Posterior Bias of the Drift Estimator in a Hierarchical Ornstein–Uhlenbeck Model for Adverse Life Events

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. 𝟏𝟔𝟐𝒑BH → 𝒏=𝟑𝟓𝟐𝒏=𝟏𝟐5