On the use of Markovian stick-breaking priors

William Lippitt, Sunder Sethuraman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Recently, a ‘Markovian stick-breaking’ process which generalizes the Dirichlet process (μ, θ) with respect to a discrete base space X was introduced. In particular, a sample from from the ‘Markovian stick-breaking’ processs may be represented in stick-breaking form i≥1PTi where {Ti } is a stationary, irreducible Markov chain on X with stationary distribution μ, instead of i.i.d. {Ti } each distributed as μ as in the Dirichlet case, and {Pi } is a GEM(θ) residual allocation sequence. Although the previous motivation was to relate these Markovian stick-breaking processes to empirical distribu-tional limits of types of simulated annealing chains, these processes may also be thought of as a class of priors in statistical problems. The aim of this work in this context is to identify the posterior distribution and to explore the role of the Markovian structure of {Ti } in some inference test cases.

Original languageEnglish (US)
Title of host publicationStochastic Processes and Functional Analysis New Perspectives
EditorsRandall J. Swift, Alan Krinik, Jennifer M. Switkes, Jason H. Park
PublisherAmerican Mathematical Society
Pages153-174
Number of pages22
ISBN (Print)9781470459826
DOIs
StatePublished - 2021
EventAMS Special Session Celebrating M.M. Rao’s Many Mathematical Contributions as he Turns 90 Years Old, 2019 - Riverside, United States
Duration: Nov 9 2019Nov 10 2019

Publication series

NameContemporary Mathematics
Volume774
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Conference

ConferenceAMS Special Session Celebrating M.M. Rao’s Many Mathematical Contributions as he Turns 90 Years Old, 2019
Country/TerritoryUnited States
CityRiverside
Period11/9/1911/10/19

ASJC Scopus subject areas

  • Mathematics(all)

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