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Based on a starter course for beginning graduate students, Core Statistics provides concise coverage of the fundamentals of inference for parametric statistical models, including both theory and practical numerical computation. Core Statistics considers both frequentist maximum likelihood and Bayesian stochastic simulation while focusing on general methods applicable to a wide range of models and emphasizing the common questions addressed by the two approaches. This compact package serves as a lively introduction to the theory and tools that a beginning graduate student needs in order to make the transition to serious statistical analysis: inference; modeling; computation, including some numerics; and the R language. Aimed also at any quantitative scientist who uses statistical methods, Core Statistics will deepen readers' understanding of why and when methods work and explain how to develop suitable methods for non-standard situations, such as in ecology, big data and genomics.
1. Random variables
3. Statistical models and inference
4. Theory of maximum likelihood estimation
5. Numerical maximum likelihood estimation
6. Bayesian computation
7. Linear models
Simon Wood works as a Professor of Statistics at the University of Bath and currently holds an established research fellowship from the Engineering and Physical Sciences Research Council. He is author of the widely used R package mgcv for smooth statistical modelling and the book Generalized Additive Models: An Introduction with R, as well as a number of well-cited papers on associated statistical methods. Originally trained in physics, before a spell in theoretical ecology, he has twenty years' experience of teaching statistics at undergraduate and postgraduate level, including teaching the 'statistical computing' module of the UK Academy for PhD training in statistics, for several years.
"The author keeps this book concise by focusing entirely on topics that are most relevant for scientific modeling via maximum likelihood and Bayesian inference. This makes it an ideal text and handy reference for any math-literate scientist who wants to learn how to build sophisticated parametric models and fit them to data using modern computational approaches. I will be recommending this well-written book to my collaborators."
– Murali Haran, Pennsylvania State University
"Simon Wood has written a must-read book for the instructor, student, and scholar in search of mathematical rigor, practical implementation, or both. The text is relevant to the likelihoodist and Bayesian alike; it is nicely topped off by instructive problems and exercises. Who thought that a core inference textbook needs to be dry?"
– Geert Molenberghs, Universiteit Hasselt and KU Leuven, Belgium
"Simon Wood's book Core Statistics is a welcome contribution. Wood's considerable experience in statistical matters and his thoughtfulness as a writer and communicator consistently shine through. The writing is compact and neutral, with occasional glimpses of Wood's wry humour. The carefully curated examples, with executable code, will repay imitation and development. I warmly recommend this book to graduate students who need an introduction, or a refresher, in the core arts of statistics."
– Andrew Robinson, University of Melbourne
"This is an interesting book intended for someone who has already taken an introductory course on probability and statistics and who would like to have a nice introduction to the main modern statistical methods and how these are applied using the R language. It covers the fundamentals of statistical inference, including both theory in a concise form and practical numerical computation."
– Vassilis G. S. Vasdekis, Mathematical Reviews