Books in the Institute of Mathematical Statistics Monographs series

"This is the first comprehensive introduction to the Conway-Maxwell-Poisson distribution and its contributions in statistical theory and computing in R, including its uses in count data modelling. An essential reference for academics in statistics and data science, as well as quantitative researchers and data analysts in applied disciplines"--

Ideal for statisticians, this book will also interest probabilists, mathematicians, computer scientists, and morphometricians with mathematical training. It presents a systematic introduction to a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important applications in medical diagnostics, image analysis and machine vision.

Blending theory and practice, this will be the standard resource for statisticians and applied researchers. Assuming only basic knowledge of (non-measure-theoretic) probability and statistical inference, it is accessible to the wide range of researchers who use statistical modelling techniques. The author's complementary R package helps readers put theory into practice.

The case-control approach is a powerful method for investigating factors that may explain a particular event. It is extensively used in epidemiology to study disease incidence, one of the best-known examples being Bradford Hill and Doll's investigation of the possible connection between cigarette smoking and lung cancer. More recently, case-control studies have been increasingly used in other fields, including sociology and econometrics. With a particular focus on statistical analysis, this book is ideal for applied and theoretical statisticians wanting an up-to-date introduction to the field. It covers the fundamentals of case-control study design and analysis as well as more recent developments, including two-stage studies, case-only studies and methods for case-control sampling in time. The latter have important applications in large prospective cohorts which require case-control sampling designs to make efficient use of resources. More theoretical background is provided in an appendix for those new to the field.

We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples.

Computing power has revolutionized the theory and practice of statistical inference. This book delivers a concentrated course in modern statistical thinking by tracking the revolution from classical theories to the large-scale prediction algorithms of today. Anyone who applies statistical methods to data will benefit from this landmark text.