IDP Statistical Package
Bayesian methods are ubiquitous in many research areas. Nevertheless, the analysis of empirical results is typically performed by frequentist tests. This implies dealing with null hypothesis significance tests and p-values, even though the shortcomings of such methods are well known.
The IDP Statistical Package aims to change this perspective by providing Bayesian nonparametric versions of the most used frequentist tests. IDP is based on a Prior Near-Ignorance Dirichlet Process. This is the class of all Dirichlet Processes obtained by fixing the prior strength of the Dirichlet Process and letting the normalized base measure vary in the set of all probability measures. A Bayesian nonparametric near-ignorance model presents several advantages with respect to a traditional approach to hypothesis testing.
- The Bayesian approach allows us to formulate the hypothesis test as a decision problem. This means that we can verify the evidence in favor of the null hypothesis and not only rejecting it and take decisions which minimize the expected loss.
- Because of the nonparametric prior near-ignorance, IDP based tests allows us to start the hypothesis test with very weak prior assumptions, much in the direction of letting data speak for themselves.
- Although the IDP test shares several similarities with a standard Bayesian approach, at the same time it embodies a significant change of paradigm when it comes to take decisions. In fact the IDP based tests have the advantage of producing an indeterminate outcome when the decision is prior-dependent. In other words, the IDP test suspends the judgment when the option which minimizes the expected loss changes depending on the Dirichlet Process base measure we focus on.
- We have empirically verified that when the IDP test is indeterminate, the frequentist tests are virtually behaving as random guessers. We regard this surprising result as an important finding, with practical consequences in hypothesis testing. Assume that we are trying to compare the effects of two medical treatments (Y is better than X) and that, given the available data, the IDP test is indeterminate. In such a situation the frequentist test always issues a determinate response (for instance I can tell that Y is better than X), but it turns out that its response is completely random, like if we were tossing of a coin. On the other side, the IDP test acknowledges the impossibility of making a decision in these cases. Thus, by saying "I do not know", the IDP test provides a richer information to the analyst. The analyst could for instance use this information to collect more data.
The IDP project is still in progress. Some IDP based tests can already be downloaded from this page (see side-bar) in R and Matlab source code or used online from CloudRunner.
IDP is an open software and it is released under the terms of the GNU GPL license.
Please, for any problem or suggestion for software improvement, contact
IDP based version of the Wilcoxon rank-sum test
IDP based version of the Wilcoxon signed-rank test
IDP based version of the Friedman test
IDP based version of the multiple comparison based on the sign test
IDP survival analysis (Wilcoxon rank-sum test for censored data and survival curve estimator)
Source code (October 2015)
Download the [Matlab] source code.
The IDP survival analysis is instead implemented in R.