Knowledge-Driven Bayesian Regression

Ohio State University, The, Columbus OH

Investigators

Abstract

The research concerns the development of Bayesian regression models that are carefully designed to include specific forms of knowledge common to many data analytic settings. Researchers who work in specialized fields accumulate quantifiable, problem-specific expert knowledge about model features based on their repeated experience designing experiments and analyzing the resulting data. The ability to build models that respect such knowledge is a critical component to good data analysis. In the Bayesian modeling paradigm, such knowledge is incorporated in the analysis through prior distributions on model parameters. Unfortunately, many standard prior models compete against this knowledge, assigning significant prior probability to events that researchers know are implausible, if not impossible. A major focus of the research is the identification of the types of information that are available to researchers for specific classes of models and the development of new prior distributions whose structures are driven by this knowledge. The project considers data-analytic settings ranging from linear regression models to models arising from conjoint choice experiments. Particular forms of prior knowledge range from information about the coefficient of determination in a linear regression model to more complex information about collinearity and grouped predictor variables. The research places emphasis on understanding how such prior information affects the comparison of competing models, and how properties of the new prior distributions affect the questions of Bayesian model comparison and variable selection. The research in new classes of prior distributions for regression problems includes investigations of new and emerging ideas about parameter regularization. Generalizations of new Bayesian regularization priors will be developed that allow empirical knowledge about correlation structures in the predictor variables to be incorporated in the regression models. Such priors will be useful in high-dimensional problems, where extensive information is not always readily available and where regularization is known to help stabilize inference. The motivation for the research comes from the social sciences, in particular Psychology and Marketing. A key question in Psychology is how the brain perceives, reacts to, and processes stimuli. Extensive experimentation in this field has led to the development of a large base of knowledge about how manipulation of particular stimuli affects the brain. Analysis of these experiments provides insight into how the brain works. A common experiment in Marketing involves assessing the attractiveness of product offerings to different groups of consumers. These assessments are then used to design products that will be successful in the marketplace. In order to provide new insights into these processes in Psychology and Marketing, researchers require methods of data analysis that are tailored to incorporate knowledge about these processes that has been accumulated by researchers. The statistical methodology developed in this research will provide investigators with sophisticated data-analytic tools that will allow them to perform focused data analysis, leading to a more accurate understanding of individual and consumer behavior.