Patiño Hoyos Alejandra E, Fossaluza Victor, Esteves Luís Gustavo, de Bragança Pereira Carlos Alberto
Facultad de Ingeniería, Institución Universitaria Pascual Bravo, Medellín 050034, Colombia.
Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo 05508-090, Brazil.
Entropy (Basel). 2022 Dec 22;25(1):19. doi: 10.3390/e25010019.
The full Bayesian significance test (FBST) for precise hypotheses is a Bayesian alternative to the traditional significance tests based on -values. The FBST is characterized by the -value as an evidence index in favor of the null hypothesis (). An important practical issue for the implementation of the FBST is to establish how small the evidence against must be in order to decide for its rejection. In this work, we present a method to find a cutoff value for the -value in the FBST by minimizing the linear combination of the averaged type-I and type-II error probabilities for a given sample size and also for a given dimensionality of the parameter space. Furthermore, we compare our methodology with the results obtained from the test with adaptive significance level, which presents the capital-P -value as a decision-making evidence measure. For this purpose, the scenario of linear regression models with unknown variance under the Bayesian approach is considered.
用于精确假设的全贝叶斯显著性检验（FBST）是基于p值的传统显著性检验的一种贝叶斯替代方法。FBST的特点是将p值作为支持原假设（）的证据指标。实施FBST的一个重要实际问题是确定反对的证据必须多小才能决定拒绝它。在这项工作中，我们提出了一种方法，通过在给定样本量和参数空间维度的情况下，最小化平均I型和II型错误概率的线性组合，来找到FBST中p值的临界值。此外，我们将我们的方法与从具有自适应显著性水平的检验中获得的结果进行比较，该检验将大写P值作为决策证据度量。为此，考虑了贝叶斯方法下方差未知的线性回归模型的情况。
