Bayesian probability theory : applications in the physical sciences - Linden, Wolfgang von der; Dose, Volker; Toussaint, Udo von (Cambridge : Cambridge University Press, 2014)
From the basics to the forefront of modern research, this book presents all aspects of probability theory, statistics and data analysis from a Bayesian perspective for physicists and engineers. The book presents the roots, applications and numerical implementation of probability theory, and covers advanced topics such as maximum entropy distributions, stochastic processes, parameter estimation, model selection, hypothesis testing and experimental design. In addition, it explores state-of-the art numerical techniques required to solve demanding real-world problems. The book is ideal for students and researchers in physical sciences and engineering.
The meaning of probability -- Basic definitions -- Bayesian inference -- Combinatrics -- Random walks -- Limit theorems -- Continuous distributions -- The central limit theorem -- Poisson processes and waiting times -- Transformation invariance -- Maximum entropy -- Qualified maximum entropy -- Global smoothness -- Bayesian parameter estimation -- Frequentist parameter estimation -- The Cramer-Rao inequality -- The Bayesian way -- The frequentist way -- Sampling distributions -- Bayesian vs frequentist hypothesis tests -- Regression -- Inconsistent data -- Unrecognized signal contributions -- Change point problems -- Function estimation -- Integral equations -- Model selection -- Bayesian experimental design -- Numerical integration -- Monte Carlo methods -- Nested sampling.
Title from publisher's bibliographic system (viewed on 01 Feb 2016).
Keywords: Probabilities; Bayesian statistical decision theory