Autor: Ivan Nagy
ISBN-13: 9783319646701
Veröffentl: 01.09.2017
Einband: Book
Seiten: 113
Gewicht: 214 g
Format: 238x154x10 mm
Sprache: Englisch

Algorithms and Programs of Dynamic Mixture Estimation

SpringerBriefs in Statistics
Unified Approach to Different Types of Components
 Book
Sofort lieferbar | * inkl. MwSt ggf. zzgl. Versandkosten
99
1 Introduction 7 1.1 On dynamic mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 General conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Basic Models 13 2.1 Regression model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.2 Point estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.3 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Categorical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.2 Point estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.3 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 State-space model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.1 State estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3 Statistical Analysis of Dynamic Mixtures 21 3.1 Dynamic mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Unified approach to mixture estimation . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.1 The component part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.2 The pointer part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.3 Main subtasks of mixture estimation . . . . . . . . . . . . . . . . . . . . . 23 3.2.4 General algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3 Mixture prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3.1 Pointer prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3.2 Data prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4 Dynamic Mixture Estimation 29 4.1 Normal regression components . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.1.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.1.2 Simple program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.1.3 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.2 Categorical components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.2.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2.2 Simple program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.2.3 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.3 State-space components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.3.1 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.3.2 Simple program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.3.3 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5 Program Codes 43 5.1 Main program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.1.1 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.2 Subroutines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.2.1 Initialization of estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.2.2 Computation of proximities . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.2.3 Update of component statistics . . . . . . . . . . . . . . . . . . . . . . . . 52 5.3 Collection of programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6 Experiments 55 6.1 Mixture with regression components . . . . . . . . . . . . . . . . . . . . . . . . . 56 6.1.1 Well separated components . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.1.
This book provides a general theoretical background for constructing the recursive Bayesian estimation algorithms for mixture models. It collects the recursive algorithms for estimating dynamic mixtures of various distributions and brings them in the unified form, providing a scheme for constructing the estimation algorithm for a mixture of components modeled by distributions with reproducible statistics. It offers the recursive estimation of dynamic mixtures, which are free of iterative processes and close to analytical solutions as much as possible. In addition, these methods can be used online and simultaneously perform learning, which improves their efficiency during estimation. The book includes detailed program codes for solving the presented theoretical tasks. Codes are implemented in the open source platform for engineering computations. The program codes given serve to illustrate the theory and demonstrate the work of the included algorithms.
Autor: Ivan Nagy, Evgenia Suzdaleva
Doc. Ing. Ivan Nagy, CSc. (Ph.D.), born 1956 in Prague, Czech Republic, received his CSc. (Ph.D.) in cybernetics from UTIA, Prague in 1983. In 1980, he started working as a researcher at the Institute of Information Theory and Automation of the Czech Academy of Sciences. Since 1998, he has also been a lecturer at the Czech Technical University Faculty of Transportation Sciences in Prague.
Ing. Evgenia Suzdaleva, CSc. (Ph.D.), born 1977 in Krasnoyarsk, Russia, obtained her CSc. (Ph.D.) in 2002 in system analysis at the Siberian State Aerospace University, Krasnoyarsk, Russia. Since 2004, she has been a researcher at the Institute of Information Theory and Automation at the Czech Academy of Sciences. At the same time, she works as a lecturer at the Czech Technical University Faculty of Transportation Sciences in Prague.

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Autor: Ivan Nagy
ISBN-13:: 9783319646701
ISBN: 3319646702
Erscheinungsjahr: 01.09.2017
Verlag: Springer-Verlag GmbH
Gewicht: 214g
Seiten: 113
Sprache: Englisch
Sonstiges: Taschenbuch, 238x154x10 mm, 27 farbige Abbildungen, Bibliographie