WSEAS Transactions on Business and Economics
Print ISSN: 1109-9526, E-ISSN: 2224-2899
Volume 23, 2026
Posterior Bias of the Drift Estimator in a Hierarchical Ornstein–Uhlenbeck Model for Adverse Life Events
Authors: , , , , , , ,
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Abstract: A hierarchical Ornstein–Uhlenbeck stochastic differential equation with event-conditional drift is fitted to monthly text-derived affect trajectories from a self-disclosure-rich Reddit subreddit (2023–2024; 254,153 users, 324,548 user-months), with the death of a close family member as the adverse life event. Event dates are recovered from free text by three regex classes of increasing specificity — coarse, explicit and recent — forming a within-corpus precision ladder. The ladder gives the first real-data test of the posterior-bias bound of the companion paper, [6], which predicts that the recovered drift magnitude grows as event-date precision tightens. The prediction is confirmed on the coarse-to-explicit step (mean drift −0.109 to −0.157 standardised VADER units; adjusted p from 0.041 to 0.008), whereas the explicit-to-recent step is underpowered because the recency filter cuts the subject pool threefold. We document this precision–power tradeoff and propose the regex ladder as a reusable proxy for event-date precision. $$ → −0.109- 0.157d- 0.117- 0.162p_{BH} → n= 352n=125 $$
Keywords:
Ornstein–Uhlenbeck process, Stochastic differential equations, Particle filter, Hierarchical Bayesian inference, Posterior bias, Adverse life events, Family loss, Text-derived event detection, Latent affect
Pages: 1424-1434
DOI: 10.37394/23207.2026.23.110