No-decision region in tests with frequentists conditional and bayesian interpretation

Carla Regina Guimarães BRIGHENTI[1]

Lucas Monteiro CHAVES [2]

§    ABSTRACT: The Bayesian Test is a Likelihood Ratio Test with critical values given by product of the ratio between prior densities and the ratio between losses. In this way, for some determined values of ρ and l there are coincident critics regions for a bayesian test and for a conditional frequentist test. The evidence measure reported in the bayesian test is the posterior probability while the conditional test is the conditional error probability (CEP). Depending on the conditioning statistic used and the ρ and l values, these values can be numerically the same, defining a “unified” test. But when the prior probability or the CEP are numerically the same and superior to 1/2, it must be incorporated a “no-decision region”, NDR. The NDR construction depends on the partitioning function H(x) of the conditional test and the p and l values. In this work, it was studied size of the NDR to hypothesis test of the parameter Exponential distribution with samples of different sizes. It was concluded that the size of the NDR depends on the size of the sample and that some situations can make the test unified inadequate.

§    KEYWORDS: Conditional error probability; no-decision region; partitioning function; posterior probability.


[1] Escola Preparatória de Cadetes do Ar, EPCAR, Comando da Aeronáutica, CEP: 36200-000, Barbacena, MG, Brasil, E‑mail:

[2] Departamento de Ciências Exatas, Universidade Federal de Lavras – UFLA, Caixa Postal 37, CEP:37200-000, Lavras,  MG, Brasil, E‑mail: