Chapter 8 264 As mentioned earlier, we assumed a heterogeneous scale term σi.j for each subgroup j that follows a gamma distribution with mode ω and standard deviation . We placed vague gamma priors on both ω and that are broad on the scale of the data by estimating the shape (k) and scale (θ) of the priors such that the mode and standard deviation are equal to and respectively: For the antibody waning rate estimation, we used a Bayesian hierarchical model that partially pooled decay rates across all study participants l. We assumed a linear function between the predicted log neutralization values 〈Y 〉 and time (t): where βl is the normalized decay rate for participant l and Cl is the participant-specific intercept. We assumed that the observed mean-centered and scaled neutralization values Y follow a Student’s t-distribution about the predicted 〈Y 〉 with error-term standard deviation σ Y with vY degrees of freedom: Y ~ T (vY , 〈Y 〉, σ Y ) We assumed that v is exponentially distributed with a mean of 30 such that high prior probability was allocated over parameter values that describe the range from normal to heavy-tailed data under the Student’s t-distribution: The intercepts cl were assumed to be normally distributed about a common mean intercept 〈c〉 with standard deviation :
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