The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine Bayesian measure of evidence, is discussed in detail. Its behavior in some problems of statistical inference like testing for independence in contingency tables is discussed.
Carlos A. de B. Pereira. Julio Michael Stern. Sergio Wechsler. "Can a significance test be genuinely Bayesian?." Bayesian Anal. 3 (1) 79 - 100, March 2008. https://doi.org/10.1214/08-BA303