Towards the Geometry of Model Sensitivity: An Illustration

In statistical practice model building, sensitivity and uncertainty are major concerns of the analyst. This paper looks at these issues from an information geometric point of view. Here, we define sensitivity to mean understanding how inference about a problem of interest changes with perturbations of the model. In particular it is an example of what we call computational information geometry. The embedding of simple models in much larger information geometric spaces is shown to illuminate these critically important issues

Default “Gunel and Dickey” Bayes factors for contingency tables

The analysis of R×C contingency tables usually features a test for independence between row and column counts. Throughout the social sciences, the adequacy of the independence hypothesis is generally evaluated by the outcome of a classical p-value null-hypothesis significance test. Unfortunately, however, the classical p-value comes with a number of well-documented drawbacks. Here we outline an alternative, Bayes factor method to quantify the evidence for and against the hypothesis of independence in R×C contingency tables. First we describe different sampling models for contingency tables and provide the corresponding default Bayes factors as originally developed by Gunel and Dickey (Biometrika, 61(3):545–557 (1974)). We then illustrate the properties and advantages of a Bayes factor analysis of contingency tables through simulations and practical examples. Computer code is available online and has been incorporated in the “BayesFactor” R package and the JASP program (jasp-stats.org)