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. • The assumption of Gaussian distribution in a single-subject test is inappropriate for skewed Student t distribution. • The skewness has different effects on the Type I error and Power of the one-sided test (less or greater), which are not fully discussed in the literature. • Key contributions: (1) A novel Bayesian Inference General Procedures for A Single-subject Test which employs the nested sampling technique is proposed under the skewed Student t distribution assumption. (2) We propose a Jeffreys prior defined by explicit mathematical formulas. • The general Bayesian framework for a single-subject test is more robust than the existing methods in terms of Type I error, power and accuracy. • The proposed method is applied to a MEG dataset, demonstrating its effectiveness in de- tecting abnormalities in the single-subject study.