Collaborative Research: Adaptive Nonparametric Markov Chain Monte Carlo Algorithms for Social Data Models with Nonparametric Priors

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This project addresses the frequent under-use of prior information in social and behavioral science Bayesian models, and provides a means of applying semi-informed priors based on mixtures of Dirichlet processes that reflect both information from observations and researcher intuition where neitherdominates. The primary outcomes of interest are categorical selections representing manifestations of a latent class variable, assumed to be drawn from a mixture of Dirichlet processes. There may also be structures in the data such as unexplained clustering effects, unit heterogeneity, autocorrelation, or missingness that cast doubt on the notion of a single model. So rather than researcher specification of a single form, the investigators suggest, a nonparametric Bayesian approach that draws from a mixture of appropriate prior distributions conditional on data and parameters. Thus the determination of the discrimination processes in the models we use is done nonparametrically in the context of a parametric hierarchical model. These models typically produce irregular and multimodal posterior distributions, a problem exacerbated with higher dimension. The investigators provide develop adaptive Markov chain Monte Carlo methods that account for posterior topology and efficiently traverse the sample space. Bayesian models represent a major improvement in scientific inference because they allow the incorporation of prior information that researchers or outside experts may have. Yet there remains some controvery about how informed these prior specifications should be relative to an acquired set of data. This project develops new paradigm for semi-informed prior information in social science research that reflects both information from observations and researcher intuition, where neither dominates. This is not possible without new simulation tools, which the investigators develop. Currently, there are no other working applications of these "mixtures of Dirichlet prior process priors" in the social or behavioral sciences, despite being able to facilitate more sophisticated modeling frameworks in these areas thus helping researchers understand complex phenomena in new and difficult datasets. Furthermore, the algorithmic developments in this project can be applied in any scientific field and will contribute to the statistical literature on computer simulation for statistical inference. The development of nonparametric prior families will help resolve the historical distrust of overtly subjective prior specifications.