Computational Issues in Model Elaboration, Diagnostics and Estimation

Ohio State University Research Foundation -Do Not Use, Columbus OH

Investigators

Abstract

The degree of complexity and sophistication in modern statistical models has various consequences. This project addresses two important, related aspects. First, how can one assess if specific features of a model provide an accurate representation of the phenomenon under study? Further, if some features are identified as problematic, in what direction should they be modified to improve the fit of the model? Second, as models become more complicated, fitting the models also becomes harder. It would be a mistake to think that raw computing power is all that is needed to keep pace with the increasing complexity. Novel algorithmic approaches are needed to tackle the challenges posed by modern modeling practices. Old techniques used on more powerful computers might only run longer, without producing the desired output. This project establishes some important and novel connections between the theoretical properties of Bayesian hierarchical models and some other areas of statistics, such as time series analysis and cluster analysis, leading to advances in the area of model diagnostics and elaboration and to the development of an effective class of algorithms for fitting Bayesian mixture models. Recent advances in computational resources have afforded modelers unprecedented opportunities to describe real life and natural phenomena in very realistic terms. As reality is inherently complex, realistic models tend to be highly sophisticated. The need for accurate and reliable modeling cannot be overemphasized. Public policy decisions are routinely made on the basis of probabilistic models that forecast economic and social indicators, predict environmental factors, assess the potential for disease outbreak, etc. Small deficiencies in the models and little estimation inaccuracies can have consequences that might impact on the welfare of large numbers of people. The proposed research will develop translational methodology that cuts across disciplines and can be used to improve modeling and forecasting in a variety of settings. Suggested areas of application include those with which the PI is most familiar because of his ongoing collaborations (quantitative psychology, marketing, and patient oriented medical investigation) but there is clear potential for the research to have an impact on other areas as well. For example, finite mixture distributions models, one of the specific research themes, are used in applied settings as diverse as human genetics and the monitoring of worldwide nuclear testing to tell explosions apart from earthquakes. The project also has a clear educational focus, both in terms of training of the graduate students who will assist the PI in the research activities and in terms of alerting the broader research community to the need for sound and modern modeling strategies.