We would like to invite you to the following talks of the Eindhoven Stochastics Colloquium:
Andreas Kyprianou (University of Bath) – Some strange results in fragmentation-coalescence models
Friday 5 October, 12.45-13.30, Room MF 11-12 (4th floor, MetaForum Building, TU/e)
We analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while fragmentation breaks up a cluster into a collection of singletons. Under mild conditions on the coalescence rates, we show that the distribution of cluster sizes becomes non-random in the large-scale limit. Moreover, we discover that, in the limit of small fragmentation rate, these processes exhibit a universal heavy tailed distribution with exponent 3/2. In addition, we observe a strange phenomenon that if coalescence of clusters always involves 3 or more blocks, then the large-scale limit has no even sided blocks. Some complementary results are also presented for exchangeable fragmentation-coalescence processes on partitions of natural numbers. In this case one may work directly with the infinite system and we ask whether the process can come down from infinity. The a
nswer reveals a remarkable dichotomy.
This is based on two different pieces of work with Tim Rogers, Steven Pagett and Jason Schweinsberg.
Joris Mulder (Tilburg University) – The Matrix-F Prior for Estimating and Testing Covariance Matrices
Friday 5 October, 15.00-15.45, Room MF 11-12 (4th floor, MetaForum Building, TU/e)
The matrix-F distribution is presented as prior for covariance matrices as an alternative to the conjugate inverted Wishart distribution. A special case of the univariate F distribution for a variance parameter is equivalent to a half-t distribution for a standard deviation, which is becoming increasingly popular in the Bayesian literature. The matrix-F distribution can be conveniently modeled as a Wishart mixture of Wishart or inverse Wishart distributions, which allows straightforward implementation in a Gibbs sampler. By mixing the covariance matrix of a multivariate normal distribution with a matrix-F distribution, a multivariate horseshoe type prior is obtained which is useful for modeling sparse signals. Furthermore, it is shown that the intrinsic prior for testing covariance matrices in non-hierarchical models has a matrix-F distribution. This intrinsic prior is also useful for testing inequality constrained hypotheses on variances. Finally through simulation it is shown that
the matrix-variate F distribution has good frequentist properties as prior for the random effects covariance matrix in generalized linear mixed models.
Upcoming events of the Eindhoven Stochastics Colloquium: http://www.win.tue.nl/StoSem/