Wilfrid Kendall will talk about curvature measures in applied stochastic geometry. The plan is to discuss the stochastic geometry theory underlying the papers.

Charemza, M., Thönnes, E., & Bhalerao, A. (2008). Integral geometry descriptors for characterizing emphysema and lung fibrosis in HRCT images. In Proceedings of the 1st MICCAI Workshop on Pulmonary Image Analysis (10 pp).

Thönnes, E., Bhalerao, A., & Parr, D. (2010). Classification of Lung Disease in HRCT Scans using Integral Geometry Measures and Functional Data Analysis. In Proc. MIUA (pp. 1–6).

These notions are likely to be very relevant to the Inside-Out project here at Warwick. Time permitting, there will be some discussion of generalizations.

Jean-Michel Marin

Consistency of the Adaptive Multiple Importance Sampling (joint work with Pierre Pudlo and Mohammed Sedki

Among Monte Carlo techniques, the importance sampling requires fine tuning of a proposal distribution, which is now fluently resolved through iterative schemes. The Adaptive Multiple Importance Sampling (AMIS) of Cornuet et al. (2012) provides a significant improvement in stability and Effective Sample Size due to the introduction of a recycling procedure. However, the consistency of the AMIS estimator remains largely open. In this work, we prove the convergence of the AMIS, at a cost of a slight modification in the learning process. Numerical experiments exhibit that this modification might even improve the original scheme.

Judith Rousseau

Asymptotic properties of Empirical Bayes procedures – in parametric and non parametric models

In this work we investigate frequentist properties of Empirical Bayes procedures. Empirical Bayes procedures are very much used in practice in more or less formalized ways as it is common practice to replace some hyperparameter in the prior by some data dependent quantity. There are typically two ways of constructing these data dependent quantities : using some king of moment estimator or some quantity whose behaviour is well understood or using a maximum marginal likelihood estimator. In this work we first give some general results on how to determine posterior concentration rates under the former setting, which we apply in particular to two types of Dirichlet process mixtures. We then shall discuss more parametric models in the context of maximum marginal likelihood estimation. We will in particular explain why some pathological behaviour can be expected in this case.

Tony Hewitt MA FIA (Imperial College Business School)

Solving business issues and dilemmas

Gareth Alexander talks about knots in liquid crystals. In the past four years it has become possible to make knotted configurations experimentally in laser light, fluid flows and liquid crystals. Furthermore, recent advances in microfabrication offer the possibility of almost arbitrary experimental control in making such states. He will describe their recent work on how knotted textures in liquid crystals can be characterised using traditional knot theory and applied topology and how the material properties are influenced by the knot type.