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This book presents modern Bayesian analysis in a format that is
accessible to researchers in the fields of ecology, wildlife
biology, and natural resource management. Bayesian analysis has
undergone a remarkable transformation since the early 1990s.
Widespread adoption of Markov chain Monte Carlo techniques has made
the Bayesian paradigm the viable alternative to classical
statistical procedures for scientific inference. The Bayesian
approach has a number of desirable qualities, three chief ones
being: i) the mathematical procedure is always the same, allowing
the analyst to concentrate on the scientific aspects of the
problem; ii) historical information is readily used, when
appropriate; and iii) hierarchical models are readily accommodated.
This monograph contains numerous worked examples and the requisite
computer programs. The latter are easily modified to meet new
situations. A primer on probability distributions is also included
because these form the basis of Bayesian inference. Researchers and
graduate students in Ecology and Natural Resource Management will
find this book a valuable reference.
This book provides a coherent framework for understanding shrinkage
estimation in statistics. The term refers to modifying a classical
estimator by moving it closer to a target which could be known a
priori or arise from a model. The goal is to construct estimators
with improved statistical properties. The book focuses primarily on
point and loss estimation of the mean vector of multivariate normal
and spherically symmetric distributions. Chapter 1 reviews the
statistical and decision theoretic terminology and results that
will be used throughout the book. Chapter 2 is concerned with
estimating the mean vector of a multivariate normal distribution
under quadratic loss from a frequentist perspective. In Chapter 3
the authors take a Bayesian view of shrinkage estimation in the
normal setting. Chapter 4 introduces the general classes of
spherically and elliptically symmetric distributions. Point and
loss estimation for these broad classes are studied in subsequent
chapters. In particular, Chapter 5 extends many of the results from
Chapters 2 and 3 to spherically and elliptically symmetric
distributions. Chapter 6 considers the general linear model with
spherically symmetric error distributions when a residual vector is
available. Chapter 7 then considers the problem of estimating a
location vector which is constrained to lie in a convex set. Much
of the chapter is devoted to one of two types of constraint sets,
balls and polyhedral cones. In Chapter 8 the authors focus on loss
estimation and data-dependent evidence reports. Appendices cover a
number of technical topics including weakly differentiable
functions; examples where Stein's identity doesn't hold; Stein's
lemma and Stokes' theorem for smooth boundaries; harmonic,
superharmonic and subharmonic functions; and modified Bessel
functions.
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