Bayesian Methods for Complex Surveys with Unit Nonresponse
Trivellore, Raghunathan
Institute for Social Research and Department of Biostatistics
University of Michigan
USA
Abstract
Bayesian methods provide a unified framework for handling complex design features and unit
nonresponse in the analysis of a survey data. This paper develops weighted estimates of
descriptive and analytical statistics and the associated probability intervals from a Bayesian
perspective that incorporates the complex design features such as clustering, stratification,
sampling with unequal probabilities, poststratification and unit nonresponse. A random effect
general location model with some known margins is used to model the joint distribution of the
survey, population, and design variables. The posterior distributions of the population quantities
so derived are used for inferential purposes. Repeated sampling properties of the point and
interval estimates are evaluated and compared to the standard randomization based estimates.
Keywords: Post-stratification, Randomization, Stratified cluster samples, Unequal selection
probabilities
Address for correspondence: T. E. Raghunathan, 426 Thompson street, University of Michigan, Ann Arbor, MI
48109-1248, USA
e-mail: teraghu@umich.edu
web site: http://www.sph.umich.edu/biostat/teraghu.html
Election forecasting: A Mexican experience
Raúl Rueda
Department of Probability and Statistics
National University of Mexico
Mexico
Abstract
In the Mexican Federal Elections, that have place every three years, it is desirable to have
preliminary results a few hours after the electoral pools close. Since many electoral pools are too
difficult to access, a clasification process, based in the Kullback-Lieble divergence, is used to
choose a sample that will be use, in a conjugate analysis, to make the electoral forecasting. Some
results of the 1994 election will be presented.
Keywords: Kulback-Liebler divergence, forecasting, conjugate analysis
Address for correspondence: Raúl Rueda, Apdo. Postal 20-276, 01000 Mexico D.F.
e-mail: pinky@sigma.iimas.unam.mx
Empirical and hierarchical Bayes small area estimation for the Italian Labour
Force Survey
Claudia, De Vitiis, Piero D., Falorsi, Stefano, Falorsi, Daniela Pagliuca and Aldo, Russo
Istituto Nazionale di Statistica
Italy
and
Roma Tre University
Italy
Abstract
The topic of small area estimation has received much attention in the recent statistics literature.
Small area estimation is concerned with using sample data from a population, scattered over a
large domain, to make inferences about the average, or total, of some quantity in sub domains of
that population. The problem of small area estimation can, in many instances, be formulated as a
special case of the general problem of predicting the realization of a random variable w based on
the value of an observable random vector y , when y follows a mixed linear model with a single
set of random effects and w is a linear combination of fixed and random effects. A primary
purpose of the present paper is to review and discuss some recent results on the general predition
problem and the special case of small area estimation. Our coverage includes both frequentist
and bayesian approches. In particular, we discuss the relationships between the approches,
examine the computations required to implement the various approches. The frequentist
properties of the bayesian and non-bayesian procedures are evaluated using sample data of
Italian Labour Force Survey.
Keywords: Small area estimators, Mixed linear models , Bayesian approches
Address for correspondence: Stefano Falorsi, via A. Depretis, 74/B 00185 Roma Italy
e-mail: stfalors@istat.it
Reversible jump MCMC analysis of spatial Poisson cluster processes
John Castelloe
Linear Models R&D
SAS Institute Inc.
USA
Abstract
A reversible jump Markov chain Monte Carlo (RJMCMC) technique for bivariate normal
mixtures with common covariance matrix is developed and applied to a special type of spatial
point process, namely the Poisson cluster process with bivariate normal offspring dispersal.
Inference for this type of process focuses on the common covariance matrix of the offspring
dispersal distribution. RJMCMC extends the traditional MCMC capabilities by providing for
transitions between different parameter spaces, which are needed in our situation due to the
unknown number of clusters. A new convergence assessment method, applicable to any
RJMCMC situation in which distinct models can be identified, is designed and theoretically
justified. A "model" in our case is a given number of clusters, in other words, the number of
components in a mixture. Output analysis methods are also developed, including anisotropy
testing/estimation and inference for number of clusters. The RJMCMC technique is flexible and
has potential to apply to more complicated spatial point processes, and also other mixture-related
problems. A second newly developed method, discussed briefly for comparison, combines EM
algorithm parameter estimates, computed separately for different numbers of clusters, in a
Bayesian model averaging type scheme. A "composite EM" estimator of the covariance matrix is
thus constructed, along with an estimated asymptotic variance computed from a combination of
observed information matrices.
Keywords: bivariate normal mixture, convergence assessment, reversible jump MCMC, Poisson
cluster process, mixture models, EM algorithm
Address for correspondence: John Castelloe, SAS Institute Inc., SAS Campus Dr., Cary, NC, 27513, USA
e-mail: john.castelloe@sas.com
web site: http://www.stat.uiowa.edu/~jcaste
Bayesian Partitioning for Estimating Disease Risk
David Denison and Chris Holmes
Department of Mathematics
Imperial College of Science, Technology and Medicine
U.K.
Abstract
This talk presents a Bayesian nonparametric approach for the analysis of spatial count data. It
extends the Bayesian partition methodology of Holmes, Denison and Mallick (1999) to handle
data, which involves counts. A demonstration involving incidence rates of leukemia in New
York state is used to highlight the methodology. The model allows us to make probability
statements on the incidence rates around point sources without making any parametric
assumptions about the nature of the influence between the sources and the surrounding location
Keywords: Bayesian computation; Leukemia incidence data; Markov chain Monte Carlo
(MCMC); Point source; Spatial count data; Voronoi tessellation
Address for correspondence: Dr D. Denison, Dept. of Mathematics, Imperial College, 180 Queen's Gate, London,
SW7 2BZ
e-mail: d.denison@ic.ac.uk
web site: http://www.ma.ic.ac.uk/~dgtd/
Bayesian Modelling of a General Class of Random Object Cluster Forms
Andrew B. Lawson
Department of Mathematical Sciences
University of Aberdeen
UK
Abstract
The analysis of spatial data where the location of events is known provides a rich area for
Bayesian modeling. When spatial coordinates are known then spatial models focussed on the
point pattern of events can be employed. In what follows we examine the possibility of modeling
the clustering behavior of events in relation to a variety of possible cluster center types, via the
use of cluster distribution functions relating locations to putative cluster centers. Our task is to
estimate or reconstruct the center locations from data where centers are unobserved. Here centers
are taken to be either a point process or a line process exhibited at (possibly) different spatial
scales. In previous work in the area of cluster detection via parametric modelling, it has been
assumed that relatively regular clusters form around putative cluster center locations. Often these
locations have isotropic radial cluster densities around them, relating the event locations to the
centers. This leads to circular forms of clustering. These forms may be unrealistic when applied
as a uniform model across a study window. An extension to the point-process cluster center
model is examined which allows two types of cluster to be modeled. As clusters often have
relatively irregular shapes, it is useful to consider how it is possible to specify a parametric
cluster form, which can capture such irregularity. The form, which we examine here, is the line
segment. This form can be defined uniquely in space and can allow a more flexible cluster
structure. We also note that given the computational framework we adopt (i.e. RJMCMC), a
variety of line segment types can be sampled within any algorithm run, and hence different
lengths and orientations of segments will be sampled. In what follows we adopt a simple
mechanism for the proposal of line segments which involves a reversible transition from point
locations and line segments (i.e we join point centers to produce line segments and vice-versa),
thereby introducing a partition of the point center configuration into two classes: points and
lines.
Keywords: cluster line P-center L-center spatial RJMCMC
Address for correspondence: Dr Andrew B. Lawson, Dept of Mathematical Sciences, University of Aberdeen,
Aberdeen, UK AB24 3UE
e-mail: a.lawson@maths.abdn.ac.uk
web site: www.maths.abdn.ac.uk/maths/department/staff/pages/lawson_a.html
Particle methods for filtering and smoothing in time-varying autoregressions
Simon Godsill and Arnaud Doucet and Mike West
Department of Engineering, University of Cambridge, UK
and
Department of Engineering, University of Cambridge,UK
and
ISDS, Duke University,USA
Abstract
We develop methods for performing smoothing in non-linear non-Gaussian dynamical models.
The methods rely on a particle cloud representation of the filtering distribution, which evolves
through time using importance sampling and resampling ideas. In particular, novel techniques
are presented for generation of random realizations from the joint smoothing distribution and for
MAP estimation of the state sequence. Realizations of the smoothing distribution are generated
in a forward-backward procedure, while the MAP estimation procedure can be performed in a
single forwards or backwards pass of the Viterbi algorithm applied to the discretised version of
the state space. An application to spectral estimation for time-varying autoregressions is
described.
Keywords: particle filter, simulation smoothing, Viterbi, MAP estimation
Address for correspondence: Simon Godsill, Signal Processing Group, University of Cambridge, Cambridge CB2
1PZ, UK
e-mail: sjg@eng.cam.ac.uk
web site: www-sigproc.eng.cam.ac.uk/~sjg
Asymptotic Results for Interacting Particle Methods with Application to NonLinear Estimation
Pierre, Del Moral
Laboratoire de Statistique et Probabilités
Université Paul Sabatier (Toulouse III)
France
Abstract
A path-valued interacting particle systems model for the genealogical structure of a genetic
algorithm is presented. We connect this historical process with a class of Feynman-Kac
formulas. We also show how these genealogical particle models can be used to solve numerically
non-linear smoothing and filtering problems.
Keywords:
Address for correspondence: Pierre Del Moral
Laboratoire de Statistique et Probabilités
118 route de Narbonne
31062 TOULOUSE Cedex France
e-mail: delmoral@cict.fr
web site: http://www-sv.cict.fr/lsp/Delmoral/
Particle Filters for Demodulation of M-ary Modulated Signals in Noisy
Fading Communication Channels
E., Punskaya, C., Andrieu, A., Doucet and W.J., Fitzgerald
Signal Processing Laboratory, Department of Engineering
University of Cambridge
UK
Abstract
The problem of recovering a message coded as a sequence of symbols and passed through a
transmission channel is of great interest in statistical signal processing and communications. The
channel will generally corrupt the original symbol sequence (due to amplitude gain, phase shifts,
interferences and thermal noise) and the aim of this paper is to recursively compute the sequence.
Recovering the original sequence from the observations is a challenging non-linear filtering
problem, and several classical schemes have, in the past, been proposed to solve it, including the
extended Kalman filter (EKF) and the Gaussian sum filter. These sub-optimal approaches are
known to fail in realistic difficult situations. In this paper, we develop an efficient simulationbased algorithm, based on particle filters, to obtain the estimates of the posterior distribution of
the symbols from the observations. The method combines sequential importance sampling, a
selection scheme, Markov chain Monte Carlo methods and variance reduction techniques. An
application to the problem of demodulation of digital M-ary differential phase shift keyed
(MDPSK) signals are presented and an extensive simulation study is carried out. The results
show that the algorithm outperforms the current methods that are routinely used in most
communication applications.
Keywords:
Address for correspondence: W.J. Fitzgerald, Signal Processing Laboratory, Department of Engineering, University
of Cambridge, Trumpington St., CB2 1 PZ, Cambridge, UK
e-mail: wjf@eng.cam.ac.uk
web site: www-com-serv.eng.cam.ac.uk/people/wjf.html