## Spring 2012/13:

**Room:**3E 2.4

**Time:**14:15

- 08/02 Julian Faraway. 'Does Data Splitting Improve Prediction?'
- 08/03 Kuntalee Chaisee. 'Using the jackknife to assess uncertainty for Bayes estimates.'
- 26/04 Two short talks:
- Marianne Menictas, Australia, School of Mathematical Sciences, University of Technology, Sydney;
- Benjamin Safken, Georg-August-Universität G\"ottingen, Germany. 'Model choice and variable selection in mixed & semiparametric models' . Note different venue: Wolfson lecture theatre 4W1.7
- 10/05 --
- 17/05 Two talks: Natasha Pya - A new invariant and consistent chi-squared type goodness-of-fit test for multivariate normality; Simon Shaw - Bayesian analysis of finite population sampling in multivariate co-exchangeable structures with separable covariance matrices. Note different venue: Wolfson lecture theatre 4W1.7
- 24/05 Two talks: Matteo Fasiolo; Gavin Shaddick. Note different venue: Wolfson lecture theatre 4W1.7

## Winter 2012/13:

- 19/10 tba
- 26/10 tba
- 16/11 Finn Lindgren: Taking advantage of model structure
- 28/11 Simon Shaw
- 14/12 Evangelos Evangelou
- 21/12 tba

## Spring 2012:

- 02/03/12 Short introductory talks to Biology
- 09/03/12 Gavin Shaddick: "Long term changes in air pollution: a case study in preferential sampling"
- 16/03/12 Dick James: "Networks in Ecology and Evolution"
- 11/05/12 Jane Temple: "Direct Sampling from the Posterior Distribution for Non-Linear Dose Response Models"

## Simon Shaw, 17/05/13, Wolfson lecture theatre 4W1.7, 14:15 - 16:00

*Department of Mathematical Sciences, University of Bath*

**Bayesian analysis of finite population sampling in multivariate co-exchangeable structures with separable covariance matrices.**

We explore the effect of finite population sampling in design problems with many variables cross-classified in many ways. In particular, we investigate designs where we wish to sample individuals belonging to different groups for which the underlying covariance matrices are separable between groups and variables. We exploit the generalised conditional independence structure of the model to show how the analysis of the full model can be reduced to an interpretable series of lower dimensional problems. The types of information we gain by sampling are identified with the orthogonal canonical directions. We first solve a variable problem, which utilises the powerful properties of the adjustment of second-order exchangeable vectors, which has the same qualitative features, represented by the underlying canonical variable directions, irrespective of chosen group, population size or sample size. We then solve a series of group problems. If the population size in each group is infinite then these problems all have the same qualitative features, represented by the underlying canonical group directions, and, in a balanced design, reduce to the sampling of second-order exchangeable vectors. If the population sizes are finite then the qualitative features of each problem will depend upon the sampling fractions in each group, mimicking the infinite problem when the sampling fractions in each group are the same.

## Finn Lindgren, 16/11/12, 3E 4.17 14:15

*Department of Mathematical Sciences, University of Bath*

**Taking advantage of model structure**

For very large Bayesian linear models with a hierarchical structure, such as those involving spatio-temporal effects, computing posterior marginal distributions of the effects can be computationally demanding. Even when the effects have Markov structure, for large enough problems eventually even the ubiquitous Cholesky factor becomes impossible to compute. While various methods can be employed to generate samples, and thus allow Monte Carlo estimates, this comes with a high penalty. However, by using the hierarchical and Markov structure of the model, it may be possible to greatly reduce the Monte Carlo error for a given sample size, via a block-wise Rao-Blackwellisation technique.

## Tony Robinson, Nicole Augustin, Julian Faraway, Simon Wood, Merrilee Hurn, Chris Jenisson, 02/03/12, the Pavilion in 4 South, 14:15

*These will be several short talks given by Bath Statistics members on the type of research they do.*

## Gavin Shaddick, 09/03/12, 3E2.4, 14:15

*Department of Mathematical Sciences, University of Bath*

**Long term changes in air pollution: a case study in preferential sampling**

## Dick James, 16/03/12, 3E2.4, 14:15

*Department of Physics & Centre for Mathematical Biology, University of Bath*

**Networks in Ecology and Evolution**

I work with biologists trying to understand the social structure of populations of animals that spend all or part of their time living in groups. We try to use networks of contacts, interactions or associations to relate social structure and dynamics to the biology of the individual. I plan to present a brief review of one or two of the projects I am involved in, highlighting the questions in social evolution that motivate our use of network analysis, the statistical approach we have used so far and questions we would like some help with.

## Jane Temple, 11/05/12, 3E2.4, 15:15

*Department of Mathematical Sciences, University of Bath*

**Direct Sampling from the Posterior Distribution for Non-Linear Dose Response Models**

In clinical trials, Bayesian inference is often used to make predictions about Phase III outcomes or to stop doses at interim analyses. In order to understand the operational characteristics of such decisions, large scale simulations may be carried out, which can be time consuming. Making inferences about the posterior distribution for non-linear models can rarely be done analytically and so common methods of inference involve generating MCMC sampling using packages such as winBUGS. This can result in problems of autocorrelation between the samples and non-convergence of the sampler. In this talk we re-write the four parameter non-linear Sigmoid Emax model as a linear model with a non-linear term, allowing us to reduce the dimensionality of the sampling problem. We use a grid to sample directly from the target density, through a combination of acceptance-rejection and importance sampling. We show that for the four parameter model, we can generate independent samples more quickly than the winBUGS alternative generates a sequence of correlated samples. This method also removes the need to check the convergence of the sampler.