Abstract:
We consider Gaussian mixtures and particularly the problem of testing
homogeneity, that is testing no mixture, against a mixture with two
components. Seven distinct cases are addressed, corresponding to the
possible restrictions on the parameters. For each case, we give a statistic
that we claim to be the likelihood ratio test statistic. The proof is given
in a simple case. With the help of a bound for the maximum of a Gaussian
process we calculate the percentile points. The results are illustrated by
simulation.

2.  Title: Time series and spatial models for solar radiation
    Author: C. Glasbey

Abstract:
Solar radiation, when adjusted for solar angle, is bimodally
distributed.  The two modes are produced by cloudy times, when radiation
is indirect, and cloud-free times, when radiation is direct.  For time
series of solar radiation at a single site, I have proposed a new form
of nonlinear autoregressive process, by specifying joint marginal
distributions at low lags to be multivariate Gaussian mixtures.  The
time series data can be interpreted as a random linear transect of an
isotropic spatial process.  However, it does not seem to be possible to
generalise the model to a spatial process.  Therefore, instead, I have
developed a model based on moving averages.

3.  Title: Mixture models in measurement error problems
    Authors: S Richardson, L Leblond, I Jaussent and P.J Green

4.  Title: The Observed Association Structure from Graphical Gaussian Models with a Single Latent Variable
  Authors : M. Fatima Salgueiro, John W. McDonald and Peter W.F. Smith

Abstract:
We investigate the observed association structure
between manifest variables arising from simple factor models. In
particular, we consider the cases of a single continuous latent
variable with either two or three continuous manifest variables.
The simple factor model is represented as a Graphical Gaussian
model. We use a simulation study to estimate the power of a
backwards elimination selection procedure. Results show that the
underlying factor model can give rise to an observed association
structure between the manifest variables that is not necessarily
the true model, i.e. the saturated model. For the two manifest
variables case power is symmetric about zero and increases with
departures from zero correlation, and also as sample size
increases. However, when three manifest variables are present,
some non-symmetry and non-monotonicity can be observed,
particularly associated with small partial correlation values.

5.  Title: Covariance Kernels from Bayesian Generative Models
    Author: Matthias Seeger

Abstract:
We propose a general method for constructing covariance kernels for
discriminative methods like Gaussian Process classifiers from posterior
information obtained by Bayesian analysis on an unlabeled sample.
The kernels can be evaluated analytically whenever the Bayesian analysis
is analytically tractable. We give some examples involving conjugate
families of distributions. The recently proposed Fisher kernel (Jaakkola &
Haussler) can be seen as a first-order approximation to one of these
kernels.

By employing the recently proposed technique of Variational Bayesian
inference (Attias, Gharamani & Beal), we can derive kernels from Bayesian
mixture models. We show how this can be done for mixtures of
full-covariance Gaussians (Attias) and for mixtures of Factor Analyzers
(Gharamani & Beal).
 

6.  Title: Using mixtures of von Mises distributions to model seasonality in sudden infant death syndrome
     Author: Jenny Mooney

7.   Title: Variational inference for Bayesian structure learning
  Authors: Matthew J. Beal and Zoubin Ghahramani

8.   Title: Phase randomisation as a convergence tool in MCMC
     Author Kerrie Mengersen

9.  Title: Integrated squared error estimation of normal mixture parameters
     Authors: P.Besbeas and B.J.T.Morgan

10.  Title: Dirichlet Process Mixture Models
     Author: Carl Edward Rasmussen

11. Title:  Constraints on the posterior distribution of a finite mixture
     Author: Agostino Nobile

12. Title:  Sequential analysis of mixtures of discrete items
     Author: Colin Aitken

Abstract:
Background to the problem:     Consider a consignment (population)
of discrete items, consisting of a mixture of an unknown number of
different categories.  The problem is to construct Bayesian probability
regions for the proportion of each of the categories in the consignment
from the proportion of each category in a sample from the consignment.

Example:  In forensic science, the consignment could be a consignment
of white tablets, homogeneous in shape, size, weight, texture etc., but
possibly a mixture of several different drugs.  It is not feasible to examine
all the tablets.  A sample is to be taken in such a way that a Bayesian
probability region in the simplex of proportions can be calculated for the
true proportions.  Other possibilities are a consignment of pornographic
computer discs or a consignment of pirated compact discs.

Mixture of two categories:    The simplest case is the one in which there
are only two categories for each tablet:  a tablet contains illicit drugs or it
does not.  Then one can sample the tablets and inspect the sampled tablets.
The distribution of the proportion ofillicit drugs can be represented by a beta
distribution for a large consignment and by a beta-binomial distribution for a
small consignment.  A criterion is required for when to stop sampling.  For
example, sampling could stop if  there were a probability of 0.95 that
the true proportion of illicit drugs in the consignment were greater than 0.5.
If all the tablets sampled contained illicit drugs then it is possible, with a fairly
general assumption for the prior distribution, to stop sampling when four tablets
have been sampled.  If one of the four were not illicit then seven tablets would
need to be sampled.

Mixture of more than two categories:   The distribution of the proportions may
be Dirichlet or Dirichlet-multinomial.   What about logistic Normal distributions?
How may the total number of categories be estimated?

Questions:  How to develop a sampling protocol?  What inference can be
made after the inspection of each tablet?  When to stop?