Bayesian Decision Rules Under Asymmetric Loss: A Parkinson’s Disease Case Study and Simulation Analysis

Abstract

A probabilistic classifier does not determine an action until prediction is combined with a

loss function. This paper studies that distinction through a synthetic Parkinson’s disease

case study and a controlled simulation analysis. Using 2105 synthetic records, we compare

maximum-likelihood, ridge, lasso, and Bayesian logistic regression under repeated stratified

cross-validation, evaluating discrimination, calibration, proper scoring rules, and decision loss

rather than accuracy alone. For false-positive cost cF P and false-negative cost cF N = λcF P ,

the Bayes action refers an observation when its calibrated risk exceeds τ∗(λ) = 1/(1 + λ).

At λ = 3, this gives τ∗ = 0.25; the out-of-fold Bayesian model yielded sensitivity 0.959 and

specificity 0.442, compared with 0.856 and 0.704 at the conventional 0.50 cutoff. Removing

UPDRS and the cardinal motor symptoms, which are components of the diagnostic definition

rather than independent measurements, drops ROC AUC from 0.881 to 0.668 while leaving

calibration intact. We further propagate posterior uncertainty into referral decisions and study

threshold regret over prevalence–cost combinations. A simulation with known data-generating

probabilities tests when Bayesian shrinkage changes calibration and decision regret relative to

maximum-likelihood and ridge estimators. The emergent result is that threshold choice is a

decision problem conditioned on probability quality, target prevalence, and relative error costs.

This is not strictly a property of the classifier.