Computational inference has taken its place alongside asymptotic
inference and exact techniques in the standard collection of statistical
methods. Computational inference is based on an approach to statistical
methods that uses modern computational power to simulate distributional
properties of estimators and test statistics. This book describes
computationally-intensive statistical methods in a unified presentation,
emphasizing techniques, such as the PDF decomposition, that arise in a
wide range of methods.
The book assumes an intermediate background in mathematics, computing,
and applied and theoretical statistics. The first part of the book,
consisting of a single long chapter, reviews this background material
while introducing computationally-intensive exploratory data analysis
and computational inference.
The six chapters in the second part of the book are on statistical
computing. This part describes arithmetic in digital computers and how
the nature of digital computations affects algorithms used in
statistical methods. Building on the first chapters on numerical
computations and algorithm design, the following chapters cover the main
areas of statistical numerical analysis, that is, approximation of
functions, numerical quadrature, numerical linear algebra, solution of
nonlinear equations, optimization, and random number generation.
The third and fourth parts of the book cover methods of computational
statistics, including Monte Carlo methods, randomization and cross
validation, the bootstrap, probability density estimation, and
statistical learning.
The book includes a large number of exercises with some solutions
provided in an appendix.
