Expanding the Computational Statistics Toolbox for General Hierarchical Models

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

Hierarchical statistical models allow analysis of patterns in complex data while accounting for relationships such as temporal or spatial patterns or shared sampling units. A great variety of analysis algorithms for hierarchical models have been developed by statistical researchers but are unavailable to practitioners such as social scientists and biologists. The NIMBLE software platform was developed to bridge this gap and make it easier for scientists to use a variety of algorithms on their specific datasets. In particular NIMBLE provides a programming environment in which researchers can implement algorithms that can then be easily used by others in the context of specific datasets. The work under this project will extend NIMBLE to provide computational methods for working with very flexible statistical methods known as Bayesian nonparametric methods. These methods allow researchers to summarize variables and quantify relationships between different variables in an analysis while making fewer assumptions than standard statistical approaches. While Bayesian nonparametric methods have developed substantially in the last 10-15 years, many of these methods are hard or time-consuming for those working with data to implement on their own. This project will implement many such methods in the NIMBLE software, thereby providing them to practitioners to use in their day-to-day analyses. Moreover, it will provide a foundation for ongoing development and sharing of new and improved such methods in the future. A large amount of research aims to improve the intertwined statistical and computational methods for analysis of hierarchical statistical models. Such research is important because problem-specific hierarchical models facilitate rapid advances in many scientific fields. However, statistical researchers have lacked a flexible software platform designed for programming and disseminating the many varieties of algorithms such as Markov chain Monte Carlo, sequential Monte Carlo, and methods that build upon them. The NIMBLE system provides such a software platform. This project helps to further fill that gap by extending the NIMBLE system to enable use of Bayesian nonparametric methods, with a focus on nonparametric mixture models, of which the Dirichlet process model and related models are widely-known. This extension will allow routine application of these nonparametric mixture models as prior distributions for parts of arbitrary hierarchical models. The project will implement a variety of techniques for fitting Bayesian nonparametric mixtures, focusing on both collapsed and blocked samplers in Markov chain Monte Carlo algorithms. Such techniques methods have been highly developed by specialists but are limited in their research and scientific applications by lack of general implementation.