Bayesian Evaluation of Informative Hypotheses in Multidimensional Scaling

• Activity Number: 374
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Kensuke Okada*+
• Companies: Senshu University
• Keywords: Informative hypothesis ; Bayes factor ; multidimensional scaling

Abstract

Informative hypotheses are researchers' expectations formulated as inequality constraints among the parameters in which they are interested. In this study, we propose a Bayesian method for evaluating informative hypotheses in multidimensional scaling. In multidimensional scaling, inequality constraints can be introduced either in the coordinates of the objects, the distances among the objects, or the transformations of the distances. In case of asymmetric multidimensional scaling, inequality constraints that confine asymmetry parameters can also be introduced. In the proposed method, the informative hypotheses are evaluated by Bayes factors against the null. The null model specifies no constraints for parameters. In this setting, the Bayes factors can be calculated simply from Savage-Dickey type density ratio. A numerical simulation study is conducted to evaluate the performance of the proposed method in terms of correct recovery of the model and prior sensitivity. Our numerical results provided some support for the proposed method.