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Author: Peter Guttorp
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 232
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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
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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
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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: Ishwar V. Basawa
Publisher: Elsevier
ISBN: 1483296148
Category : Mathematics
Languages : en
Pages : 455
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Book Description
Stats Inference Stochasic Process
Author: Ishwar V. Basawa
Publisher: Academic Press
ISBN:
Category : Mathematics
Languages : en
Pages : 464
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Book Description
Introductory examples of stochastic models; Special models; General theory; Further approaches.
Author: Miguel González Velasco
Publisher: John Wiley & Sons
ISBN: 1119484561
Category : Mathematics
Languages : en
Pages : 215
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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
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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: Asmussen
Publisher: Springer Science & Business Media
ISBN: 1461581559
Category : Mathematics
Languages : en
Pages : 468
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Book Description
Branching processes form one of the classical fields of applied probability and are still an active area of research. The field has by now grown so large and diverse that a complete and unified treat ment is hardly possible anymore, let alone in one volume. So, our aim here has been to single out some of the more recent developments and to present them with sufficient background material to obtain a largely self-contained treatment intended to supplement previous mo nographs rather than to overlap them. The body of the text is divided into four parts, each of its own flavor. Part A is a short introduction, stressing examples and applications. In Part B we give a self-contained and up-to-date pre sentation of the classical limit theory of simple branching processes, viz. the Gal ton-Watson ( Bienayme-G-W) process and i ts continuous time analogue. Part C deals with the limit theory of Il!arkov branching processes with a general set of types under conditions tailored to (multigroup) branching diffusions on bounded domains, a setting which also covers the ordinary multitype case. Whereas the point of view in Parts A and B is quite pedagogical, the aim of Part C is to treat a large subfield to the highest degree of generality and completeness possi"ble. Thus the exposition there is at times quite technical.
Author: Patsy Haccou
Publisher: Cambridge University Press
ISBN: 9780521832205
Category : Mathematics
Languages : en
Pages : 342
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Book Description
This book covers the mathematical idea of branching processes, and tailors it for a biological audience.
Author: Miguel González
Publisher: Springer Science & Business Media
ISBN: 3642111564
Category : Mathematics
Languages : en
Pages : 304
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Book Description
One of the charms of mathematics is the contrast between its generality and its applicability to concrete, even everyday, problems. Branching processes are typical in this. Their niche of mathematics is the abstract pattern of reproduction, sets of individuals changing size and composition through their members reproducing; in other words, what Plato might have called the pure idea behind demography, population biology, cell kinetics, molecular replication, or nuclear ?ssion, had he known these scienti?c ?elds. Even in the performance of algorithms for sorting and classi?cation there is an inkling of the same pattern. In special cases, general properties of the abstract ideal then interact with the physical or biological or whatever properties at hand. But the population, or bran- ing, pattern is strong; it tends to dominate, and here lies the reason for the extreme usefulness of branching processes in diverse applications. Branching is a clean and beautiful mathematical pattern, with an intellectually challenging intrinsic structure, and it pervades the phenomena it underlies.
Author: Peter Olofsson
Publisher: John Wiley & Sons
ISBN: 0470889748
Category : Mathematics
Languages : en
Pages : 573
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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.
