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
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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.