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Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics

Part of the SpringerBriefs in Statistics Book Series

DOI: 10.1007/978-4-431-55888-0

ISBN: 978-4-431-55886-6

Publisher: Springer Japan - Springer Journals

Jul 13, 2018

Available

Introduction

Mano, Shuhei

Pages: 1 –9

[Partitions appear in various statistical problems. Moreover, stochastic modeling of partitions naturally assumes the exchangeability. This chapter introduces this monograph by providing minimum definitions and terminologies related to partitions and exchangeability. To illustrate the content of...
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Measures on Partitions

Mano, Shuhei

Pages: 11 –43

[After brief introduction of the multiplicative measure, defined as a family of measures on integer partitions, which include typical combinatorial structures, this chapter introduces the exponential structure, which plays important roles in statistical inference. It then introduces the Gibbs...
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A-Hypergeometric Systems

Mano, Shuhei

Pages: 45 –70

[This chapter introduces the A-hypergeometric system of linear partial differential equations. It presents the known results of the A-hypergeometric system with a two-row matrix A and explains its relationship with integer partitions. The A-hypergeometric distribution is a class of discrete...
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Dirichlet Processes

Mano, Shuhei

Pages: 71 –103

[After preparing some basic facts in probability theory, this chapter introduces de Finetti’s representation theorem. We, then, introduce the Dirichlet process and the Poisson–Dirichlet distribution, which are closely related to exchangeability. We discuss two constructions of the Dirichlet...
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Methods for Inferences

Mano, Shuhei

Pages: 105 –122

[This chapter introduces inference methods based on the models presented in previous chapters. We discuss samplers, which are required for hypothesis testing and posterior sampling. After a brief introduction of Markov chain Monte Carlo (MCMC) samplers from A-hypergeometric distributions...

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