Type: Seminar

Modified: Mon 21 Sep 2009 1510

Distribution: World

Expiry: 22 Sep 2009

Auth: jkoonin@pisa.maths.usyd.edu.au

3pm Tuesday 22nd September Carslaw 157 Speaker: Neil Saunders Title: Strict Inequalities for Minimal Degrees of Direct Products The minimal faithful permutation degree of a finite group G denoted by μ(G) is the least nonnegative integer n such that G embeds inside the symmetric group Sym(n). Johnson and Wright first established conditions for when μ(G×H) = μ(G)+μ(H). Wright proved that nilpotent groups obey this equality and constructed a class of groups C with the defining property that for all groups G 2 C there is a nilpotent subgroup G1 of G such that μ(G1) = μ(G). At the time of these results, both Johnson and Wright were unaware of examples where μ(G × H) < μ(G)+μ(H). The referee to Wright’s paper provided an example of degree 15. Since then, examples of degree 12 and 10 have been produced and in this talk, we prove that 10 is the smallest degree where this occurs and this example is essentially unique. Time permitting, we will also detail the extent of the class C to date. Speaker: Wai Yin Wan Title: Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions We propose a robust Poisson geometric process model with heavy-tailed distributions to cope with the problem of outliers as it may lead to an overestimation of mean and variance resulting in inaccurate interpretations of the situations. Two heavy-tailed distributions namely Student-t and exponential power distributions with different tail shape and kurtosis are used and they are represented in scale mixture of normal and scale mixture of uniform respectively. The proposed model is capable of describing the trend and meanwhile the mixing parameters in the scale mixture representations can detect the outlying observations. Simulations and real data analysis are performed to investigate the properties of the model.