In Honor of John Deely
Co-organizers: Bruce Craig, Professor of Statistics and Director of Statistical Consulting, Department of Statistics, Purdue University; and Wesley O. Johnson, Professor Emeritus, Department of Statistics, University of California, Irvine
Chair: Bruce Craig, Professor of Statistics and Director of Statistical Consulting, Department of Statistics, Purdue University
Speakers
- Wesley O. Johnson, Professor Emeritus, Department of Statistics, University of California, Irvine
- Ronald Christensen, Professor, Department of Mathematics and Statistics, University of New Mexico
- A. James O'Malley, Professor of Biomedical Data Science and Professor of The Dartmouth Institute, Department of Biomedical Data Science, Dartmouth College
- Purushottam W. (Prakash) Laud, Professor, Division of Biostatistics and Institute for Health and Society, Medical College of Wisconsin
Wednesday, June 6, 10:00 a.m.-12:00 p.m. in STEW 214 AB
| Time | Speaker | Title |
|---|---|---|
| 10:05-10:30 a.m. | Ronald Christensen | On Rereading Deely and Lindley |
| Abstract: In 1981 John Deely and Dennis Lindley published "Bayes Empirical Bayes" in JASA. It was the first definitive statement on solving Empirical Bayes problems in a Bayesian fashion. We will discuss the historical context of the paper, its results, and its impact on subsequent research. | ||
| 10:30-10:55 a.m. | Purushottam Laud | Low Information Omnibus (LIO) Priors for Dirichlet Process Mixture Models |
| Abstract: Dirichlet process mixture (DPM) models provide flexible modeling for distributions of data as an infinite mixture of distributions from a chosen collection. Specifying priors for these models in individual data contexts can be challenging. We introduce a scheme which requires the investigator to specify only simple scaling information. This is used to transform the data to a fixed scale on which a low information prior is constructed. Samples from the posterior with the rescaled data are transformed back for inference on the original scale. The low information prior is selected to provide a wide variety of components for the DPM to generate flexible distributions for the data on the fixed scale. The method can be applied to all DPM models with kernel functions closed under a suitable scaling transformation. Construction of the low information prior, however, is kernel dependent. Using DPM-of-Gaussians and DPM-of-Weibulls models as examples, we show that the method provides accurate estimates of a diverse collection of distributions that includes skewed, multimodal, and highly dispersed members. With the recommended priors, repeated data simulations show favorable performance against standard empirical estimates. | ||
| 10:55-11:20 a.m. | Wesley Johnson | Some Thoughts on Objective Versus Subjective Bayes Factors for the Two Sample Comparison |
| Abstract: Many Bayes factors have been proposed for comparing population means in two-sample studies. Considerable attention has been paid to certain objective criteria, and some of those criteria have been used to argue against the use of subjective methods by pointing to so-called undesirable behavior of the latter. A wonderful aspect of Bayesian models is that they provide an opportunity to lay all cards on the table. The distinguishing feature of various BFs, in particular in the two-sample problem, is the choice of priors (cards) for the model parameters. We attempt to shed light on some aspects of prior selection for BFs. | ||
| 11:20-11:45 a.m. | James O'Malley | Modeling a Bivariate Residential-Workplace Neighborhood Effect when Estimating the Effect of Proximity to Fast-Food Establishments on Body Mass Index |
| Abstract: Hierarchical modeling is the preferred approach of modeling neighborhood effects. When both residential and workplace neighborhood are known, a bivariate (residential-workplace) neighborhood random effect that quantifies the extent that a neighborhood's residential and workplace effects are correlated may be modeled. However, standard statistical software for hierarchical models does not easily allow correlations between the random effects of distinct clustering variables to be incorporated. To overcome this challenge, we develop a Bayesian model and accompanying estimation procedure that allows for correlated bivariate neighborhood effects and also allows individuals to reside or work in multiple neighborhoods, cross-sectional and longitudinal heterogeneity between individuals, and serial correlation between repeated observations over time. Simulation studies that vary key model parameters evaluate how well each aspect of the model is identified by the data. We apply the model to the motivating Framingham Heart Study linked food establishment data to examine whether (i) Proximity to fast-food establishments is associated with Body Mass Index (BMI); (ii) Workplace neighborhood exposure associations are larger than those for residential neighborhood exposure; (iii) Residential neighborhood exposure associations correlate with workplace neighborhood exposure. Comparisons of the full model to models with restricted versions of the covariance structure illustrate the impact of including each feature of the covariance structure. | ||
| 11:45 a.m.-12:00 p.m. | Open Discussion | |