Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics
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Tokyo : : Springer Japan : Imprint: Springer,,
2018

Edition:  1st ed. 2018. 
Series:  JSS Research Series in Statistics,, ISSN 23640057 
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Online Access:  https://doi.org/10.1007/9784431558880 
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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 szövegfájl PDF rda JSS Research Series in Statistics, 23640057 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 Ahypergeometric distribution is a class of discrete exponential families and appears as the conditional distribution of a multinomial sample from logaffine models. The normalizing constant is the Ahypergeometric polynomial, which is a solution of a system of linear differential equations of multiple variables determined by a matrix A, called Ahypergeometric system. The book presents inference methods based on the algebraic nature of the Ahypergeometric 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 Ahypergeometric distribution, as well as the maximum likelihood estimation of the Ahypergeometric distribution of tworow 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 ekönyvek a teljes ELTE IPtartományon belül online elérhetők. könyv ebook 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/10.1007/9784431558880 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 23640057 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 23640057 
series2 
JSS Research Series in Statistics, 
publishDate 
2018 
publishDateSort 
2018 
physical 
VIII, 135 p. 9 illus. : online forrás 
edition 
1st ed. 2018. 
isbn 
9784431558880 
issn 
23640057 
callnumberfirst 
Q  Science 
callnumbersubject 
QA  Mathematics 
callnumberlabel 
QA276280 
callnumberraw 
979837 
callnumbersearch 
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/10.1007/9784431558880 
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Not Illustrated 
deweyhundreds 
500  Science 
deweytens 
510  Mathematics 
deweyones 
519  Probabilities & applied mathematics 
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519.5 
deweysort 
3519.5 
deweyraw 
519.5 
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519.5 
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20220213T19:57:24Z 
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Tokyo : : Springer Japan : Imprint: Springer, 
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1726986597170151425 
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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 Ahypergeometric distribution is a class of discrete exponential families and appears as the conditional distribution of a multinomial sample from logaffine models. The normalizing constant is the Ahypergeometric polynomial, which is a solution of a system of linear differential equations of multiple variables determined by a matrix A, called Ahypergeometric system. The book presents inference methods based on the algebraic nature of the Ahypergeometric 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 Ahypergeometric distribution, as well as the maximum likelihood estimation of the Ahypergeometric distribution of tworow 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. 