Probability and Statistical Inference From Basic Principles to Advanced Models
Probability and Statistical Inference: From Basic Principles to Advanced Models covers aspects of probability, distribution theory, and inference that are fundamental to a proper understanding of data analysis and statistical modelling. It presents these topics in an accessible manner without sacrificing mathematical rigour, bridging the gap between the many excellent introductory books and the more advanced, graduate-level texts. The book introduces and explores techniques that are relevant to modern practitioners, while being respectful to the history of statistical inference. It seeks to provide a thorough grounding in both the theory and application of statistics, with even the more abstract parts placed in the context of a practical setting.
•Complete introduction to mathematical probability, random variables, and distribution theory.
•Concise but broad account of statistical modelling, covering topics such as generalised linear models, survival analysis, time series, and random processes.
•Extensive discussion of the key concepts in classical statistics (point estimation, interval estimation, hypothesis testing) and the main techniques in likelihood-based inference.
•Detailed introduction to Bayesian statistics and associated topics.
•Practical illustration of some of the main computational methods used in modern statistical inference (simulation, boostrap, MCMC).
This book is for students who have already completed a first course in probability and statistics, and now wish to deepen and broaden their understanding of the subject. It can serve as a foundation for advanced undergraduate or postgraduate courses. Our aim is to challenge and excite the more mathematically able students, while providing explanations of statistical concepts that are more detailed and approachable than those in advanced texts. This book is also useful for data scientists, researchers, and other applied practitioners who want to understand the theory behind the statistical methods used in their fields.
3. Random Variables and Univariate Distributions
4. Multivariate Distributions
5. Conditional Distributions
6. Statistical Models
7. Sample Moments and Quantiles
8. Estimation, Testing, and Prediction
9. Likelihood-based Inference
10. Inferential Theory
11. Bayesian Inference
12. Simulation Methods
"This book provides a comprehensive and thorough coverage of probability and distribution theory and statistical inference. Based on a popular undergraduate course at the London School of Economics, the content and its presentation have been honed by the authors over many years of teaching. The result is an extremely clear and engaging text, which achieves that rare balance of explaining statistical concepts in an intuitive and accessible way while maintaining precision and rigour. Concepts are introduced and illustrated using real-world examples, which aids understanding and highlights their practical relevance. The book covers foundational and advanced topics in probability and statistical inference, with an excellent overview of statistical modelling, and detailed treatments of Bayesian approaches and modern simulation-based estimation methods. Each chapter includes an extensive and graduated set of exercises. I highly recommend the book for advanced undergraduate and postgraduate students in statistics and data science, but also as an essential reference for researchers."
- Fiona Steele, London School of Economics and Political Science