“…To investigate the relationship between sex and Brain2ICV, we built the probabilistic Bayesian model expressed in Equations (2a)–(2d): B i ∼ N( µ i , σ) µ i = γ X[i] γ j ∼ N (0, 1), for j = 1, 2 σ ∼ Hal f Normal(1) where B i denotes the variable Brain2ICV or the ratio between the brain volume at an old age and the maximum brain volume at a young age for Subject i , and this is normally distributed with a mean µ i and a standard deviation σ . The index variable for sex γ j , with the index j = 1, 2, represents the average of Brain2ICV for male ( j = 1) and female ( j = 2) subjects (no order implied), which are normally distributed using the same prior, N (0, 1), for both male and female subjects [ 52 ]. The prior σ is assumed to be normally distributed, half-normally to be exact, with a standard deviation equal to 1 (a half-normal distribution can be directly sampled from a normal distribution by taking the absolute value of each sampled value).…”