Asymptotic scaling in logistic regression sampling experiments

Ascertain whether the numerical experiments for Bayesian logistic regression reach sufficiently high dimensions to reveal asymptotic behavior, and determine if the observed approximately linear time-to-threshold behavior in Kernel Stein discrepancy transitions to the theoretically predicted logarithmic scaling at larger dimensions.

Background

The authors simulate Bayesian logistic regression using an idealized thermodynamic sampler and monitor the Kernel Stein discrepancy (KSD) as a function of time and dimension, observing approximately linear scaling of the crossing time with dimension in the tested range.

They explicitly note uncertainty about whether simulations reach high enough dimensions to reveal asymptotic behavior, raising the empirical question of whether the predicted logarithmic scaling emerges at larger dimensions or under alternative metrics/bandwidth selections.