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Author: Peter Guttorp Publisher: Wiley-Interscience ISBN: Category : Mathematics Languages : en Pages : 232
Book Description
An examination of the difficulties that statistical theory and, in particular, estimation theory can encounter within the area of dependent data. This is achieved through the study of the theory of branching processes starting with the demographic question: what is the probability that a family name becomes extinct? Contains observations on the generation sizes of the Bienaymé-Galton-Watson (BGW) process. Various parameters are estimated and branching process theory is contrasted to a Bayesian approach. Illustrations of branching process theory applications are shown for particular problems.
Author: Peter Guttorp Publisher: Wiley-Interscience ISBN: Category : Mathematics Languages : en Pages : 232
Book Description
An examination of the difficulties that statistical theory and, in particular, estimation theory can encounter within the area of dependent data. This is achieved through the study of the theory of branching processes starting with the demographic question: what is the probability that a family name becomes extinct? Contains observations on the generation sizes of the Bienaymé-Galton-Watson (BGW) process. Various parameters are estimated and branching process theory is contrasted to a Bayesian approach. Illustrations of branching process theory applications are shown for particular problems.
Author: Tom Britton Publisher: Springer Nature ISBN: 3030309002 Category : Mathematics Languages : en Pages : 477
Book Description
Focussing on stochastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on "Stochastic models of epidemics" which took place in Ziguinchor, Senegal, December 5–16, 2015. The text is divided into four parts, each based on one of the courses given at the school: homogeneous models (Tom Britton and Etienne Pardoux), two-level mixing models (David Sirl and Frank Ball), epidemics on graphs (Viet Chi Tran), and statistics for epidemic models (Catherine Larédo). The CIMPA school was aimed at PhD students and Post Docs in the mathematical sciences. Parts (or all) of this book can be used as the basis for traditional or individual reading courses on the topic. For this reason, examples and exercises (some with solutions) are provided throughout.
Author: Miguel González Velasco Publisher: John Wiley & Sons ISBN: 1119484561 Category : Mathematics Languages : en Pages : 215
Book Description
The purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reproduction is a fundamental assumption in the classical branching processes. Alternatively, the controlled branching processes (CBPs) allow the number of reproductive individuals in one generation to decrease or increase depending on the size of the previous generation. Generating a wide range of behaviors, the CBPs have been successfully used as modeling tools in diverse areas of applications.
Author: Romain Azais Publisher: John Wiley & Sons ISBN: 1786303027 Category : Mathematics Languages : en Pages : 300
Book Description
Piecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications: biology, insurance, neuroscience, networks, finance... Such processes are defined by a deterministic motion punctuated by random jumps at random times, and offer simple yet challenging models to study. Nevertheless, the issue of statistical estimation of the parameters ruling the jump mechanism is far from trivial. Responding to new developments in the field as well as to current research interests and needs, Statistical inference for piecewise-deterministic Markov processes offers a detailed and comprehensive survey of state-of-the-art results. It covers a wide range of general processes as well as applied models. The present book also dwells on statistics in the context of Markov chains, since piecewise-deterministic Markov processes are characterized by an embedded Markov chain corresponding to the position of the process right after the jumps.
Author: Miguel González Velasco Publisher: John Wiley & Sons ISBN: 1786302535 Category : Mathematics Languages : en Pages : 240
Book Description
The purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reproduction is a fundamental assumption in the classical branching processes. Alternatively, the controlled branching processes (CBPs) allow the number of reproductive individuals in one generation to decrease or increase depending on the size of the previous generation. Generating a wide range of behaviors, the CBPs have been successfully used as modeling tools in diverse areas of applications.
Author: Peter Olofsson Publisher: John Wiley & Sons ISBN: 0470889748 Category : Mathematics Languages : en Pages : 573
Book Description
Praise for the First Edition ". . . an excellent textbook . . . well organized and neatly written." —Mathematical Reviews ". . . amazingly interesting . . ." —Technometrics Thoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, Probability, Statistics, and Stochastic Processes, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields. Beginning with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions, the book goes on to present limit theorems and simulation. The authors combine a rigorous, calculus-based development of theory with an intuitive approach that appeals to readers' sense of reason and logic. Including more than 400 examples that help illustrate concepts and theory, the Second Edition features new material on statistical inference and a wealth of newly added topics, including: Consistency of point estimators Large sample theory Bootstrap simulation Multiple hypothesis testing Fisher's exact test and Kolmogorov-Smirnov test Martingales, renewal processes, and Brownian motion One-way analysis of variance and the general linear model Extensively class-tested to ensure an accessible presentation, Probability, Statistics, and Stochastic Processes, Second Edition is an excellent book for courses on probability and statistics at the upper-undergraduate level. The book is also an ideal resource for scientists and engineers in the fields of statistics, mathematics, industrial management, and engineering.
Author: Götz Kersting Publisher: John Wiley & Sons ISBN: 1786302527 Category : Mathematics Languages : en Pages : 306
Book Description
Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that the conditions of reproduction may vary in a random fashion from one generation to the next. This book offers an introduction to the basics of BPREs and then presents the cases of critical and subcritical processes in detail, the latter dividing into weakly, intermediate, and strongly subcritical regimes.
Author: Narahari Umanath Prabhu Publisher: American Mathematical Soc. ISBN: 0821850873 Category : Mathematics Languages : en Pages : 406
Book Description
Comprises the proceedings of the AMS-IMS-SIAM Summer Research Conference on Statistical Inference from Stochastic Processes, held at Cornell University in August 1987. This book provides students and researchers with a familiarity with the foundations of inference from stochastic processes and intends to provide a knowledge of the developments.
Author: Peter Guttorp
Author: Peter Guttorp
Author: Tom Britton
Author: Ishwar V. Basawa
Author: Miguel González Velasco
Author: Romain Azais
Author: Miguel González Velasco
Author: Patsy Haccou
Author: Peter Olofsson
Author: Götz Kersting
Author: Narahari Umanath Prabhu