Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics

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Language:English
Published: Tokyo : : Springer Japan : Imprint: Springer,, 2018
Edition:1st ed. 2018.
Series:JSS Research Series in Statistics,, ISSN 2364-0057
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Online Access:https://doi.org/10.1007/978-4-431-55888-0
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id opac-EUL01-000979837
collection e-book
institution L_200
EUL01
spelling Mano, Shuhei. szerző aut http://id.loc.gov/vocabulary/relators/aut
Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics by Shuhei Mano.
1st ed. 2018.
Tokyo : Springer Japan : Imprint: Springer, 2018
VIII, 135 p. 9 illus. online forrás
szöveg txt rdacontent
számítógépes c rdamedia
távoli hozzáférés cr rdacarrier
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JSS Research Series in Statistics, 2364-0057
This book focuses on statistical inferences related to various combinatorial stochastic processes. Specifically, it discusses the intersection of three subjects that are generally studied independently of each other: partitions, hypergeometric systems, and Dirichlet processes. The Gibbs partition is a family of measures on integer partition, and several prior processes, such as the Dirichlet process, naturally appear in connection with infinite exchangeable Gibbs partitions. Examples include the distribution on a contingency table with fixed marginal sums and the conditional distribution of Gibbs partition given the length. The A-hypergeometric distribution is a class of discrete exponential families and appears as the conditional distribution of a multinomial sample from log-affine models. The normalizing constant is the A-hypergeometric polynomial, which is a solution of a system of linear differential equations of multiple variables determined by a matrix A, called A-hypergeometric system. The book presents inference methods based on the algebraic nature of the A-hypergeometric system, and introduces the holonomic gradient methods, which numerically solve holonomic systems without combinatorial enumeration, to compute the normalizing constant. Furher, it discusses Markov chain Monte Carlo and direct samplers from A-hypergeometric distribution, as well as the maximum likelihood estimation of the A-hypergeometric distribution of two-row matrix using properties of polytopes and information geometry. The topics discussed are simple problems, but the interdisciplinary approach of this book appeals to a wide audience with an interest in statistical inference on combinatorial stochastic processes, including statisticians who are developing statistical theories and methodologies, mathematicians wanting to discover applications of their theoretical results, and researchers working in various fields of data sciences.
Nyomtatott kiadás: ISBN 9784431558866
Nyomtatott kiadás: ISBN 9784431558873
Az e-könyvek a teljes ELTE IP-tartományon belül online elérhetők.
könyv
e-book
Mathematical statistics.
Statistics.
Statistical Theory and Methods.
Statistics and Computing/Statistics Programs.
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
elektronikus könyv
SpringerLink (Online service) közreadó testület
Online változat https://doi.org/10.1007/978-4-431-55888-0
EUL01
language English
format Book
author Mano, Shuhei., szerző
spellingShingle Mano, Shuhei., szerző
Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics
JSS Research Series in Statistics,, ISSN 2364-0057
Mathematical statistics.
Statistics.
Statistical Theory and Methods.
Statistics and Computing/Statistics Programs.
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
elektronikus könyv
author_facet Mano, Shuhei., szerző
SpringerLink (Online service)
author_corporate SpringerLink (Online service)
author_sort Mano, Shuhei.
title Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics
title_short Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics
title_full Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics by Shuhei Mano.
title_fullStr Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics by Shuhei Mano.
title_full_unstemmed Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics by Shuhei Mano.
title_auth Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics
title_sort partitions hypergeometric systems and dirichlet processes in statistics
series JSS Research Series in Statistics,, ISSN 2364-0057
series2 JSS Research Series in Statistics,
publishDate 2018
publishDateSort 2018
physical VIII, 135 p. 9 illus. : online forrás
edition 1st ed. 2018.
isbn 978-4-431-55888-0
issn 2364-0057
callnumber-first Q - Science
callnumber-subject QA - Mathematics
callnumber-label QA276-280
callnumber-raw 979837
callnumber-search 979837
topic Mathematical statistics.
Statistics.
Statistical Theory and Methods.
Statistics and Computing/Statistics Programs.
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
elektronikus könyv
topic_facet Mathematical statistics.
Statistics.
Statistical Theory and Methods.
Statistics and Computing/Statistics Programs.
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
elektronikus könyv
Mathematical statistics.
Statistics.
Statistical Theory and Methods.
Statistics and Computing/Statistics Programs.
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
url https://doi.org/10.1007/978-4-431-55888-0
illustrated Not Illustrated
dewey-hundreds 500 - Science
dewey-tens 510 - Mathematics
dewey-ones 519 - Probabilities & applied mathematics
dewey-full 519.5
dewey-sort 3519.5
dewey-raw 519.5
dewey-search 519.5
first_indexed 2022-02-13T19:57:24Z
last_indexed 2022-03-11T08:12:42Z
recordtype opac
publisher Tokyo : : Springer Japan : Imprint: Springer,
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score 13,338533
generalnotes This book focuses on statistical inferences related to various combinatorial stochastic processes. Specifically, it discusses the intersection of three subjects that are generally studied independently of each other: partitions, hypergeometric systems, and Dirichlet processes. The Gibbs partition is a family of measures on integer partition, and several prior processes, such as the Dirichlet process, naturally appear in connection with infinite exchangeable Gibbs partitions. Examples include the distribution on a contingency table with fixed marginal sums and the conditional distribution of Gibbs partition given the length. The A-hypergeometric distribution is a class of discrete exponential families and appears as the conditional distribution of a multinomial sample from log-affine models. The normalizing constant is the A-hypergeometric polynomial, which is a solution of a system of linear differential equations of multiple variables determined by a matrix A, called A-hypergeometric system. The book presents inference methods based on the algebraic nature of the A-hypergeometric system, and introduces the holonomic gradient methods, which numerically solve holonomic systems without combinatorial enumeration, to compute the normalizing constant. Furher, it discusses Markov chain Monte Carlo and direct samplers from A-hypergeometric distribution, as well as the maximum likelihood estimation of the A-hypergeometric distribution of two-row matrix using properties of polytopes and information geometry. The topics discussed are simple problems, but the interdisciplinary approach of this book appeals to a wide audience with an interest in statistical inference on combinatorial stochastic processes, including statisticians who are developing statistical theories and methodologies, mathematicians wanting to discover applications of their theoretical results, and researchers working in various fields of data sciences.