Filling a gap in current Bayesian theory, Statistical Inference: An
Integrated Bayesian/Likelihood Approach presents a unified Bayesian
treatment of parameter inference and model comparisons that can be
used with simple diffuse prior specifications. This novel approach
provides new solutions to difficult model comparison problems and
offers direct Bayesian counterparts of frequentist t-tests and
other standard statistical methods for hypothesis testing. After an
overview of the competing theories of statistical inference, the
book introduces the Bayes/likelihood approach used throughout. It
presents Bayesian versions of one- and two-sample t-tests, along
with the corresponding normal variance tests. The author then
thoroughly discusses the use of the multinomial model and
noninformative Dirichlet priors in "model-free" or nonparametric
Bayesian survey analysis, before covering normal regression and
analysis of variance. In the chapter on binomial and multinomial
data, he gives alternatives, based on Bayesian analyses, to current
frequentist nonparametric methods. The text concludes with new
goodness-of-fit methods for assessing parametric models and a
discussion of two-level variance component models and finite
mixtures. Emphasizing the principles of Bayesian inference and
Bayesian model comparison, this book develops a unique methodology
for solving challenging inference problems. It also includes a
concise review of the various approaches to inference.
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