Speaker 1: J. Rougier (Bristol)
Modelling the eruption processes of a large number of similar but not identical volcanoes
Extreme value theory suggests a three-parameter model for large eruptions for a specific volcano. Unfortunately, we only have reliable records going back a few hundred years at most, and in that time sometimes have only one or two eruptions per volcano. Pooling the volcanoes is unattractive (although it is commonly done); one alternative is to model them exchangeably. I'll discuss an exchangeable model for many volcanoes, and some of the issues that arise in implementing it. These include squeezing information out of unreliable data, transforming the parameters to apply informative priors, and computational approximations based on discretisation (no MCMC!). I will present return period curves for the eleven currently active Japanese stratovolcanoes. This is joint work with Profs Steve Sparks and Kathy Cashman.

Speaker 2: R. Ryder (Université Paris-Dauphine)
Bayesian methods for Historical Linguistics
Languages change through time in a manner comparable to biological evolution. Models have been developed for many aspects of human languages, including vocabulary, syntax and phonology. The complexity of these models, as well as the nature of the questions of interest, make the Bayesian framework quite natural in this setting, which explains why much of the research in Statistics applied to Historical Linguistics uses Bayesian methods. I shall present an overview of various models, starting with Morris Swadesh's failed attempts at glottochronology in the 1950s, then looking at some models developed in the last decade. I shall go into more detail for a model of so-called "core" lexical data by a stochastic process on a phylogenetic tree, with an initial focus on the Indo-European family of languages and on the issue of dating the most recent common ancestor to these languages. This will allow me to discuss issues of model robustness and validation, before I present applications to several data sets. If time allows, I shall conclude with some ongoing work about long-term trends in changes of syntactical features, especially word order. The work on lexical data is joint with Geoff Nicholls; the work on word order is joint with Isabelle Charnavel, Hilda Koopman and Dominique Sportiche.

Mr Lilun Du (University of Wisconsin Madison)
Single-Index Modulated Multiple Testing

Abstract: In the context of large-scale multiple testing, hypotheses are often accompanied with certain prior information. In this talk, we present a single-index modulated (SIM) multiple testing procedure, which maintains control of the false discovery rate while incorporating prior information, by assuming the availability of a bivariate p-value, $(p_1, p_2)$, for each hypothesis, where $p_1$ is a preliminary p-value from prior information and $p_2$ is the primary p-value for the ultimate analysis. To find the optimal rejection region for the bivariate p-value, we propose a criteria based on the ratio of probability density functions of $(p_1, p_2)$ under the true null and non-null. This criteria in the bivariate normal setting further motivates us to project the bivariate p-value to a single-index, $p(\theta)$, for a wide range of directions $\theta$. The true null distribution of $p(\theta)$ is estimated via parametric and nonparametric approaches, leading to two procedures for estimating and controlling the false discovery rate. To derive the optimal projection direction $\theta$, we propose a new approach based on power comparison, which is further shown to be consistent under some mild conditions. Simulation evaluations indicate that the SIM multiple testing procedure improves the detection power significantly while controlling the false discovery rate. Analysis of a real dataset will be illustrated.

Gareth Peters (UCL)
Sequential Monte Carlo Samplers for capital allocation under copula-dependent risk models
In this talk we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation conditional to a rare event, which can be challenging to evaluate in practice. We exploit the copula-dependence within the portfolio risks to design a Sequential Monte Carlo Samplers based estimate to the marginal conditional expectations involved in the problem, showing its efficiency through a series of computational examples.

Leonard Held (University of Zurich)
Adaptive prior weighting in generalized linear models
The prior distribution is a key ingredient in Bayesian inference. Prior information in generalized linear models may come from different sources and may or may not be in conflict with the observed data. Various methods have been proposed to quantify a potential prior-data conflict, such as Box's $p$-value. However, the literature is sparse on methodology what to do if the prior is not compatible with the observed data. To this end, we review and extend methods to adaptively weight the prior distribution. We relate empirical Bayes estimates of prior weight to Box's p-value and propose alternative fully Bayesian approaches. Prior weighting can be done for the joint prior distribution of the regression coefficients or - under prior independence - separately for each regression coefficient or for pre-specified blocks of regression coefficients. We outline how the proposed methodology can be implemented using integrated nested Laplace approximations (INLA) and illustrate the applicability with a logistic and a log-linear Poisson multiple regression model. This is joint work with Rafael Sauter.

The Learning Forum is an event in which students and staff meet to discuss teaching and learning in the Mathematical Sciences at Warwick.

Peter Diggle (Lancaster/Liverpool)
River Blindness, Eyeworm and a Calibration Problem
Onchocerciasis (River blindness) is a major public health problem in the wet tropical regions of the world, including most of sub-Saharan Africa. A multi-national programme to control the disease by mass administration of a protective drug has been very successful, with more than 60 million treatments to date over 19 countries. However, the programme has been hampered by the recognition that people heavily infected with the Loa loa (eye worm) parasite. Before the drug is administered in a community, it is relatively easy to estimate the prevalence of eye worm infection, much harder under field conditions to estimate how many people are heavily infected, defined as carrying more than 8,000 parasites per ml of blood. This leads to the following prediction problem: given a sample of n people, of whom Y are infected with eye worm, how many people in the community from which the sample is drawn are carrying more than 8,000 parasites per ml of blood? To address this problem we first develop a model for the variation in parasite count between individuals within a village, and then explore how the parameters of this distribution vary between villages. The model will be used to calculate the predictive probability that an individual in a com­munity will be carrying more than 8,000 parasites per ml of blood, given an estimate of community-level prevalence and any other relevant information in the form of covariates and/or prevalence estimates from neighboring villages.