Probability and
Statistics Seminars: Spring 2007
Our seminars our usually held at 2.15 p.m. on Fridays
in room 3E
2.4 . If you wish to find out more, please
contact one of the organisers.
2/2/07: Takis Konstantopoulos
(Heriot-Watt)
RESCHEDULED
There will be a CAKE talk this week instead.
16/2/07: James Norris
(Cambridge)
Stochastic integrals in the plane,
and applications
I will discuss a two-parameter generalization of Ito
calculus and present some applications to diffusion
processes.
23/2/07: Nuala Sheehan
(Leicester)
RESCHEDULED
There will be a CAKE talk this week instead.
2/3/07: William Browne
(Nottingham)
Using complex random effect models
in epidemiology and ecology
In this talk we will first introduce extensions to
the standard nested random effect modelling framework
that allow crossed classifications and multiple
membership structures giving example applications to
datasets for artificial insemination in humans and
salmonella cases in Danish chickens. We will then
extend the modelling framework to multivariate mixed
responses with an ecological example of nesting
attempts of Great tits. The dataset used is a subset
from a larger dataset from Wytham Woods in
Oxfordshire and consists of 34 years of breeding
attempts. We look here at models that aim to
partition both the variability of several breeding
attempt responses (clutch size, nestling mass, lay
date, bird success and parental survival) and the
correlation between pairs of responses into genetic
and environmental influences. All models are fitted
using MCMC methods and the sparsity of the data
structures pose some interesting methodological and
practical problems which we will discuss.
16/3/07: Goran Peskir
(Manchester)
The law of the supremum of a
stable Lévy process
Abstract
23/3/07: Takis Konstantopoulos
(Heriot-Watt)
Stationary flows and uniqueness of
invariant measures
We consider a flow on a probability space which
preserves the underlying (probability) measure and
derive a relation between (i) the mean number of
visits to set A, by the trajectory of a point, until
the first time another set B is visited with (ii) the
measure of A on the event that the first time that
the set B is visited in backwards time. It turns out
that this relation generalises a classical formula
due to Mark Kac and reduces, in special cases, to the
so-called Neveu's exchange formula between Palm
probabilities (a simple relation in discrete time).
It gives a new method for proving uniqueness of
invariant measures in stochastic models such as
Harris ergodic Markov chains in general state space.
30/3/07: Günter Last
(Karlsruhe)
On Poisson Voronoi
tessellations
** Note Venue: 1W2.7 **
20/4/07: Jeremy Taylor
(Michigan)
Survival Analysis Using Auxiliary
Variables via Multiple Imputation,
with Application to AIDS Clinical
Trial Data
We develop an approach, based on multiple imputation,
that estimates the marginal survival distribution in
survival analysis using auxiliary variables to
recover information for censored observations. To
conduct the imputation, we use two working survival
models to define a nearest neighbor imputing risk
set. One model is for the event times and the other
for the censoring times. Based on the imputing risk
set, twononparametric multiple imputation methods are
considered: risk set imputation, and Kaplan-Meier
imputation. For both methods a future event or
censoring time is imputed for each censored
observation. With a categorical auxiliary variable,
we show that with a large number of imputes the
estimates from the Kaplan-Meier imputation method
correspond to the weighted Kaplan-Meier estimator. We
also show that the Kaplan-Meier imputation method is
robust to misspecificationof either one of the two
working models. In a simulation study with time
independent and time dependent auxiliary variables,
we compare the multiple imputation approaches with an
inverse probability of censoring weighted method. We
show that all approaches can reduce bias due to
dependent censoring and improve the efficiency. We
apply the approaches to AIDS clinical trial
datacomparing ZDV and placebo, in which CD4 count is
the time-dependent auxiliary variable.
27/4/07: Ian Dryden
(Nottingham)
Face shape identification: how
different are we?
How different are people's faces? Could information
on the 3D shape of faces be used for identification
purposes? How common are faces like yours or mine? A
multidisciplinary team from the Universities of
Sheffield, Nottingham and Kent recently undertook a
project with the aim of answering such questions.
Several thousand three dimensional scans were taken
from volunteers and sets of landmarks were placed on
each scan by different observers. Techniques from
statistical shape analysis, including Procrustes
analysis and tangent space multivariate analysis of
variance are used to select key landmarks and assess
the differences between individual scans and landmark
observers. Shape variation due to covariates such as
age and sex is examined, and a face likelihood
measure is proposed as a potential tool for use in
face identification.
10/5/07: Len Thomas (St
Andrews)
[Joint Seminar with CMB]
Sequential Monte Carlo Methods to Fit Models of
Wildlife Population Dynamics **Note Time &
Venue**
Effective conservation and management of many
wildlife species depends on our being able to predict
their population response to management actions.
Mathematical models can provide a useful tool for
doing this, but only if they are realistic enough to
reflect key aspect of the species' biology and can be
calibrated to available data. We show how state-space
models provide such a framework, enabling complex
(semi-)realistic models to be constructed from simple
building blocks. Fitting the models to available data
is rather less simple - we give a brief overview of
the available methods, and describe in more detail a
computer-intensive Bayesian method we have used
called sequential Monte Carlo (aka sequential
importance sampling or particle filtering). We
illustrate all this using the example of British Grey
Seals, which spent the last century recovering from
historical over-exploitation and are now viewed by
many fishermen as a threat to their livelihood. The
seminar should be comprehensible to numerate
biologists as well as statisticians.
Time: 13.15, Venue:1W 3.6
|
University
· Search
· A-Z
Index ·
Contacts
