Invited Commentary: Bayesian Inference with Multiple Tests

Dr. Leonhard presents a comprehensive and insightful critique of the existing malingering research literature and its implications for neuropsychological practice. Their statistical critique primarily focuses on the crucial issue of diagnostic inference when multiple tests are involved. While Leonhard effectively addresses certain misunderstandings, there are some overlooked misconceptions within the literature and a few new confusions were introduced. In order to provide a balanced commentary, this evaluation considers both Leonhard's critiques and the malingering research literature. Furthermore, a concise introduction to Bayesian diagnostic inference, utilizing the results of multiple tests, is provided. Misunderstandings regarding Bayesian inference are clarified, and a valid approach to Bayesian inference is elucidated. The assumptions underlying the simple Bayes model are thoroughly discussed, and it is demonstrated that the chained likelihood ratios method is an inappropriate application of this model due to one reason identified by Leonhard and another reason that has not been previously recognized. Leonhard's conclusions regarding the primary dependence of incremental validity on unconditional correlations and the alleged mathematical incorrectness of the simple Bayes model are refuted. Finally, potential directions for future research and practice in this field are explored and discussed.