Statistical Laboratory Seminars
Lent Term 2002
Centre for Mathematical Sciences
Wilberforce Road, Cambridge, CB3 0WB
Tel: (01223) 337958
Fax: (01223) 337956
Email: [log in to unmask]

Seminars will be held in Meeting Room 12
All interested are welcome


2.00 pm Friday, 15 February
Shaun Seaman (MRC Biostatistics Unit, Cambridge)

Equivalence of Prospective and Retrospective Models in the Bayesian
Analysis of Case-Control Studies

The natural likelihood to use for a case-control study is a
`retrospective' likelihood, i.e. a likelihood based on the probability of
exposure given disease status. Prentice & Pyke (1979) showed that the
maximum likelihood estimates obtained from the retrospective likelihood
are the same as those obtained from the `prospective' likelihood
(i.e. that based on probability of disease given exposure). Until now, no
such result was available for the Bayesian analysis.
I shall show how Prentice & Pyke's result may be proved more easily and
how an analogous result may be obtained for the Bayesian analysis. That
is, I shall show that Bayesian analysis of case-control studies may be
done using a relatively simple model, the logistic regression model, which
treats data as though generated prospectively and which does not involve
nuisance parameters for the exposure distribution. This model can be
fitted using the software WinBUGS.

2.00 pm Friday, 22 February

Alan Welsh (University of Southampton)

Incomplete detection in enumeration surveys

We consider the problem of undercount or incomplete detection in
enumeration surveys which are intended to estimate population counts or
population abundance. The problem is widespread in ecology but also occurs
in other surveys: The census undercount is a well-known example of the
problem. After framing the problem in a general context, we focus on line
transect sampling and the distance sampling methodology which has been
widely applied in surveys of ecological populations. We describe distance
sampling data and present a graphical derivation of the distance sampling
estimator. Our graphical analysis leads to an expression for the distance
sampling estimator which gives useful insights into the nature of the
estimator. We discuss the uniformity assumption on which distance sampling
depends and describe the properties of the distance sampling estimator
when uniformity does not hold. We then explore the relationship between
this and other evaluations of distance sampling. We mention briefly some
statistical ideas for treating the general incomplete detection problem
and conclude with some reflections on general insights arising from the
research.
The talk will blend biometric and survey ideas. The intention throughout
is to develop and explore the key ideas conceptually so the presentation
should be accessible to a wide audience.

2.00pm Friday, 1 March

Alastair Young (Statistical Laboratory, Cambridge)

Resampling and Adjusted Nonparametric Profile Likelihood

As is the case in the parametric context, a nonparametric profile
likelihood is not a genuine likelihood, in that the expectation of the
profile score is not identically zero, and does not even vanish
asymptotically. Asymptotic expansion of the expectation of the profile
score allows construction of adjusted versions of nonparametric profile
likelihood, but what is the effect of the adjustment on estimators and the
accuracy of asymptotic approximations to the distributions of test
statistics? Cases where the appropriate estimator is understood suggest
that the adjustments do indeed produce the desired results, but, by
contrast to what is seen in the parametric context, the asymptotic
approximation to the distribution of the likelihood ratio statistic
constructed from adjusted nonparametric profile likelihood can be
inadequate. Bootstrap calibration is therefore necessary to replace the
asymptotic distribution. But, in that case, what gains are to be made from
bootstrapping the adjusted nonparametric profile likelihood ratio
statistic, rather than bootstrapping the unadjusted one, which is already
known to provide very accurate inference?
[This is joint work with Tom DiCiccio and Anna Clara Monti.]

2.00pm Friday, 8 March

Hein Putter (Department of Medical Statistics, Leiden University Medical
Centre)

A Bayesian approach to parameter estimation in HIV dynamical models

In the context of a mathematical model, describing HIV-infection, we
discuss a Bayesian modelling approach to a nonlinear random effects
estimation problem. The model and the data exhibit a number of features
that make the use of an ordinary nonlinear mixed effects model
intractable: 1. the data are from two compartments fitted simultaneously
against the implicit numerical solution of a system of ordinary
differential equations, 2. data from one compartment are subject to
censoring, and 3. random effects for one variable are assumed to be from a
beta distribution. We show how the Bayesian framework can be exploited by
incorporating prior knowledge on some of the parameters, and by combining
the posterior distributions of the parameters to obtain estimates of
quantities of interest that follow from the postulated model.

Seminar Organiser: Dr S.M.Pitts