Convergence of Stochastic Processes
by D. Pollard
Publisher: Springer 1984
Number of pages: 223
An exposition od selected parts of empirical process theory, with related interesting facts about weak convergence, and applications to mathematical statistics. The high points of the book describe the combinatorial ideas needed to prove maximal inequalities for empirical processes indexed by classes of sets or classes of functions.
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by O. Melchert - arXiv
In these lecture notes, a selection of frequently required statistical tools will be introduced and illustrated. They allow to post-process data that stem from, e.g., large-scale numerical simulations (aka sequence of random experiments).
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This text is an attempt to give a reasonably self-contained presentation of the basic theory of stochastic partial differential equations, taking for granted basic measure theory, functional analysis and probability theory, but nothing else.
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This is a short book about the principles of data analysis. The emphasis is on why things are done rather than on exactly how to do them. If you already know something about the subject, then working through this book will deepen your understanding.
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Triggered by a recent interesting article on the too frequent incorrect use of probabilistic evidence in courts, the author introduces the basic concepts of probabilistic inference with a toy model, and discusses several important issues.