For an algebraic structure admitting a given signature Σ of operations, see Universal algebra. In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra"; also σ-field) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair is called a measurable space. A σ-algebra of subsets is a set alge

This 3-part tutorial addresses a machine learning audience, not assumed to be familiar with measure theory or the theory of stochastic processes. The course is intended to provide (1) an overview of what nonparametric Bayesian models exist beyond those already used in machine learning, and (2) a basic understanding of the mathematical construction of ''process'' models, both existing ones and new

Empirical Bayes methods are procedures for statistical inference in which the prior probability distribution is estimated from the data. This approach stands in contrast to standard Bayesian methods, for which the prior distribution is fixed before any data are observed. Despite this difference in perspective, empirical Bayes may be viewed as an approximation to a fully Bayesian treatment of a hie

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Professor Institute for Language, Cognition and Computation School of Informatics University of Edinburgh I'm also part of Edinburgh NLP and the Centre for Doctoral Training in Natural Language Processing email me (sgwater) here: inf.ed.ac.uk In my research, I aim to discover the computational processes and constraints that are needed to learn linguistic structure, either in humans or in machines.