Name: Andres Felipe Florez
Institution: IME, USP, Brazil
Co-authors: Luis Gustavo Esteves
The problem of statistical hypotheses testing consists of a decision problem in which the objective is to choose a statistical hypothesis among $k$ ($k>2$) hypotheses. Each of these hypotheses defines a specific subset of the parameter space. Usually, some of these subsets do not have the same dimensions and this makes it difficult to compare them. This challenge can be resolved by using weighted likelihoods which are defined under the subset of the parameter space specific to each hypothesis. This idea was initially proposed by Irony & Pereira [T. Z Irony & C. A. B Pereira, Bayesian hypothesis test: using surface integrals to distribute prior information among the hypotheses, (1995), Resenhas 2(1)27-46].
This proposal aims to avoid the “Statistical Paradox” showed by Lindley [D.V Lindley (1957), Biometrika 44 (1–2): 187–92] and the misuse of canonical values of significance. Pericchi & Pereira’s adaptive significance level is applied [LR Pericchi C. A. B Pereira, Adaptive significance levels using optimal decision rules: Balancing by weighting the error probabilities. BJPS, (2016), 30(1):70-90] to compare the means of two Poisson distributions with an unknown parameter. For this propose, the analysis is carried out by conditioning on a suitable statistic in order to satisfy Berger and Wolper’s principle of the non-informative nuisance parameter [Berger J and Wolpert R. The likelihood principle. Hayward, CA: Institute of Mathematical Statistics, 2:704,1988.].