Bayesian estimation in a U.S. government survey of
income using respondent generated intervals
S James Press
University of California at Riverside
U.S.A.
Abstract
This paper presents some preliminary results of a U.S. Census Bureau research survey of income
in a national household sample. The survey questionnaire contained Respondent Generated
Intervals (RGI) questions requesting bounds on the estimates of items recalled. A two-stage
Bayesian hierarchical model was used to estimate population means for selected income-related
items. Questionnaire design and testing was carried out as a joint effort of statisticians and
cognitive scientists using the laboratory facilities of the U.S. Census Bureau. A Markov Chain
Monte Carlo Gibbs sampler was used to find numerical Bayesian estimates of population
parameters
Keywords:
Address for Correspondance: S. James Press
Tel. (909) 787-4241
Fax (909) 787-3286
e-mail: jpress@ucrac1.ucr.edu
Bayesian Methods for Monitoring a Comprehensive Test Ban Treaty
Robert H. Shumway
Division of Statistics
University of California, Davis
U.S.A.
Abstract
In preparation for monitoring the proposed Comprehensive Test Ban Treaty (CTBT), signed by a
majority of nations, a global array of sensors producing seismic, acoustic, and radionuclide data
is being developed that will forward data to a Prototype International Data Center (PIDC) for
analysis. Two problems of special interest to the monitoring community are (1) the location of a
presumed nuclear test and (2) the estimated yield produced by that test. Because there will be
potential violations in uncalibrated regions and data from given event may be quite limited, it is
natural to exploit the advantages available from introducing specified prior distributions and a
Bayesian perspective. We develop posterior probability ellipses for location, based on a
nonlinear regression relating estimated wave-number coordinates from several infrasound arrays
to an unknown location. For seismic yield estimation, the posterior predictive distribution of a
vector magnitude is inverted, using a multivariate regression model with joint normal -Wishart
priors. The methods are applied to the 1998 nuclear tests carried out by India and Pakistan.
Keywords: Calibration, predictive Bayes, nonlinear regression, yield estimation, event location
Address for correspondence: Robert H. Shumway, Division of Statistics, University of California, Davis, CA
95616, U.S.A.
e-mail: shumway@wald.ucdavis.edu
web site: www.stat.ucdavis.edu/~shumway
Bayesian Modeling of Economies and Data Requirements
Arnold Zellner and Bin Chen
Graduate School of Business University of Chicago
and
Abstract
In previous work, we have used Bayesian methods in the analysis of various models to explain
and forecast growth rates of real output (GDP) of 18 industrialized countries. Using these
models, point and turning point forecasts were calculated and found to be reasonably accurate
compared to those of benchmark and other models' forecasts. In current work, Marshallian
demand, supply and entry relations have been formulated for major sectors of economics along
with factor market models for input variables to provide a new Marshallian macroeconomic
model (MMM). These sectoral models are being employed using data for the U.S. to provide
various shrinkage and non-shrinkage Bayesian forecasts of sectoral outputs. These sectoral
output forecasts are summed to provide a forecast of total output that is compared to past and
recent forecasts of aggregate output using models for aggregate output. Theoretical and empirical
results indicate that it pays to disaggregate. Some overall properties of the MMM will be
described. In addition, data requirements for implementing current and future MMMs will be
discussed.
Keywords:
Address for correspondence: Arnold Zellner H.G.B. Alexander Dist. Service Prof. Emeritus of Economics
and Statistics
1101 E. 58 St., Chicago, IL 60637
e-mail: arnold.zellner@gsb.uchicago.edu
web site: http://gsbwww.uchicago.edu/fac/arnold.zellner/index.html
Twenty five years of Bayesian Inference in Psychology
Henry Rouanet
Centre de Recherche en Informatique de Paris 5
Universitι Renι Descartes
France
Abstract
Since 1974, a great deal of Bayesian research has been conducted at the Universite Rene
Descartes in close connection with psychological applications. The constant objective of this
research has been to complement the conventional statistical tools by providing sensible and
practical answers to major methodological issues such as assessing importance of effects,
especially in ANOVA (see Lecoutre's paper) and categorized data (see Bernard's paper).
Landmarks of this research are: Rouanet, Lepine, Pelnard-Considere (1976) in Advances in
psychological and Educational Measurement (Wiley); Rouanet, Lepine, Holender (1978) in
Attention & Performance VII; Rouanet, Lecoutre (1983) in Brit. J. Math. Psych.; Rouanet (1996)
in Psychological Bulletin; Rouanet, Bernard, Bert, B. Lecoutre, M.P. Lecoutre, Le Roux with a
Foreword by P. Suppes (1998) New ways in statistical methodology (Peter Lang).
Address for correspondence:
e-mail: Henry.Rouanet@math-info.univ-paris5.fr
web site:
Bayesian Analysis of Contingency Tables: Applications to Developmental
Psychology
Jean-Marc Bernard
Laboratoire Cognition et Activites Finalisees
University Paris 8 & CNRS
France
Abstract
We present a series of Bayesian data analysis methods (Bernard, Charron, 1996a and 1996b,
Math. Inf. Sci. Hum., 134, pp. 5-38 and 135, pp. 5-18; Danis, Bernard, Leproux, in press, Brit. J.
Devel. Psych.) which all aim at analyzing local dependencies within an AxB contingency table
and thus allow a detailed investigation of the direction of association, rather than merely
focussing on the global dichotomy "independence vs. association". A basic idea in these methods
is to confront the observed data with some specific association model which may be either a
logical model -- which predicts the absence of some cells in the table --, or a less strong model -which only predicts some particular pattern of over-/under-representation of the cells in the table.
These two kinds of issues are illustrated with experimental data from Developmental Psychology
research (experimental investigation of the Piaget's stage concept, sequential analysis of
adult/child interactions in a situation of picture-book reading). The methods combine descriptive
and inductive aspects. At the descriptive level, the existence and the strength of local association
is measured by several related association indices: association rates, mean association rates,
implicative indices, and the "Del" index proposed by Hildebrand, Laing & Rosenthal (1977,
Prediction Analysis of Cross Classifications, Wiley). The inductive step -- generalizing the
descriptive conclusions to a larger population (multinomial sampling) -- is envisaged from an
"objective" Bayesian viewpoint using either standard non-informative Dirichlet priors or the
imprecise Dirichlet model (Walley, 1996, JRSS B, 58, pp. 5-37). We stress the high flexibility of
the Bayesian approach to inference, in the sense that it enables one to investigate the
generalisability of any conclusion emerging from the descriptive step, and, in particular here, one
that states that the data support some particular association model of interest. Finally, we briefly
describe some recent extensions to the analysis of higher dimensional contingency tables
(Bernard, to appear, J. Stat. Plann. Inf.).
Keywords: Measure of association, Logical model, Quasi-implication, Association model, Noninformative prior, Imprecise Dirichlet model.
Address for correspondence:
Jean-Marc Bernard
Laboratoire Cognition et Activites Finalisees
CNRS ESA 7021
Universite Paris 8
2 rue de la Liberte
93526 Saint-Denis Cedex
France
e-mail: berj@univ-paris8.fr
Bayesian predictive procedures for designing and planning experiments
Bruno Lecoutre
C.N.R.S.
Universit de Rouen
France
Abstract
In recent years many authors have stressed the interest of the Bayesian predictive approach for
designing ("how many subjects?") and monitoring ("when to stop?") experiments. The predictive
distribution of a test statistic can be used to include and extend the frequentist notion of power in
a way that has been termed predictive power or expected power. More generally, Bayesian
predictive procedures give the researcher a very appealing method to evaluate the chances that
the experiment will end up showing a conclusive result, or on the contrary a non-conclusive
result. The prediction can be explicitly based on either the hypotheses used to design the
experiment, expressed in terms of the prior distribution, or on partial available data, or on both.
Keywords:Experimental data monitoring, Predictive distributions, Sample size determination,
Stochastic curtailment, Average power.
Address for correspondence: Bruno Lecoutre, UPRESA 6085, Analyse et Mod?les Stochastiques, C.N.R.S. et
Universit? de Rouen, Math?matiques, Site Colbert, 76821 Mont-Saint-Aignan Cedex, France.
e-mail: bruno.lecoutre@univ-rouen.fr
Perfect sampling of Bayesian mixtures
Duncan Murdoch and Xiao-Li Meng
Department of Statistical and Actuarial Sciences
University of Western Ontario
Canada
and
Department of Statistics
University of Chicago
U.S.A.
Abstract
Perfect sampling using the coupling from the past (CFTP) algorithm was introduced by Propp
and Wilson in 1996. In much the way rejection sampling allows one to convert samplers from
one distribution into samplers from another, CFTP allows one to convert Markov chain Monte
Carlo algorithms from approximate samplers from the steady-state distribution into perfect ones.
Since 1996 CFTP has been applied to many different Markov chains. In this paper we describe
our work applying it to Bayesian mixture priors and mixture likelihoods
Keywords: Coupling from the past, perfect sampling, mixtures.
Address for correspondence: Duncan Murdoch, Dept. of Stat. and Act. Sci, University of Western Ontario,
London, ON N6A 5B7 Canada
e-mail: murdoch@stats.uwo.ca
web site: http://www.stats.uwo.ca/murdoch
Perfect MCMC tempering for sample-based Bayesian inference
Jesper Moeller and Geoff Nicholls
Department of Mathematical Statistics
Aalborg University
Denmark
and
Department of Mathematics
University of Auckland
New Zealand
Abstract
Perfect simulation algorithms based on Propp and Wilson (1996) have so far been of limited use
for sampling problems of interest in statistics. We specify a new family of perfect sampling
algorithms obtained by combining MCMC tempering algorithms with dominated coupling from
the past, and demonstrate that our algorithms will be useful for sample based inference.
Keywords: Dominated coupling; Exact sampling; MCMC; tempering.
Address for correspondence: Geoff Nicholls, Mathematics Department, Auckland University, Private Bag 92019,
Auckland, New Zealand
e-mail: nicholls@math.auckland.ac.nz
web site: http://www.math.auckland.ac.nz/~nicholls/
Parallel Antithetic Coupling for Perfect Bayesian Simulation
Xiao-Li Meng and Radu V. Craiu
Department of Statistics
The University of Chicago
USA
Abstract
Constructing efficient perfect simulation algorithms has been a very active area of research since
the innovative work of Propp and Wilson (1996). In this talk we propose the use of antithetic
variates in parallel implementation of perfect simulation, aiming for substantial reduction of
Monte Carlo error with little increase in computational load. We will discuss various methods for
generating antithetic variates, in particularly the iterative hypercube sampling method, which
incidentally generates a set of intriguing fractals. The theory of negative association, which
studies the preservation of negative correlation under monotone transformations, will be central
in our constructions. To illustrate the potential of our method in perfect Bayesian simulation, we
apply it to perfect sampling from the posterior distribution of the mixing parameter when the
prior belongs to the beta family.
Keywords: antithetic variates, negative association, hypercube sampling, backward coupling,
mixture model.
Address for correspondence: Xiao-Li Meng, 5734 S University Ave., Chicago, Il 60637, U.S.A.
e-mail: meng@galton.uchicago.edu
web site: http://galton.uchicago.edu