Practical Bayesian inference : a primer for physical scientists - Bailer-Jones, Coryn A. L. (Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2017)
"Science is fundamentally about learning from data, and doing so in the presence of uncertainty. Uncertainty arises inevitably and avoidably in many guises. It comes from noise in our measurements: we cannot measure exactly. It comes from sampling effects: we cannot measure everything. It comes from complexity: data may be numerous, high dimensional, and correlated, making it difficult to see structures. This book is an introduction to statistical methods for analysing data. It presents the major concepts of probability and statistics as well as the computational tools we need to extract meaning from data in the presence of uncertainty"--
Probability basics -- Estimation and uncertainty -- Statistical models and inference -- Linear models, least squares, and maximum likelihood -- Parameter estimation: single parameter -- Parameter estimation: multiple parameters -- Approximating distributions -- Monte Carlo methods for inference -- Parameter estimation: Markov Chain Monte Carlo -- Frequentist hypothesis testing -- Model comparison -- Dealing with more complicated problems.
Includes bibliographical references (pages 289-209) and index.
Keywords: Bayesian statistical decision theory; Mathematical physics