This text presents key topics in mathematical statistics in a rigorous yet accessible manner. It covers aspects of probability, distribution theory, and random processes that are fundamental to a proper understanding of inference. The book also discusses the properties of estimators constructed from a random sample of ends, with sections on methods for estimating parameters in time series models and computationally intensive inferential techniques. The text challenges the more mathematically inclined students while providing an approachable explanation of advanced statistical concepts for students who struggle with existing texts.
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.
Features:
-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.
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"Learning statistics is one thing; learning to think like a statistician is something else. This book grabs readers by the hand and takes them on a journey through statistics, by the end of which they are well-equipped to think like a statistician. For a book at intermediate level this is no mean feat: ideas are subtle and require a delicate balance of formal mathematics and statistical insight, a balance that is deftly maintained throughout the book. The mathematics is rigorous, but not so much so that underlying intuition is lost. And the statistical concepts themselves are explained with a clarity that is rare in textbooks at a similar level. I wish this book had been available when I was first learning statistics. And I wouldn't hesitate now to use it as the basis for teaching on any intermediate statistics course. The best compliment I can give is that it was a pleasure to read and gave me new insights, even on material with which I am very familiar. I love this book and congratulate the authors on writing with such clarity and vision. I hope many readers take the opportunity to follow the statistical journey the authors provide."
~Stuart Coles, author of An Introduction to Statistical Modeling of Extreme Values
"Overall, I give Probability and Statistical Inference: From Basic Principles to Advanced Models a solid thumbs up! It's well suited as a primary introductory probability theory textbook for undergraduates or applied masters students in statistics or data science. It's also appropriate as a primary textbook for an advanced survey course in probability and statistics. Further, I recommend this textbook to working professionals in any field who seek further insight on probability theory and statistical inference."
~Gabriel J. Young, The American Statistician
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