Bayesian Analysis in Official Statistics: The EUROSTAT "Bayoff" Project
D., Rios-Insua, J. L., Cervera and P., Dellaportas
Department of Statistics, University Rey Juan Carlos, Spain
INE, Spain
and
Department of Statistics,University of Athens,Greece
Abstract
BayOff is an exploratory project supported by EUROSTAT to study the feasibility of the
application of Bayesian methods to the analysis of official statistics. We describe the
development and main findings of the project, providing a strategy for the adoption of Bayesian
methods within NSIS
Keywords: Official Statistics, Bayesian Methods
Address for correspondence: Rios-Insua, D., ESCET, Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles,
Madrid (Spain)
e-mail: drios@escet.urjc.es
web site: www.urjc.es
Institutional Evaluation: An Application of Bayesian Ordinal Regression
Arminda Moreno Diaz and David Rios Insua
Artificial Intelligence
Technical University of Computer Science
Spain
and
School of Experimental Science and Technology
Rey Juan Carlos University
Spain
Abstract
We present a model which is a multivariate extension of cumulative ordinal models in the special
framework considered by Albert and Chib (1998) and it can be viewed also as a polychotomous
extension of multivariate probit models considered in Chib and Greenberg (1998). We also
provide a simulation-based Bayesian algorithm for sampling the posterior distribution. The
model is illustrated in detail with a real data example on customer satisfaction surveys whose
nature is that of a bivariate ordinal response.
Keywords: Cumulative Models, Gibbs sampling, Latent variable, Metropolis-Hastings
algorithm, Ordinal variable.
Address for correspondence: Arminda Moreno Diaz
Departamento de Inteligencia Artificial
Facultad de Inform?tica. U.P.M
Campus de Montegancedo. Boadilla del Monte.
28660 Madrid.
e-mail: amoreno@fi.upm.es
web site:
PLAZA: A Tourism Management System
E., Fern?ndez, J. M., Mar?n, I., Olmeda and D., R?os-Insua
Statistics
University Rey Juan Carlos
Spain
Abstract
PLAZA is a project sponsored by the government of the Balear Islands to manage tourism,
which is their main economic resource. The project involves many statistical issues such as
forecasting the number of tourists visitors and the hotel occupancy rates, based on data from
automatic booking systems, as well as implementation issues relative to heterogeneus databases
and web designs. We describe different phases of the project with emphasis on statistical issues.
Keywords: Dynamic Linear Models, Tourism
Address for correspondence: R?os-Insua, D., ESCET, Universidad Rey Juan Carlos, Tulipan s/n, 28933 Mostoles,
Madrid (Spain)
e-mail: drios@escet.urjc.es
web site: www.urjc.es
Spatial mixtures of Poisson distributions
Sylvia Richardson and Peter J. Green
Unitι 170
INSERM
France
and
Department of Mathematics
University of Bristol
UK
Abstract
We present a mixture-model based approach to the analysis of spatial data. Building on the
conventional formulation used in geographical epidemiology: yi ~ Poisson((iEi), independently
for i = 1, 2 ...n, where yi denotes the observed count of cases in region i and Ei the expected
count (adjusted for age, sex ...), we consider mixture models for (i of the form (i = (zi , where zi
are allocation variables taking values in {1, 2, ..., k} and {(j, j=1,2, ...k} characterise k
components. The novelty lies in the allocation model which follows a spatially correlated
process, the Potts model, and in treating the number of components k of the spatial mixture as
unknown, using reversible jump MCMC. Performance of the model and comparison with
alternative approaches will be demonstrated on synthetic data sets. Analyses of the mortality for
rare cancer in France at the level of the 95 French departments will be presented.
Keywords: Mixtures, Spatial modeling, Potts model, geographical epidemiology
Address for correspondence: Sylvia Richardson, INSERM U. 170, 16 avenue P. V. Couturier, 94807 Villejuif,
France
e-mail: richardson@vjf.inserm.fr
web site: http://ifr69.vjf.inserm.fr/~u170/sylvia/
Joint Disease Mapping
Leonhard Knorr-Held and Nicola G. Best
Institute of Statistics University Munich
Germany
and
Department of Epidemiology and Public Health
Imperial College School of Medicine
UK
Abstract
The study of spatial variations in disease rates (disease mapping) is a classic epidemiological
technique, where location is used as a surrogate for the mix of lifestyle, environmental and
possibly genetic factors that may underly geographical differences in risk. The purpose is both to
describe such variations and to generate hypotheses about the possible `causes' which could
explain them. The last decade has seen an enormous development in Bayesian methodology
available to carry out such analyses, including the use of realistically complex models to account
for overdispersion and spatial correlation. These developments have focused almost exclusively
on modelling of a single disease; however, many diseases share common risk factors (smoking
being an obvious example) and hence a joint formulation which simultaneously models spatial
variations in the risk of two or more related diseases may be a more powerful design for
detecting geographical patterns in the underlying risk surface.
This talk introduces various formulations for the joint spatial analysis of two diseases. The
proposed methodology can be divided into two classes: multivariate models, which focus on the
correlation structure between the diseases; and joint component models, which aim to identify
shared and disease-specific spatially-varying latent risk factors. The methodology will be
illustrated through various examples.
Keywords: cluster models;hierarchical modelling; joint disease mapping; latent variables;
Markov chain Monte Carlo; shared component models
Address for correspondence:Leonhard Knorr-Held
Institute of Statistics
University Munich
Ludwigstr. 33
80539 Munich
Germany
e-mail:leo@stat.uni-muenchen.de
web site: http://www.stat.uni-muenchen.de/~leo/
Assessing the Fit of Disease Mapping Models
Hal S. Stern and Noel Cressie
Department of Statistics
Iowa State University
USA
and
Department of Statistics
Ohio State University
USA
Abstract
Disease incidence or disease mortality rates for small areas are often displayed on maps. Maps
of raw rates, disease counts divided by the total population at risk, have been criticized as
unreliable due to nonconstant variance associated with heterogeneity in base population size.
This has led to the use of model-based Bayes or empirical Bayes point estimates for map
creation. Because the maps have important epidemiological and political consequences, for
example, they are often used to identify small areas with unusually high or low unexplained risk,
it is important that the assumptions of the underlying models be scrutinized. We review the use
of posterior predictive model checks, which compare features of the observed data to the same
features of replicate data generated under the model, for assessing model fitness. One crucial
issue is whether extrema are potentially important epidemiological findings or merely evidence
of poor model fit.
Keywords: Bayesian methods, spatial models, posterior predictive model checks
Address for correspondence: Hal S. Stern, Department of Statistics, Iowa State University, Snedecor Hall,
Ames, IA 50011, USA
e-mail: hstern@iastate.edu
Prior Distributions on Symmetric Groups
Paul, Damien and Jayanti, Gupta
School of Business Administration
University of Michigan
USA
and
Department of Statistics
University of Michigan
USA
Abstract
Using the notion of conjugacy classes, prior distributions are constructed on the symmetric
group. Full Bayesian inference is illustrated for fully and partially ranked data.
Keywords: Conjugacy classes, Binary Tree, Coset spaces, Permutation group
Addresses for correspondence: Paul Damien, University of Michigan Business School, USA
e-mail: pdamien@umich.edu and
Jayanti Gupta, Department of Statistics, University of Michigan, USA
e-mail: jayanti@umich.edu
Dependent Nonparametric Processes
Steven, MacEachern
Department of Statistics
The Ohio State University
USA
Abstract
Nonparametric Bayesian methods have proven to be extremely useful for providing flexible
models that are capable of fitting an extraordinarily wide array of data sets. Two of their most
natural uses are in providing distributions for random effects and in providing large classes of
models that elaborate on a parametric model. However, current nonparametric models are
inadequate in that they do not easily accomodate covariates. Currently, two distinct distributions
of random effects are (conditionally) independent realizations from a nonparametric prior
distribution; either a single elaboration or several independent elaborations are conducted.
The remedy for these, and many other inadequacies, lies in dependent nonparametric processes.
In particular, extension of the Dirichlet process provides a class of models that are attractive
conceptually and computationally, and that capture many fundamental modeling strategies,
which have heretofore been inaccessible. These models facilitate Bayesian data analysis,
enabling the Bayesian statistician to directly investigate issues for which other methodologies
provide only tangential approaches.
In this talk, I will motivate and introduce these distributions, describe their basic properties, and
indicate their usefulness in a number of problems.
Keywords: Dirichlet process, regression.
Address for correspondence: Steven MacEachern, Department of Statistics,
Ohio State University, 404 Cockins Hall, 1958 Neil Ave., Columbus, OH 43210, USA
e-mail: snm@stat.ohio-state.edu
Full Bayesian Inference Under Dirichlet Process Modeling
Alan E. Gelfand
University of Connecticut, Storrs,
CT, U.S.A
Abstract
For k-sample problems there is no evident benefit to working with parametric models. A fully
nonparametric approach can be as easily handled. Many classical nonparametric approaches are
limited to hypothesis testing. Those that allow estimation are limited to certain functionals of the
underlying distributions. Moreover, the associated inference often relies on asymptotics when, in
practice, nonparametric specifications are most appealing for smaller sample sizes.
Bayesian nonparametric approaches avoid asymptotics but, to date, have been limited in the
range of inference. Working with Dirichlet process priors, we show how to obtain the entire
posterior for very general classes of functionals. We provide a variety of illustrations, including a
one-way ANOVA, comparison of survival distributions under censoring, and stochastic order
restrictions.
Keywords:
Address for correspondence:
e-mail: alan@merlot.stat.uconn.edu