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.
