General Audience Maths Edinburgh Seminars
Speakers from the School of Mathematics will explain their research to a general mathematical audience, including mature undergraduates, postgraduates, postdocs and staff. Each session will contain two 25 minutes talks.
In this talk, we present a Bayesian framework for semi-supervised binary classification on graphs. We develop several Bayesian models through the construction of a Gaussian prior from the graph Laplacian. Connections to the Ginzburg-Landau model are also made through the notion of a push-forward of the Gaussian prior under the double-well thresholding. We introduce efficient MCMC methods designed for large data sets to effectively sample from the posterior distribution for large scale problems. Through a variety of numerical experiments, we demonstrate the ability to perform uncertainty quantification by sampling from the posterior distribution. In particular, we observe empirically that the posterior mean and variance aligns well with certain external notions of uncertainty.
In this talk, we will show a very general version of a trust-region algorithm for unconstrained optimization problems. The idea is to extract only the important conditions that a model should have in order to successfully prove convergence of the algorithm. The described algorithm can then be used in a derivative-free implementation.
Mathematical and computer modelling is widely used to support decisions in energy systems planning and in development of government energy policy. This talk will explore key issues in the use of modelling for decision support (with the help of a few experts from history), and give a flavour of what we at Edinburgh are doing about these.