I expect from you more than just being able to reproduce the results therein.

Extensions of the models/variations over the models proposed, cleverer algorithms to fit these models

and original applications are very welcome.

One can propose to use a Voronoi tessellation of the prediction space based on Euclidean distance. Propose a Bayesian model for the centers of these locations, their number and the

unknown parameters associated to these partitions. Develop an MCMC algorithm to fit this model. Evaluate the performance of this approach on several datasets.

Please read Bayesian partitioning for classification and regression by D. Denison, C.C. Holmes and B. Mallick, Technical report Imperial College, 2001.

additionally performed so as to reduce the set of explanatory variables. Assess the performance of your model and algorithm on several datasets.

Please read Bayesian auxiliary variable models for binary and polychotomous regression. by C.C. Holmes and K. Held

to the local background rate.

Please read Recombination hostpots as a point process by De Iorio et al., Philosophical Transactions of the Royal Society: Biological Sciences, 2005.

using the output of an MCMC algorithm sampling the posterior. However if the loss function is not standard, the minimization can be very tricky.

The aim of this project is to develop a stochastic approximation (e.g. Robbins-Monro) algorithm combined to the MCMC ouput

to optimize non-standard loss functions. This algorithm will be demonstrated on several (non-trivial) examples.

The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the space where the process is defined.

The method is based on modeling a density function, defined on this bounded region, that is directly related with the intensity function of the Poisson process.

We want to develop a flexible nonparametric Bayesian mixture model for this density using a bivariate Beta distribution for the mixture kernel and a Dirichlet process prior

for the mixing distribution. An MCMC algorithm will be developed to fit these data

Please read: A Bayesian Nonparametric Approach to Inference for Spatial Poisson Processes by A. Kottas and B. Sanso, Technical Report, UCSC, 2005.

the population, called an attribute ensemble, may depend on the cluster being considered. The model is based on a P'olya urn cluster model, which is

equivalent to a Dirichlet process mixture of multivariate normal distributions.

This model-based approach allows for the incorporation of application-specific data features into the clustering scheme. For example, in an analysis of

genetic CGH array data we account for spatial correlation of genetic abnormalities along the genome

Please read: Model-based subspace clustering by Hoff, P.D. (2006),

Please read: Bayesian Factor Regression Models in the ``Large p, Small n'' Paradigm by M. West, Bayesian Statistics, 2003.

linear models. These methods are NOT Bayesian. The aim of this project is to derive and implement a Bayesian version

of these methods.

Please read: Alternative prior distributions for variable selection with very many more variables than observations by J. Griffin and P. Brown, Technical report 2005

The class of models assumes independence between the posterior distribution of the parameters associated with segments of data between successive changepoints.

Exact calculations can be performed but the computational complexity is quadratic in the number of observations.

In a sequential framework, it is thus necessary to perform some approximations. The aim of this project is to develop several sequential Monte Carlo algorithms

in such contexts.

Please read: Exact and Efficient Bayesian inference for Multiple Changepoint Problems. by P. Fearnhead, Statistics and Computing, 2006. To appear.

Online Inference for Multiple Changepoint Problems. by P. Fearnhead & Z. Liu. Technical report, 2006.

and frequency selecting fast fading channels.

Please read: Sequential Monte Carlo Methods for Digital Communications, Elena Punskaya, PhD thesis, Cambridge University Engineering Department, 2003.

to some financial time series models.

Please read: Likelihood based inference for diffusion driven models by S. Chib, M.K. Pitt and N. Shephard, Technical report, 2004.