Bayesian Probability Theory: Applications in the Physical Sciences

Description

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 Content: The meaning of 'probability' -- Basic definitions for frequentist statistics and Bayesian inference -- Bayesian inference -- Combinatorics -- Random walks -- Limit theorems -- Continuous distributions -- The central limit theorem -- Poisson processes and waiting times -- Prior probabilities by transformation invariance -- Testable information and maximum entropy -- Quantified maximum entropy -- Global smoothness -- Bayesian parameter estimation -- Frequentist parameter estimation -- The Cramer-Rao inequality -- The Bayesian way -- The frequentist approach -- Sampling distributions -- Comparison of Bayesian and frequentist hypothesis tests -- Regression -- Consistent inference on inconsistent data -- Unrecognized signal contributions -- Change point problems -- Function estimation -- Integral equations -- Model selection -- Bayesian experimental design -- Numerical integration -- Monte Carlo methods -- Nested sampling.