The use of frequentist Null Hypothesis Significance Testing (NHST) is so an integral part of scientists' behavior that its uses cannot be discontinued by flinging it out of the window. Faced with this situation, our teaching strategy involves a smooth transition towards the Bayesian paradigm. Its general outlines are as follows. (1) To present natural Bayesian interpretations of NHST outcomes to call attention about their shortcomings. (2) In this way to create the need for a change of emphasis in the presentation and interpretation of results. (3) Finally to equip the students with a real possibility of thinking sensibly about statistical inference problems and behaving in a more reasonable manner. Our conclusion is that teaching the Bayesian approach for teaching statistical inference in the context of experimental data analysis appears both desirable and feasible.

Keywords: Teaching Bayesian procedures, Experimental data analysis, Bayesian interpretation of p-values, Effect sizes.
 
 

Address for correspondence: Marie-Paule Lecoutre
ERIS, Laboratoire Psy.co,
E.A. 1780, Université de Rouen, UFR Psychologie, Sociologie,
Sciences de l’Éducation, 76821 Mont-Saint-Aignan Cedex, France.
e-mail: marie-paule.lecoutre@univ-rouen.fr
 
 

We introduce Bayesian methods for decision-making in inventory models under a single period inventory model with various demand distributions. Bayesian updating is used for optimal stocking levels. We motivate the Bayesian methods through model development and choice of prior distribution. In particular, we show how to incorporate supplier uncertainty, to update in the presence of censoring and/or truncation, and to estimate perishing and demand rates. We also consider a more realistic continuous review (s, S) inventory system with uncertain demand and positive leadtimes. A sequential ordering policy is adopted where every time an order is placed, the demand distribution is estimated by Bayesian methods which utilizes the realized previous demand. The order quantity and the reorder point at so determined that the expected cost rate within the order cycle is minimized.

Keywords: newsboy problem, demand distribution, perishable inventory, backlog, lost sales, posterior updating.
 
 

Address for correspondance: Richard A. Levine
Division of Statistics,
One Shields Avenue, University of California,
Davis, CA, 95616, USA
email: ralevine@ucdavis.edu
web site: anson.ucdavis.edu/~levine
 
 

A Bayesian approach for a multidimensional item response model is proposed. We analyze multiple choice responses in multiple choice tests when there are penalties for each wrong answer such as a subtraction of points (a widely used technique that attempts to prevent student from guessing); the literature is still sparse and the usual item response theory models are inappropriately used. We extend the use of item response models to capture this situation by including guessing and threshold latent parameters. We also separate the ability of each student into several parts, which express different cognitive tasks by a multidimensional scaling approach. A Pseudo-Bayes factor model choice approach (based on cross-validation predictive densities) is used to select the number of dimensions that fit the data better. We also include appropriate latent variables so as to capture the different scenarios that may lead to an incorrect answer or to an «Non answer» response.

Keywords: Latent variables; Multidimensional scaling; Threshold parameters.
 
 

Address for correspondence: Petros Dellaportas
Athens University of Economics and Business,
76 Patission str, Athens, Greece
e-mail: petros@aueb.gr
web site: www.stat-athens.aueb.gr/~ptd/
 
 

Wavelet transformation is found a useful tool in processing 2 dimensional image data. Mallat (1989) noticed that for a variety of signals and images, the distributions of wavelet coefficients appeared to be similar. He proposed that a ``random wavelet coefficient'' can be modeled by a distribution from the family of Exponential Power Distributions. In the 2 dimensional images we examined, the auto correlation of the wavelet coefficients dampens rapidly after the first order. We propose an AR(1) process with innovations following exponential power distribution to model the wavelet coefficients and provide a MCMC simulation scheme for such model. Through a simulated example, we show that our posterior inference captures the 'true value' of the parameters.

Keywords: image processing, wavelet transformation, AR model, exponential power distribution, stable distribution, MCMC.
 
 

Address for correspondence: Jane Liu
9 W. 57th Street, 35th floor, New York, NY 10019

or Mike West
Box 90251, Duke University
Durham, NC 27708
e-mail: jane@isds.duke.edu, mw@isds.duke.edu
web site: www.isds.duke.edu/~jane,www.isds.duke.edu/~mw

The stochastic behavior of commodity prices plays a central role in Modelling approaches to the evaluation of commodity-related securities.

We develop models for commodity prices by exploiting the common latent structure of multiple time series of prices of futures contracts, based on traditional economic theories about the short-term and long-term behavior of spot prices and the relationship with futures contracts. We build on previous work of E. Schwartz and J. Smith (1998) in terms of basic model forms, and explore developments and analyses of oil future series. This work involves a new class of Bayesian dynamic multivariate time series models for analyzing the latent structure of series of futures contract prices with different maturities. This class of models is based on two latent factor processes: a notional equilibrium price level, and a process representing short-term deviations from equilibrium levels. The idea is that movements in prices for long-maturity futures contracts provides information about the equilibrium price level and differences between the prices for the short and long term contracts provides information about short-term variations in prices.

The structure of the model includes novel ideas on singular observational variance matrices that allow for a general analysis regarding uncertainty about the rank of such matrices. A major component of this project involves the development of customized MCMC simulation algorithms for model fitting and forecasting. Extensions that involve stochastic volatility components for latent processes are mentioned, and we study the application of the models and approaches in analyses of weekly crude oil futures prices.

Keywords: Commodity Futures, Dynamic Modelling, Model uncertainty, Singular variance-covariance matrix, Singular densities, Oil future prices.
 
 

Address for correspondence: Viridiana Lourdes
Box 90251. Duke University
Durham, NC 27708-0251.
e-mail: vl@stat.duke.edu
web site: http://www.isds.duke.edu

State-space models offer a flexible framework for the analysis of serially correlated data, see e.g. West & Harrison (1997) and Fahrmeir & Tutz (1994), chapter 8. The Kalman filter furnishes the state-space models with an elegant and efficient tool for inference. For non-Gaussian data these methods are only approximate. However, when applying Monte Carlo methods, a much wider class of state-space models becomes tractable. Filtering and parameter estimation can be performed in models with very complex dependence structures, by the introduction of random hyper parameters. For Gaussian or conditionally Gaussian models Gibbs sampling and block Gibbs sampling have been suggested and discussed by e.g Carlin, Polson & Stoffer (1992), Carter & Kohn (1994), and Fr?hwirth-Schnatter (1994). More recently Durbin & Koopmann (2000) have developed Monte Carlo methods for inference in certain state-space model. These methods are based on independent samples rather than on Markov chains. See also Koopmann, Shepard & Doornik (1998).

As an example we will present an analysis of time series for 20 heart-valve operated patients on self-managing oral anticoagulant therapy (OAT). The purpose of OAT is to prevent thrombosis by medication with an anticoagulant drug and close monitoring is necessary to avoid over-anticoagulation, which may lead to serious bleedings. The patients were followed from one up to four years, and in this period they regularly reported to a monitoring center, see Hasenkam et al. (1997a, 1997b). The data consist of the patients' reports of daily dosage of anticoagulant drug and weekly measurements of International Normalized Ratio (INR), which is commonly used to measure the coagulate activity.

Our analysis of the INR data has the following objectives:

1. To identify a suitable model, which adequately describes the relation between dose and response for a given patient.
2. To obtain reliable estimates for the parameters in the model.
3. To use these results to suggest a monitoring and quality assurance scheme for patients on OAT.

References

• Carlin, B., Polson, N. & Stoffer, D. (1992)  A Monte Carlo Approach to Nonnormal and Nonliniar State-Space Modelling. J. Amer. Statist. Assoc. 87, 493-500.
• Carter, C.K.. & Kohn, R. (1994) On Gibbs Sampling for State Space Models. Biometrika 81, 541-553.
• Durbin, J. & Koopman, S.J. (2000) Timeseries analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives (with discussion). To appear in J. Roy. Statist. Soc. B.
• Fahrmeir, L. & Tutz, W. (1994) Multivariate Statistical Modelling Based on Generalized Linear Models. Springer Verlag.
• Fr?hwirth-Schnatter, S. (1994) Data Augmentation and Dynamic Linear Models. Journal of Time Series Analysis 15, 183-202.
• Hasenkam, J.M., Knudsen, L., Kimose, H.H., Gr?nnesby, H., Attermann, J., Andersen, N.T. & Pilegaard, H.K. (1997a) Practicability of Patient Self-Testing of Oral Anticoagulant Therapy by the International Normalized Ratio (INR) using a Portable Whole Blood Monitor. Thromb. Res. 85, 77-82.
• Hasenkam, J.M., Kimose, H.H., Knudsen, L. Gr?nnesby, H., Halborg, J., Christensen, T.D., Attermann, J. & Pilegaard, H.K. (1997b) Self Management of Oral Anticogulant Therapy After Heart Valve Replacement. Eur. J. Cardio-Thorac. Surg. 11, 935-942.
• Koopman, S.J., Shepard, N. & Doornik, J.A. (1998) Statistical algorithms for models in state space using SsfPack 2.2*. Econometrics Journal 1, 1-55.
• West, M. & Harrison, J.F. (1997) Bayesian Forecasting and Dynamic Models. Springer Verlag.

Address for correspondence: Soren Lundbye-Christensen
Department of Mathematical Sciences, Aalborg University
Fredrik Bajers Vej 7, Dk-9220 Aalborg, Denmark
e-mail: s0ren@math.auc.dk
web site: www.math.auc.dk/~s0ren

In human genetics research, twin studies are commonly used for evaluating the possible influence of genetics on human traits. Although Bayesian methods are used in some analyses of human genetic data, such as segregation and linkage analyses, they are not typically used for analyses of human twin data. Often, the twin data are comprised of a small number of subjects and the variance component estimates representing additive genetic effects, common environmental effects and residual effects are available from prior studies. We develop a scheme for a Bayesian analysis of human twin data by developing prior elicitation schemes to incorporate historical information. We use the variance component estimates from prior studies to develop the prior distribution and use Markov chain Monte Carlo sampling algorithms to facilitate Bayesian computation. A real data example is used to illustrate the proposed methodologies.

Keywords: Bayesian methods; Gibbs sampling; Human genetics; Likelihood; Markov chain Monte Carlo; Variance Components.
 
 

Address for correspondence: Amita Manatunga
Dept of Biostatistics, Emory University,
Atlanta, GA 30322.
e-mail: amanatu@sph.emory.edu

Modelling the dispersion of pollutants in the atmosphere is necessary for a variety of reasons, including environmental protection and environmental impact assessment, amongst others. However, the physical processes involved in this dispersion are very complex and not fully understood; this creates uncertainty throughout the Modelling process. A better understanding of the uncertainties involved in Modelling is required to enable improved environmental impact assessment and also the setting of improved pollution standards.

Recently various new statistical approaches have been developed for improving this understanding and for guiding future areas of research. In this work we extend one such approach - the Generalised Likelihood Uncertainty Estimation (GLUE) method put for forward by Beven and Binley (1992). GLUE is a Bayesian approach to model calibration and uncertainty estimation that updates the likelihood for each of many sets of inputs using calibration data. Previous work using GLUE has concentrated on the input variables to the model. Here we investigate the parameters within the model and the plausibility of the values assigned them; we also investigate the output uncertainty from the model due to this parameter uncertainty.

Various atmospheric models exist; this presentation concentrates on the short range point source model, R91 (Clarke (1979)). This model assumes that a plume released from the source will diffuse according to a Gaussian distribution downwind from the source; it has long been used for environmental regulation in the UK. The work presented here uses data from the Model Validation Kit - a collection of air dispersion experiments packaged by Olesen (1995) - to calibrate the parameters and to derive distributions for the model outputs incorporating all sources of uncertainty.

References:

• Beven, K.J. and Binley, A. (1992), The future of distributed models: calibration and uncertainty prediction, Hydrological Processes, 6, 279-298.
• Clarke, R.H., (1979) A Model for Short and Medium Range Dispersion of Radionuclides Released into the Atmosphere, National Radiological Protection Board, Harwell, UK.
• Olesen, H.R., (1995), The model validation exercise at Mol: overview of results, International Journal of Pollution and the Environment, 5, 761-784.

Address for correspondence: John D. McClure,
Statistics Department, University of Glasgow, Glasgow G12 8QW, U.K.
e-mail: johndm@stats.gla.ac.uk

Graduation and overestimation of death rates play a key role in the construction of mortality tables. The usual actuarial methods deal with each of these aspects separately. Moreover, the statistical nature of these problems is typically ignored. In this paper, a simple method to produce mortality tables is proposed which simultaneously takes both issues into account. The approach is entirely statistical and allows the user to select a table providing a precisely defined level of protection against deviations in mortality. The problem is analyzed from a predictive perspective and the solution makes use of the concept of value at risk.

Address for correspondence:
e-mail: mendoza@itam.mx

Most of the methods dealing with logistic models with random intercept assume that the random intercept follows a Gaussian probability distribution. In this work, two methods allowing to relax this assumption are compared. The first one is based on a nonparametric maximum likelihood approach for mixed effect models, and it does not make any hypothesis on the random intercept distribution. The second one takes place in the context of Bayesian framework and proposes to model the prior distribution of the random intercept by Gaussian mixtures with an unknown number of components. The two methods will be compared on simulated data and on an application, which is aimed at estimating the center-effect in the prognosis of liver transplants.

Keywords: Non parametric estimation, Maximum likelihood, Bayesian estimation, MCMC, Gaussian mixture, Liver transplantation.
 
 
 
 

Address for correspondence: Florence Mesnil
INSERM U436,
CHU Pitié-salpêtrière, 91, bd de l’hôpital, 75634 Paris cedex 13, France
e-mail: fme@biomath.jussieu.fr

Assessing the relationship between spawning stock size and the resulting number of adult offspring (recruitment) is one of the most fundamental issues in fisheries stock assessment and an important cornerstone for management decisions on harvest policies in many fisheries. This paper proposes a Bayesian state-space model for fitting stock-recruitment curves. This approach eliminates at least two of the four major problems encountered in traditional stock-recruitment analyses, that of ``errors-in-variables bias’’ and ``time-series bias’’. The state-space model takes the temporal dependencies of the observations into account through a conditional Modelling of the observations, given unknown states, and specification of Markovian transition of states. Both process and observation errors are explicitly captured in the state-space model and quantified through posterior distributions of the parameters via the Bayesian paradigm. Beyond bias elimination, this approach is capable of quantifying fundamental uncertainties in parameter estimates and risks of management policies. Problems with posterior computations are overcome using Metropolis-Hastings-within-Gibbs sampling. This novel Bayesian state-space approach to stock-recruitment analysis is illustrated using a dataset on Fraser River pink salmon. The Ricker curve is employed to describe the dependence of recruitment on the spawning stock size.

Keywords: fisheries stock assessment, nonlinear state-space model, MCMC, Ricker model.
 
 

Address for correspondence: Renate Meyer
Department of Statistics, The University of Auckland,
Private Bag 92019, Auckland, New Zealand
e-mail: meyer@stat.auckland.ac.nz
web site: http://www.stat.auckland.ac.nz/meyer

This paper investigates the value relevance of accounting and financial variables. Since the changes in firm value are unobservable, studies in the literature measured the value relevance using stock returns as a proxy of the value changes. However, there has been evidence that stock returns might not reflect fully information about firm performance. This paper formulates a probability model that incorporates unobserved changes in firm value. After estimating the value changes using the Gibbs sampler, it measures the extent to which alternative variables are related to the estimates. This method does not use stock returns as a proxy of value changes, and therefore allows for a variety of value relevance analyses. The results are consistent with the ones of previous studies that stock returns is not a perfect measure of value changes and that accounting accruals increase the value relevance of current earnings.

Keywords: Gibbs sampler, value-relevance, unobserved variable.
 
 

Address for correspondence: Chung-ki Min
Department of Accountancy, The Hong Kong Polytechnic University,
Hung Hom, Kowloon, Hong Kong
e-mail: accmin@inet.polyu.edu.hk

In a Metropolis-Hastings algorithm, rejection of proposed moves is an intrinsic part of ensuring that the chain converges to the intended target distribution. However, persistent rejection, perhaps in particular parts of the state space, may indicate that locally the proposal distribution is badly calibrated to the target. As an alternative to careful off-line tuning of state-dependent proposals, the basic algorithm can be modified so that on rejection, a second attempt to move is made. A different proposal can be generated from a new distribution that is allowed to depend on the previously rejected proposal. We generalize this idea of delaying the rejection and adapting the proposal distribution, due to Tierney and Mira (1999), to generate a more flexible class of methods, that in particular applies to a variable dimension setting. The approach is illustrated by a pedagogical example, and a more realistic application, to a change-point analysis for point processes.

Keywords: Markov chain Monte Carlo methods, Metropolis-Hastings algorithms, Asymptotic variance, Peskun ordering.
 
 

Address for correspondence: Antonietta Mira,
Facolta' di Economia,
Via Ravasi 2, 21100 Varese, Italy.
e-mail: anto@ipvaim.unipv.it
web site: http://aim.unipv.it/~anto
 
 

Many experiments on human cognition involve having a subject make a judgment as quickly and accurately as possible. Both reaction times and error rates are widely used indices of human performance in such experiments. A difficulty in relying on either one of these indices alone is the problem of a speed/accuracy trade-off; subjects who react quickly are more likely to have higher error rates, whereas subjects who are more accurate are likely to have slower reaction times. Based on a competing risks approach, we propose a single measure, the error-free mean reaction time, as an index of performance. A hierarchical model is constructed for reaction times that allows natural use of Bayesian computational tools, such as data augmentation and MCMC posterior simulation.

The model is flexible enough to incorporate person-level covariates on a multi-subject setting. The approach is applied to (a) a data set on a subject's reaction times in a working memory test, and (b) a data set with multiple subjects, including covariate information.
 
 

Address for correspondence: Carlos Morales
Department of Mathematics
Boston University
111 Cummington Street, Boston, MA 02215, USA
e-mail:carlosm@math.bu.edu
 
 

From a Bayesian point of view, testing whether an observation is an outlier is usually reduced to a testing problem concerning a parameter of a contaminating distribution. This requires elicitation of both i) the contaminating distribution that generates the outlier and ii) prior distributions on its parameters. However, very little information is typically available about how the possible outlier could have been generated. Thus easy, preliminary checks in which these assessments can often be avoided may prove useful. Several such measures of surprise are derived for outlier detection in normal models. Results are applied to several examples. Default Bayes factors where the contaminating model is assessed but not the prior distribution are also computed.
 
 

Keywords: Bayes factors, nuisance parameters, plug-in p-value, prior predictive p-value, posterior predictive p-value, partial posterior predictive p-value.
 
 

Address for correspondence: Javier Morales
Department of Statistics and A.M., University Miguel Hernendez,
Avda. ferrocarril s/n, 03202 Elche (Alicante-Spain)
e-mail: j.morales@umh.es

The Bayes estimators are derived for some lifetime parameters, as well as the parameters of the Weibull model from a right censored sample. The estimators for these parameters are obtained using the squared error loss function, Varian’s linear-exponential (linex) loss function and the weighted linex loss function. A discrete prior probability distribution is placed on the shape parameter and the prior information regarding the scale parameter is summarised in the noninformative and conjugate prior probability density functions. To place a discrete prior distribution on the shape parameter for values smaller than one and greater than one, the estimator of the hazard function reduces to the bathtub-shaped hazard function of the additive Weibull model. The prediction of a future lifetime is derived using the noninformative and the conjugate prior distributions. An example illustrates the proposed estimators for the Weibull model.

Keywords: bathtub-shaped, hazard function, linex loss function, Weibull model.
 
 

Address for correspondence: Paul J Moster
Department of Statistics and Actuarial Science, University of Stellenbosch,
Private Bag X1, Matieland 7602,South Africa
e-mail: pjmos@fharga.sun.ac.za
web site: http://www.sun.ac.za
 
 

The daily newspapers regularly publish the predictions of several predictors of forthcoming horse races in the country. These predictions play an important role among punters who may believe more in one predictor than in another on a trifecta box betting. Introducing covariates such as place where the race will hold, etc. The logits of the probabilities of the one, two and three variate Bernoulli distributions are expressed as a linear function of the covariates. The parameters were estimated using the Gibbs sampler.
 

e-mail: Dries@wwg3.uovs.ac.za

Hi-tech consumer electronics is a dynamic, constantly evolving market where frequent product innovations are the norm. The rapid introduction of new models and products makes forecasting sales of new product performance very critical. Due to the dynamic environment, generating sales forecasts for new products in this industry is fraught with uncertainty.

Researchers have proposed several alternative methods to generate new product forecasts (example analogical forecasting, hierarchical Bayes (Lenk and Rao 1990)). Characteristics of high-tech product markets that make the application of existing models difficult are as follows. First, while extant research has focussed on forecasting product category size, managers in high tech markets require forecasts at a disaggregate brand-model level. High technology product markets are characterized by recurrent introduction of new models by a set of competitors.  Few observations are available at the level of each model. Second, each model provides consumers a different bundle of attributes and managers need to understand and forecast the relation between the attribute bundles and prices and the attribute bundles and sales.

We specify a model that takes into account the characteristics of high-technology markets. Sales for each model are specified as a function of price, competitive price index, lagged sales, index of competitive sales, attribute bundles and seasonality. Price is modeled as a function of exogenous costs, attribute bundles and competitive price index. Attribute bundles are specified as a function of their past values. This Modelling framework is used to generate three types of forecasts: (a) sales of existing models in future time periods (b) sales of unlaunched models and (c) sales of models that could potentially be launched by competitors as well as new R & D projects.

We use monthly data on digital cameras for three years in our empirical analysis. The number of models available in the market range from two to eighty three. The small number of observations at the model level and the sequential availability of additional data suggests DLM (Dynamic Linear Models) to be the appropriate Modelling approach (West and Harrison 1997). In particular, we model sales with a dynamic regression model with trend and growth components. The observational variance is assumed to be unknown and constant. The system variance matrix is set using the discount concept. Similar model formulations are employed for the price and attribute bundle models also. Prior information is assumed to be weak in all cases. Output from the price and attribute bundle models are used as inputs in the sales model to generate forecasts. Multi-period forecasts are generated for the last twelve months in the data set.

Our data consists of several time series at the brand-model level. However, in contrast to previous research on multivariate time series (Quintana and West (1987, 1988)), we do not have the same number of observations for each of the series. Our model estimation needs to account for the sequential arrival of different amounts of information while at the same time pooling information across models. We do this by specifying a hierarchical statistical model. A probabilistic distribution is specified for the parameter vector and hyperparameters are estimated using empirical Bayes methods (Duncan, Gorr and Szczypula 1993).

Our analysis provides insights into the relative effects of different attribute bundles and prices on sales. We also obtain an understanding of the effects of different attributes on price setting decisions. We compare the forecasting performance of our model with a hierarchical Bayes model with brand-level parameters and a naïve pooled OLS model.

References

• Duncan, G, Gorr, W, Szczypula, J. (1993), Bayesian forecasting for seemingly unrelated time series: Application to local government revenue forecasting, Management Science v39, n3 (Mar):275-293.
• Lenk, P J. and Rao, A. (1990), "New Models from Old: Forecasting Product Adoption by Hierarchical Procedures" Marketing Science v9, n1 (Winter):42-57.
• Quintana, J. M. and West, M. (1987), Multivariate time series analysis: new techniques applied to international exchange rate data, The Statistician 36, 275-281.
• Quintana, J. M. and West, M. (1988), Time series analysis of compositional data. In Bayesian Statistics 3, J.M. Bernardo, M.H. DeGroot, D.V. Lindley, and A.F.M. Smith (Eds). Oxford University Press.
• West, M., and Harrison, J. (1997), Bayesian forecasting and dynamic models, 2nd ed. Springer, New York.

Address for correspondence: Ramya Neelamegham
College of Business & Administration, University of Colorado
Boulder, CO 80309
e-mail: rneelamegham@hotmail.com

The 1992 Demographic and Health Surveys (DHS) dataset from Malawi, Tanzania and Zambia are used in this poster.

We estimate a bayesian semiparametric additive regression models with dependent variables respectively Height-for-Age Z-score (Stunting), Weight-for-Height Z-score (Wasting) and Weight-for-Age Z-score (Underweight) for the Undernutritional regression models and Infants and Child mortality rates as a responses variables for the mortality logistic regression models using modern Markov chain Monte Carlo simulation techniques. We present a unified approach for Bayesian inference via Markov chain Monte Carlo (MCMC) simulation in generalized additive mixed models. Different types of covariates, such as usual covariates (categorical) with fixed effects, metrical covariates such as birth order, the preceding interbirth interval...with nonlinear effects, unstructure random effects in surveys data are all treated within the same general framework by assigning appropriate priors with different forms and degrees of smoothness  to explore the effects of metrical covariates , asses and explain substantial variation and differences in mortality risk and Undernutrition status across socioeconomic and demographic segments of national population.

We estimate random effect models to show substantial variation on the proportion Stunted, wasted and underweight child, and Infants and Child mortality rates between countries and within countries

Keywords: generalized semiparametric mixed models, Markov chain Monte Carlo, random effects, semiparametric Bayesian inference, Anthropometric measures, Undernutrition status.
 
 

Address for correspondence: Kandala Ngianga-Bakwin
Institut fur Statistik,
Ludwigstr.33, D-80539 M?nchen, University of Munich, Germany
Email: kandala@stat.uni-muenchen.de
web site: www.stat.muenchen.de
 
 

This work considers a statistical analysis framework for inverse problems involving Poisson data based on Bayesian tree-structured models. Such problems arise in medical image tomography and computer network tomography applications.

For medical imaging, the tree-structured framework is based on a multiscale analysis associated with recursive partitioning of the underlying image intensity, a corresponding multiscale factorization of the likelihood (induced by this analysis), and a choice of prior probability distribution made to match this factorization by Modelling the ``splits'' in the underlying partition and reflect prior belief as to the smoothness of the unknown intensity. Adopting the expectation-maximization (EM) algorithm for use in computing the maximum a posteriori estimate corresponding to the model, we find that the model permits remarkably simple, closed-form expressions for the EM update equations and leads to high quality image reconstructions.

Network tomography is a promising new technique for studying the (internal) behaviour of large-scale computer networks based solely on end-to-end measurements. Tree-structured models arise naturally here due to the physical topology of computer networks. Based on these models, we demonstrate that it is only possible to resolve internal losses if reasonable prior information and constraints are identified and incorporated in an Modelling/inference framework. Inference calculation is carried out using a novel factor graph representation. Simulation experiments demonstrate the potential of our new framework.
 
 

Address for correspondence: Robert Nowak
Electrical and Computer Engineering
George R. Brown School of Engineering,
Rice University 2041 Duncan Hall, Houston, TX USA
e-mail: nowak@ece.rice.edu

We consider the problem of prior specification for model selection with emphasis on the normal linear model. The main problem in prior specification when no information is available is that we cannot use improper priors on model parameters due to the unknown normalizing constants involved in the calculation of the posterior odds. Moreover, even if we use proper prior distributions on model parameters, the posterior odds are very sensitive on the magnitude of the prior variance, tending to support the simpler models the prior variance increases (Lindley-Bartlett paradox, 1957). The aim is to find a prior distribution that will be non-informative within each model (in the sense that the posterior modes will be close to the maximum likelihood estimates), and coherent in terms of dimension penalty imposed between models. We further investigate whether we can use simpler prior distributions in variable selection setups and we argue that in collinear cases this leads to paradoxes. An alternative prior specification technique, which enables us to eliminate the prior variance effect on the posterior odds, to impose the penalty we prefer for each additional parameter included in the model and to achieve the desired coherency, is proposed.

Keywords: Collinearity, Information Criteria, Penalty, Variance Effect.
 
 

Address for correspondence: Ioannis Ntzoufras
78, Fleming Street, 16233, Byronas, Athens, Greece.
e-mail: jbn@stat-athens.aueb.gr
 
 

We present multivariate Polya tree based methods for Modelling multidimensional probability distributions. The Polya tree prior is applied to a multidimensional Euclidean space. Using binary perpendicular recursive partitioning of a hyper cube in R^K, a simulation scheme for exploring conditional relationships among K variables in a K-dimensional space is developed. Its usefulness for missing data imputation is also discussed. To address partition dependence—a critical limitation of Polya trees—the Randomized Polya tree is defined and developed. This new framework inherits the structure of Polya trees but induces smoothing of discontinuities in predictive distributions. Methodological and computational is sues arising in implementation will be discussed. Data analyses will highlight aspects of inference with randomized trees.
 
 

Keywords: Randomized trees, Polya trees, nonparametric Bayes, trees.

Address for correspondence: SusanPaddock
RAND Corporation
1700, MainSt., SantaMonica, CA90407-2138
e-mail: paddock@rand.org
website: www.isds.duke.edu
 
 

In this work we analyze several elliptical error-in-variable models under a Bayesian framework. Specifically, we consider two classes of models: differential and non-differential elliptical measurement error models. In both cases, we obtain robustness results from a sensitivity analysis. In order to compute the necessary posterior distributions we implement MCMC methods. The problem of model selection is also addressed. Finally, an application to Modelling levels of air pollution in Santiago, Chile, is presented.
 
 

Keywords: Bayesian analysis, elliptical measurement error model, robustness, MCMC
 

Address for correspondence: Wilfredo Palma
Casilla 306, Santiago 22,Chile.
e-mail: wilfredo@mat.puc.cl
web site: www.mat.puc.cl
 
 

We discuss the various problems that arise when using the Bayesian approach to analyze regression models whose errors follow an autoregressive process. Through particular examples and the general analysis of the model we describe the nature of the problems and suggest possible solutions for some particular cases. Some examples illustrate the difficulties and show that one should be careful in applying Gibbs sampling methods to these models, even when proper priors and stationary autoregressive models are used.
 
 

Keywords: time series, autocorrelated errors, Gibbs sampling.
 

Address for correspondence: J. Lynn Palmer
Department of Biostatistics, Box 213, UT M.D. Anderson Cancer Center,
1515 Holcombe Boulevard, Houston, TX USA 77030
e-mail: jlp@odin.mdacc.tmc.edu
web site: http://odin.mdacc.tmc.edu/~jlp