The image above links to the pdf file (5 Mb) of my talk at the ICIC yesterday afternoon. My idea was to use my allotted time to introduce weak convergence as a statistical/topological concept of both *intrinsic interest* (e.g. for neat examples whereby the CLT proof for nested sampling by Chopin & Robert 2010 invokes the weak convergence of a sequence of piecewise constant random functions to Brownian motion; the latter the shared focus of study in physics and probability theory) and *practical interest *as it underpins a number of contemporary techniques in non-parametric Bayesian analysis (e.g. Dirichlet processes and the SPDE approach to random fields). It was fun to try to put these ideas together in a coherent way that might be appreciated by an audience with a range of statistical and non-statistical backgrounds and experience levels ranging from first-year PhD students to their professors. Not sure how well I achieved that, but I enjoyed trying and I got to have some interesting discussions before & after.

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