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The Coordinate-Free Approach to Linear Models
This book is about the coordinate-free, or geometric, approach to the theory of linear models; more precisely, Model I ANOVA and linear regression models with non-random predictors …
Model Selection and Model Averaging
Given a data set, you can fit thousands of models at the push of a button, but how do you choose the best? With so many candidate models, overfitting is a real danger. Is the …
Statistical Principles for the Design of Experiments
This book is about the statistical principles behind the design of effective experiments and focuses on the practical needs of applied statisticians and experimenters engaged in …
Random Networks for Communication
When is a random network (almost) connected? How much information can it carry? How can you find a particular destination within the network? And how do you approach these …
The Fundamentals of Heavy Tails
Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet …
A User's Guide to Measure Theoretic Probability
Rigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students of statistics, …
Measure Theory and Filtering
The estimation of noisily observed states from a sequence of data has traditionally incorporated ideas from Hilbert spaces and calculus-based probability theory. As conditional …
Semiparametric Regression
Semiparametric regression is concerned with the flexible incorporation of non-linear functional relationships in regression analyses. Any application area that benefits from …
Regression for Categorical Data
This book introduces basic and advanced concepts of categorical regression with a focus on the structuring constituents of regression, including regularization techniques to …
Model-Based Clustering and Classification for Data Science
Cluster analysis finds groups in data automatically. Most methods have been heuristic and leave open such central questions as: how many clusters are there? Which method should I …
Quantum Stochastics
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of …
Probability on Trees and Networks
Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, …