Stereology, or quantitative microscopy, is a basic research tool in science and technology. The emergence of design-based methods has greatly increased the power, flexibility, adaptability, and scope of stereology applications, establishing a closer connection between statistics and quantitative microscopy. Despite its scientific importance, modern stereology remains largely unknown to the statistical community, with valuable information either widely scattered or inaccessible to newcomers to the field. Now is the perfect time for a book that enables biostatisticians and statistical consultants to give beneficial advice to researchers in microscopy.

Stereology for Statisticians sets out the principles of stereology from a statistical viewpoint, focusing on both basic theory and practical implications. This book discusses ways to effectively communicate statistical issues to clients, draws attention to common methodological errors, and provides references to essential literature.

The first full text on design-based stereology, it opens with a review of classical and modern stereology, followed by a treatment of mathematical foundations such as geometry, probability, and statistical inference. The book then presents core techniques, including estimation of absolute geometrical quantities, relative quantities, and statistical inference for populations of discrete objects. The final chapters discuss implementing techniques in practical sampling designs, summarize understanding of the variance of stereological estimators, and describe open problems for further research.

The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.