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This paper proposes a Bayesian model to compare multiple algorithms onmultiple data sets, on any metric. The model is based on the Bradley-Terrymodel, that counts the number of times one algorithm performs better thananother on different data sets. Because of its Bayesian foundations, theBayesian Bradley Terry model (BBT) has different characteristics thanfrequentist approaches to comparing multiple algorithms on multiple data sets,such as Demsar (2006) tests on mean rank, and Benavoli et al. (2016) multiplepairwise Wilcoxon tests with p-adjustment procedures. In particular, a Bayesianapproach allows for more nuanced statements regarding the algorithms beyondclaiming that the difference is or it is not statistically significant.Bayesian approaches also allow to define when two algorithms are equivalent forpractical purposes, or the region of practical equivalence (ROPE). Differentthan a Bayesian signed rank comparison procedure proposed by Benavoli et al.(2017), our approach can define a ROPE for any metric, since it is based onprobability statements, and not on differences of that metric. This paper alsoproposes a local ROPE concept, that evaluates whether a positive differencebetween a mean measure across some cross validation to the mean of some otheralgorithms is should be really seen as the first algorithm being better thanthe second, based on effect sizes. This local ROPE proposal is independent of aBayesian use, and can be used in frequentist approaches based on ranks. A Rpackage and a Python program that implements the BBT is available.

A Bayesian Bradley-Terry model to compare multiple ML algorithms on multiple data sets