• Part of the 2009 Program on Space-time Analysis for Environmental Mapping, Epidemiology and Climate Change
• Meeting time/location: Wednesday, 11:00am - 12:45pm, SAMSI, Room 150
• Leaders: Dongchu Sun
• Webmaster: Jun Zhang
• Wiki manual: DokuWiki and its syntax

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Speaker: Sivaganesan, Siva

Institute: University of Cincinatti

Title: Objective Priors for testing hypotheses in some Poison Models.

Abstract : In the absence of prior information, use of objective priors is often crucial for testing hypotheses, when using the Bayesian approach. In this context, the use of objective priors such as intrinsic priors and Zellner's g-priors have gained much interest. In this talk, we consider the use of these priors for testing hypotheses about means and regression coefficients when observations come from Poisson distributions. We start with intrinsic prior for testing the equality of several Poisson means. We then focus on g-priors, giving a new motivation for a mixture g-prior for normal linear models proposed by Liang et a l(2008), based on shrinkage and minimal training sample arguments. Using the same motivation, we propose a mixture g-prior for Poisson regression model. While the proposed g prior is similar to the one used by Wang and George(2007), it is also different in certain aspects. Specifically, we show that the Bayes factor derived from the proposed prior is consistent. We also provide examples using simulated and real data.

Speaker: Jaeyong Lee

Institute: Soeul National University

Title: Bayesian Regression Based on Principal Components for High Dimensional Data

Abstract: Motivated by a climate prediction problem, we consider high dimensional Bayesian regression where the number of covariates is much larger than the number of obser- vations. To reduce the dimension of the covariate, the response is regressed on the principal components obtained from the covariates, and it is argued that the PCA regression is equivalent to the original model in terms of prediction. In the PCA regression setting under the sparsity condition, we examine large sample properties of two different modeling strategies: regression with and without covariate selection. For the regression without covariate selection, we obtain the consistency results of the estimators and posteriors with normal priors with constant and decreasing vari- ances, and James-Stein estimator; for the regression with covariate selection, we obtain convergence rates of Bayesian model averaging (BMA) and median prob- ability model (MPM) estimators, and the posterior with variable selection prior. Based on the large sample properties, we conclude that variable selection is essen- tial in high dimensional Bayesian regression. A simulation study also confirms the conclusion. The methodologies are applied to a climate prediction problem.

Speaker: Chong He

Institute: University of Missouri

Title: Bayesian Generalized Linear Mixed Models with Applications\ Missouri Turkey Harvest Survey

Abstract: Small area estimation is a big challenge in estimating wildlife hunting success rate and hunting pressure at the sub-domain level. Wildlife harvest surveys are conducted after hunting seasons which excludes the stratify sampling to increase the sample sizes at interested sub-domain level. Post-stratification is used instead. This causes small area estimation problem and yields random sample sizes at the sub-domain level. In this work, three Bayesian generalized linear mixed models (partial likelihood generalized linear mixed model, complete likelihood generalized linear mixed model, and double generalized linear mixed model) are developed to estimate hunting success rates and hunting pressure simultaneously.

Speaker: Michael Levins

Institute: Purdue University

Title: An EM algorithm for estimation of nonparametric finite multivariate mixtures

Abstract: Benaglia et al (2009) introduce an algorithm for nonparametric estimation of finite multivariate mixtures that resembles an EM algorithm. Conditional independence for coordinates of the random vectors is assumed. The algorithm works for any number of components and any dimensionality. However, this algorithm does not have an ascent property. Motivated by regularization argument of Eggermont and LaRiccia in their series of papers on the mixing density estimation in 1990’s, we apply a similar approach to the problem of nonparametric estimation of finite mixtures. This algorithm possesses an ascent property and is a true EM algorithm. To the best of our knowledge, this is the first true EM algorithm that can fit a mixture of an arbitrary number of multivariate nonparametric components. Extensive simulations demonstrate an excellent performance of the new algorithm in a variety of situations.

Speaker: Marco Ferreira

Institute: University of Missouri

Title: Objective Bayesian Analysis for Exponential Power Regression Models

Abstract: We develop objective Bayesian analysis for the linear regression model with random errors distributed according to the exponential power distribution. More specifically, we derive explicit expressions for three different Jeffreys priors for the model parameters. We show that only one of these Jeffreys priors leads to a proper posterior distribution. In addition, we develop fast posterior analysis based on Laplace approximations. Moreover, we show that our proposed Bayesian analysis compares favorably to MLE-based methodology previously proposed in the literature. Finally, we illustrate our methodology with applications of the exponential power regression models to two different datasets. This is joint work with Esther Salazar and Helio S. Migon.

Speaker: Paul Speckman

Institute: University of Missouri

Title: Irregular Second Order Gaussian Markov Random Fields

Gaussian Markov random fields are standard for analysis of areal data or data on a grid. The common models for areal data (e.g., CAR models) are first order. On the other hand, there are higher order priors for gridded data. This talk discusses a general method for constructing second order priors for general point-referenced data. The priors approximate Gaussian processes arising as solutions to stochastic differential or partial differential equations. Thus they can have higher order smoothness properties. On the other hand, they are constructed to have sparse precision matrices. In this way, the new class of priors generalize higher order Gaussian Markov random fields to arbitrary (gridded or not) data. The method is illustrated with an application to a rainfall data set.

2009-10 Program on Space-time Analysis One-day workshop on Objective Bayesian for Spatial and Temporal Models

Doubletree Market Square Hotel, San Antonio, Texas

Here is the meeting summary in word format: meeting summary

We will not have meetings in next two weeks. Our next meeting will be on 03/24/2010.

Jose Bernardo from UNIVERSITY OF VALENCIA will give a talk about Spatial data analysis and reference priors.

Garritt Page will present “Measurement error caused by spatial misalignment in environmental epidemiology” by Gryparis, A., Paciorek, C.J., Zeka, A., Schwartz, J., and B.A. Coull. 2009. The paper is available in Reference List Section.

* Miguel Ángel Martínez Beneito will give a talk on “Spatio-temporal smoothing of risks based on spatial moving averages.” Slides can be downloaded in Meeting Activities Section.

* Frank's slides are available in Meeting Activity Section.

* Jian (Frank) Zou will give a talk on “Bayesian Methods in Syndromic Surveillance”

* A paper by Wang and Zou on “Vast Volatility Matrix Estimation for High-Frequency Financial Data” is added in Reference Section.

* Chester Schmaltz, from University of Missouri, will give a talk on “Smoothed ANOVA with Spatial Effects as a Competitor to MCAR in Multivariate Spatial Smoothing” written by Zhang, Hodges and Banerjee (2009). His slides are available in the Meeting Activities Section.

* 09/30/2009 Please download two papers in Reference List Section for this group meeting. Before you can download papers, you need to log into wiki. Please check your email for username and password.

* Jin, Banerjee and Carlin (2007). Order-free co-regionalized areal data models with application to multiple-disease mapping, JRSS-B. To be presented by Dr. Jing zhang, Miami University.

* Zhang, Hodges and Banerjee (2009). Smoothed ANOVA with Spatial Effects as a Competitor to MCAR in Multivariate Spatial Smoothing. To be presented by Chester Schmaltz, University of Missouri.

Clicking on a date will take you to that date on the Meeting Summary page.

To upload an attachment, go to 'Edit', click on 'Add images or other files' tab (picture frame icon). Please add private pages and files to the appropriate namespace ('private:pageorfilename').

E-mail alias for the group is sp-fund AT samsi.info.

1. Kazianka H., and Pilz J., (2009b), Bayesian spatial modeling and interpolation using copulas, Submitted to Computers & Geosciences (September 2009). [ bib|pdf ]
2. Kazianka H., and Pilz J., (2009a), Copula-based geostatistical modeling of continuous and discrete data including covariates. Stochastic Environmental Research and Risk Assessment (in press). [bib|pdf]
3. Gryparis, A., Paciorek, C.J., Zeka, A., Schwartz, J., and B.A. Coull, (2009), Measurement error caused by spatial misalignment in environmental epidemiology. Biostatistics 10, 258–274. [bib|pdf]
4. Zhang Y., Hodges J., and Banerjee S., (2009), Smoothed ANOVA with Spatial Effects as a Competitor to MCAR in Multivariate Spatial Smoothing, Submitted to the Annals of Applied Statistics.[bib | pdf ]
5. Jin X., Banerjee S., and Carlin B, (2007), Order-free co-regionalized areal data models with application to multiple-disease mapping, JRSS-B, 69(5), 817–838. [bib| pdf ]
6. Wang Y., and Zou J., (2009), Vast Volatility Matrix Estimation for High-Frequency Financial Data, to appear on Annals of Statistics. [bib|pdf]
7. Heffernan R., Mostashari F., Das D., Karpati A., Kulldorff M., and Weiss D., (2004) Syndromic Surveillance in Public Health Practice, New York City, Emerging Infectious Diseases, 10(5), 858–864. [bib|pdf]
8. Loh J. and Zhu Z., (2007), Accounting for Spatial Correlation in the Scan Statistic, preprint. [bib|pdf ]
9. Banks D., Datta G., Kaar A., Lynch J., Niemi J. and Vera F., (2009), Bayesian CAR Models for Syndromic Surveillance on Multiple Data Streams: Theory and Practice, preprint. [bib|pdf]
10. Zhou F., and Lawson A.,(2008) EWMA smoothing and Bayesian spatial modeling for health surveillance,Statist. Med., [bib|pdf]

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