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Probability and Bayesian Modeling (Hardcover)
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Probability and Bayesian Modeling (Hardcover)
Series: Chapman & Hall/CRC Texts in Statistical Science
Expected to ship within 12 - 17 working days
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Probability and Bayesian Modeling is an introduction to probability
and Bayesian thinking for undergraduate students with a calculus
background. The first part of the book provides a broad view of
probability including foundations, conditional probability,
discrete and continuous distributions, and joint distributions.
Statistical inference is presented completely from a Bayesian
perspective. The text introduces inference and prediction for a
single proportion and a single mean from Normal sampling. After
fundamentals of Markov Chain Monte Carlo algorithms are introduced,
Bayesian inference is described for hierarchical and regression
models including logistic regression. The book presents several
case studies motivated by some historical Bayesian studies and the
authors' research. This text reflects modern Bayesian statistical
practice. Simulation is introduced in all the probability chapters
and extensively used in the Bayesian material to simulate from the
posterior and predictive distributions. One chapter describes the
basic tenets of Metropolis and Gibbs sampling algorithms; however
several chapters introduce the fundamentals of Bayesian inference
for conjugate priors to deepen understanding. Strategies for
constructing prior distributions are described in situations when
one has substantial prior information and for cases where one has
weak prior knowledge. One chapter introduces hierarchical Bayesian
modeling as a practical way of combining data from different
groups. There is an extensive discussion of Bayesian regression
models including the construction of informative priors, inference
about functions of the parameters of interest, prediction, and
model selection. The text uses JAGS (Just Another Gibbs Sampler) as
a general-purpose computational method for simulating from
posterior distributions for a variety of Bayesian models. An R
package ProbBayes is available containing all of the book datasets
and special functions for illustrating concepts from the book. A
complete solutions manual is available for instructors who adopt
the book in the Additional Resources section.
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