TY - GEN

T1 - On the use of Markovian stick-breaking priors

AU - Lippitt, William

AU - Sethuraman, Sunder

N1 - Funding Information: This research was partly supported by ARO-W911NF-18-1-0311 and a Simons Foundations Sabbatical grant. Publisher Copyright: © 2021 American Mathematical Society.

PY - 2021

Y1 - 2021

N2 - 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≥1PiδTi 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.

AB - 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≥1PiδTi 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.

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U2 - 10.1090/conm/774/15571

DO - 10.1090/conm/774/15571

M3 - Conference contribution

SN - 9781470459826

T3 - Contemporary Mathematics

SP - 153

EP - 174

BT - Stochastic Processes and Functional Analysis New Perspectives

A2 - Swift, Randall J.

A2 - Krinik, Alan

A2 - Switkes, Jennifer M.

A2 - Park, Jason H.

PB - American Mathematical Society

T2 - AMS Special Session Celebrating M.M. Rao’s Many Mathematical Contributions as he Turns 90 Years Old, 2019

Y2 - 9 November 2019 through 10 November 2019

ER -