The Property of $\chi^2_{01}$ -Concordance for Bayesian Confirmation Measures

The paper considers evaluation of rules with particular interestingness measures being Bayesian confirmation measures. It analyses the measures with regard to their agreement with a statistically significant dependency between the evidence and the hypothesis. As it turns out, many popular confirmation measures were not defined to possess such a form of agreement. As a result, even in situations when there is only a weak dependency in data, measures could indicate strong confirmation or disconfirmation, encouraging the user to take some unjustified actions. The paper employs a i¾ź 2-based coefficient allowing to assess the level of dependency between the evidence and hypothesis in experimental data. A method of quantifying the level of agreement concordance between this coefficient and the measure being analysed is introduced. Experimental results for 12 popular confirmation measures are additionally visualised with scatter-plots and histograms.

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