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Books > Science & Mathematics > Mathematics > Probability & statistics
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Bayesian Inference for Stochastic Processes (Hardcover)
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Bayesian Inference for Stochastic Processes (Hardcover)
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This is the first book designed to introduce Bayesian inference
procedures for stochastic processes. There are clear advantages to
the Bayesian approach (including the optimal use of prior
information). Initially, the book begins with a brief review of
Bayesian inference and uses many examples relevant to the analysis
of stochastic processes, including the four major types, namely
those with discrete time and discrete state space and continuous
time and continuous state space. The elements necessary to
understanding stochastic processes are then introduced, followed by
chapters devoted to the Bayesian analysis of such processes. It is
important that a chapter devoted to the fundamental concepts in
stochastic processes is included. Bayesian inference (estimation,
testing hypotheses, and prediction) for discrete time Markov
chains, for Markov jump processes, for normal processes (e.g.
Brownian motion and the Ornstein-Uhlenbeck process), for
traditional time series, and, lastly, for point and spatial
processes are described in detail. Heavy emphasis is placed on many
examples taken from biology and other scientific disciplines. In
order analyses of stochastic processes, it will use R and WinBUGS.
Features: Uses the Bayesian approach to make statistical Inferences
about stochastic processes The R package is used to simulate
realizations from different types of processes Based on
realizations from stochastic processes, the WinBUGS package will
provide the Bayesian analysis (estimation, testing hypotheses, and
prediction) for the unknown parameters of stochastic processes To
illustrate the Bayesian inference, many examples taken from
biology, economics, and astronomy will reinforce the basic concepts
of the subject A practical approach is implemented by considering
realistic examples of interest to the scientific community WinBUGS
and R code are provided in the text, allowing the reader to easily
verify the results of the inferential procedures found in the many
examples of the book Readers with a good background in two areas,
probability theory and statistical inference, should be able to
master the essential ideas of this book.
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