This text combines stochastic modeling and statistical inference in a variety of standard and less common models, such as point processes, Markov random fields and hidden Markov models, in a clear, thoughtful and succinct manner. The main distinguishing feature of this work is that, in addition to probability theory, it contains statistical aspects of model fitting and a variety of data sets that are either analysed in the text or used as exercises. Markov chain Monte Carlo methods are introduced for evaluating likelihoods in complicated models and the forward - backward algorithm for analysing hidden Markov models is presented. The numerous examples and exercises drawn from astronomy, geology, genetics, hydrology, neurophysiology and physics, make this an ideal textbook for researchers, neurophysiology and physics, make this an ideal textbook for researchers, lecturers and graduate students studying statistics and probability, especially applied probability and stochastic processes.

Table of contents; Discrete time Markov chains; Continuous time Markov chains; Markov random fields; Point processes; Brownian motion and diffusion; Appendix 1: Statistical theory for the multinomial distribution; Appendix 2: Linear difference equations with constant coefficients; Appendix 3: Some theory of partial differential equations.