Research Seminar

Learning more from empirical data using prior knowledge


Herbert Hoijtink


Department of Methods and Statistics, Faculty of Social Sciences, University Utrecht

Abstract: Inference from data to a population traditionally proceeds by null hypothesis testing. This tells whether the data support the hypothesis that in the population some quantity is zero (a difference between means, a correlation, an indicator of growth over time). However, this is seldom the focus of interest for the researcher who collected the data. Researchers tend to be more interested in the alternative situation in which the null hypothesis fails to hold. Usually the alternative hypothesis is uninformative (e.g., 'the means at our four time points are not all equal') although researchers often possess informative and competing hypotheses (e.g., 'the means are increasing from time point 1 to 4' or 'the means at time points 1 and 4 are smaller than at time points 2 and 3'). This presentation adresses the evaluation of informative hypotheses.

Point of departure is that adequate statistical tools should be available to researchers who have informative hypotheses (prior knowledge) in the form of hypothesized order relations between statistical parameters. Such knowledge may come from theories, earlier research expertise or difference of opinion with colleagues. Bayesian model selection applied to order-restricted alternatives has recently become feasible when enough computing power became available for the required algorithms. This presentation will focus on use of the Bayes factor to select the best of a set of informative hypotheses.

Two examples will be used to illustrate the approach proposed: order restricted analysis of variance, and order restricted models for the analysis of contingency tables. A potential drawback of the Baysian approach is the sensitivity with respect to the prior distributions that have to be specified. Supported by theoretical derivations, both examples will be used to discuss the prior sensitivity of the Bayesian approach proposed.


Keywords: Applied Statistics, Competing Theories, Inequality Constraints, Model Selection, Prior Knowledge, Bayes factor
Date: Tue Dec 9, 12:15 pm - 1:15 pm
Place: room 02.51 (Department of Psychology, Tiensestraat 102, 3000 Leuven)