Postgraduate Seminar: Saunders/Wan

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) < &#956;(G)+&#956;(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.