Bayesian Inference General Procedures for A Single-subject Test Study

Abnormality detection in identifying a single-subject which deviates from the majority of a control group dataset is a fundamental problem. Typically, the control group is characterised using standard Normal statistics, and the detection of a single abnormal subject is in that context. However, in many situations, the control group cannot be described by Normal statistics, making standard statistical methods inappropriate. This paper presents a Bayesian Inference General Procedures for A Single-subject Test (BIGPAST) designed to mitigate the effects of skewness under the assumption that the dataset of the control group comes from the skewed Student \( t \) distribution. BIGPAST operates under the null hypothesis that the single-subject follows the same distribution as the control group. We assess BIGPAST's performance against other methods through simulation studies. The results demonstrate that BIGPAST is robust against deviations from normality and outperforms the existing approaches in accuracy nearest to the nominal accuracy 0.95. BIGPAST can reduce model misspecification errors under the skewed Student $t$ assumption by up to 12 times, as demonstrated in Section 3.3. We apply BIGPAST to a Magnetoencephalography (MEG) dataset consisting of an individual with mild traumatic brain injury and an age and gender-matched control group. For example, the previous method failed to detect abnormalities in 8 brain areas, whereas BIGPAST successfully identified them, demonstrating its effectiveness in detecting abnormalities in a single-subject.