Matt Moores, Department of Statistics, University of Warwick
Title: bayesImageS: a case study in Bayesian computation using Rcpp and OpenMP
Abstract: There are many approaches to Bayesian computation with intractable likelihoods, including the exchange algorithm, approximate Bayesian computation (ABC), thermodynamic integration, and composite likelihood.
These approaches vary in accuracy as well as scalability for datasets of significant size. The Potts model is an example where such methods are required, due to its intractable normalising constant. This model is a type of Markov random field, which is commonly used for image segmentation. The dimension of its parameter space increases linearly with the number of pixels in the image, making this a challenging application for scalable Bayesian computation. My talk will introduce various algorithms in the context of the Potts model and describe their implementation in C++, using OpenMP for parallelism. I will also discuss the process of releasing this software as an open source R package on the CRAN repository.
Joshua Loftus, Alan Turing Institute
Title: Post-selection inference for models characterized by quadratic constraints
Abstract: To address the fundamental statistical problem of conducting inference after model selection a recent approach formed in Fithian et al. (2014) and Lee et al. (2016) conditions on the selected model and uses the corresponding truncated probability laws for inference. Though simple to state, the application of this principle varies in difficulty depending on which model selection procedure is under consideration. This work identifies a general mathematical framework encompassing many model selection procedures. The simple algebra of quadratic constraints allows computation of one-dimensional truncated supports for conditional versions of standard test statistics like the chi-squared and F tests used in regression. Several important examples illustrate the utility of this framework, including forward selection with groups of variables and linear model selection with cross-validation.