρησιακή Έρευνα
Library of the School of Science

2023-10-11

2023

Machera Kalliopi

Τρέβεζας Σάμης, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών ΕΚΠΑ

Bayesian beta-Stacy non-parametric semi-Markov models

English

Bayesian beta-Stacy non-parametric semi-Markov models

This thesis explores the properties and applications of the Dirichlet distribution, which is a multivariate continuous distribution that generalizes the Beta distribution. It discusses three different methods for generating random variables with a Dirichlet distribution and shows its importance as a conjugate prior for the Multinomial distribution in Bayesian statistics. Additionally, this thesis introduces the Dirichlet process and its relationship with the Dirichlet distribution.

The thesis also introduces the beta-Stacy process as a non-parametric prior for the Bayesian analysis of semi-Markov models. It examines the conjugacy property of this process with respect to the observation of one or more processes for a fixed time, and characterizes it using a reinforced urn process. Moreover, the thesis provides a comprehensive understanding of discrete-time semi-Markov processes and their estimation methods using observed trajectory. It focuses on the empirical and exact maximum likelihood estimators for the semi-Markov kernel based on a single observed trajectory and examines the asymptotic properties of these estimators.

Overall, this thesis provides a thorough investigation of the Dirichlet distribution and its applications in Bayesian statistics and stochastic processes. It presents a novel approach using the beta-Stacy process and a reinforced urn process to characterize the Bayesian analysis of Semi-Markov models.

Science

beta-Stacy, non-parametric, Bayesian, semi-Markov, Dirichlet process, Dirichlet distribution

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https://pergamos.lib.uoa.gr/uoa/dl/object/3360604