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Bayesian Predictive Inference for Numerous Sub-Areas Using Logistic Regression

时间:2017-05-29

Statistics Seminar2017-12

Topic:Bayesian Predictive Inference for Numerous Sub-Areas Using Logistic Regression

Speaker:Balgobin Nandram, Department of Mathematical Sciences, Worcester Polytechnic Institute, USA

Time:Monday, May 29, 14:00-15:00

Place:Room 216, Guanghua Building 2

Abstract:

We analyze binary data with covariates, which are available for numerous sub-areas within small areas. Predictive inference is required for the finite population proportion of individuals with a specific character for each sub-area. As an investigative study, we use a standard hierarchical Bayesian logistic regression model with each sub-area, rather than small areas, having its own random effect. This modeling helps to correct for over-shrinkage so common in small area estimation and to warn against using a single random effect for each area. Because there are numerous sub-areas, the computational time to obtain samples from the joint posterior density using standard Markov chain Monte Carlo (MCMC) methods is prohibitive and tuning is time-consuming. Therefore, the joint posterior density of the hyper-parameters is approximated using an integrated nested normal approximation (INNA) via the multiplication rule. This approach provides a sampling-based method that permits fast computation, thereby avoiding very time-consuming MCMC methods. Then, the random effects are obtained from the exact conditional posterior density using parallel computing, non-sampled covariates are obtained using the Bayesian bootstrap, and Bayesian predictive inference is implemented for the finite population mean of each sub-area. We describe the methodology and an example on health severity using Nepal's Living Standards Survey, where wards are small areas and households are sub-areas.

Introduction:

Bal came to Worcester Polytechnic Institute (WPI), Massachusetts, USA, 1989. Since 2003 he has been Senior Professor of Statistics at WPI. He is a fellow of the American Statistical Association, an elected member of the International Statistical Institute, and an elected member of the Sigma Chi, the Scientific Society of America. He has made numerous invited presentations worldwide (over one hundred) on his research and he has advised several MS theses (more than thirty) and PhD dissertations (more than ten) on these topics both nationally and internationally.

Bal does research at the interface of survey sampling and Bayesian statistics. He specializes in hierarchical Bayesian models and predictive inference of finite population parameters. The common theme is hierarchical Bayesian modeling for the analysis of data from small areas in finite populations, and their implementations using Markov chain Monte Carlo methods. Bal has been doing this for nearly thirty years. Indeed, Bal is a well established researcher in these areas and is well known for his prolific research on hierarchical Bayesian models. His citation (2003) from the ASA Fellowship Committee includes his great strength on the hierarchical Bayesian models.

Bal has written extensively for theory and methods journals and methods and applications journals. His major research papers appear in JASA, Theory and Methods, JASA, Applications and Case studies and JRSSB. He has many papers in purely theoretical journals such as Statistica Sinica and Journal of Statistical Planning and Inference. He also has many papers on Bayesian Computations in the Journal of Statistical Computation and Simulation. Many of his papers have received more than twenty five citations each. One example, Nandram and Chen (1996) receives at least one hundred citations. This is ground breaking work because it shows how to accelerate the Gibbs sampler via a simple idea of reparameterization. Overall he has more than one hundred refereed articles in statistical journals and more than one thousand citations.

During the most recent fifteen years Bal's research efforts have been focused on nonignorable nonresponse and selection for continuous data and mostly categorical data in which multinomial-Dirichlet models are used extensively. Nandram and Choi (2002a,b) studied mainly data for small areas from the National Health Interview Survey and the National Crime Survey. In particular, Nandram and Choi (2002a) provide an expansion model which incorporates different degrees of nonignorability over different small areas. This is indeed ground breaking research and many scientists at the Government Agencies have used his method extensively. More recently Nandram and Choi (2005, 2010) studied the nonignorable nonresponse problem for continuous data. This latter nonresponse model includes a component for selection bias. This is a very clever idea as nonignorable nonresponse and selection bias are simultaneously included in a single model.

Bal is well known for his research among the US government agencies. In particular, Bal has collaborated with scientists at the National Center for Health Statistics (NCHS), the Census Bureau, the Bureau of Labor Statistics and National Agricultural Statistics Service (NASS), USDA. For example, during the academic year 2003/2004 Bal spent a sabbatical at the NCHS working on nonresponse problems. He served as a research team leader June 1, 2009 - May 31, 2011 on a NASS project via the National Institute of Statistical Sciences (NISS). He has given workshops on Bayesian statistics and Bayesian computations in these agencies as well. In 2006 WPI won the prestigious SPAIG award from the ASA through outstanding collaboration of Bal and his students with the NCHS. Much of his outstanding research work on nonresponse started at the NCHS, January 1, 1999 to June 30, 2000, when he was the first ASA/NCHS Research Fellow, Hyattsville, Maryland. He has also worked at the NCHS on Bayesian models for mortality data (Nandram, Sedransk and Pickle, 1999, 2000). In 2015 Bal won the Simon's Foundation Award for Collaborative Research in Mathematical Sciences, a travel grant for five years, for his work on nonignorable nonresponse and selection. Since June 2015 Bal has a half-time appointment with US National Agricultural Statistical Service (USDA).

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