A statistical model is a probability distribution constructed to enable inferences to be drawn or decisions made from data. This idea is the basis of most tools in the statistical workshop, in which it plays a central role by providing economical and insightful summaries of the information available.

This book is intended as an integrated modern account of statistical models covering the core topics for studies up to a masters degree in statistics. It can be used for a variety of courses at this level and for reference. After outlining basic notions, it contains a treatment of likelihood that includes non-regular cases and model selection, followed by sections on topics such as Markov processes, Markov random fields, point processes, censored and missing data, and estimating functions, as well as more standard material. Simulation is introduced early to give a feel for randomness, and later used for inference. There are major chapters on linear and nonlinear regression and on Bayesian ideas, the latter sketching modern computational techniques. Each chapter has a wide range of examples intended to show the interplay of subject-matter, mathematical, and computational considerations that makes statistical work so varied, so challenging, and so fascinating.

The target audience is senior undergraduate and graduate students, but the book should also be useful for others wanting an overview of modern statistics. The reader is assumed to have a good grasp of calculus and linear algebra, and to have followed a course in probability including joint and conditional densities, moment-generating functions, elementary notions of convergence and the central limit theorem, for example using Grimmett and Welsh (1986) or Stirzaker (1994).