# Enhancing Migraine Trigger Surprisal Predictions: A Bayesian Approach to Establishing Prospective Expectations

## TL;DR

This paper explores using Bayesian methods to predict migraine triggers in real time by dynamically updating expectations based on limited personal data.

## Contribution

The novel contribution is applying Bayesian modeling to estimate trigger surprisal prospectively, improving real-time migraine risk prediction.

## Key findings

- Dynamic Bayesian surprisal values differ from retrospective estimates, especially early in data collection.
- Empirically informed priors yield more stable and less biased surprisal predictions.
- Individual variability is high, particularly for exercise behavior.

## Abstract

Prior work has demonstrated that higher surprisal, a measure quantifying the unexpectedness of a trigger exposure, predicts headache onset over 12 to 24 h. However, these analyses relied on retrospective expectations of trigger exposure formed after extended data collection. To operationalize surprisal prospectively, Bayesian methods could update expectations dynamically over time. The objective of this study was to extend the application of surprisal theory for predicting migraine attack risk by developing methods to estimate trigger variable likelihood in real time, under conditions of limited personal observation. In a prospective daily diary study of individuals with migraine (N = 104), data were collected over 28 days, including stress, sleep, and exercise exposures. Bayesian models were applied to estimate daily expectations for each variable under uninformative and empirical priors derived from the sample. Stress was modeled using a hurdle-Gamma distribution, sleep using discrete outcomes from a Normal distribution, and exercise using a Bernoulli distribution. Surprisal was calculated based on the predictive distribution at each time point and compared to static empirical surprisal values obtained after full data collection. Dynamic Bayesian surprisal values systematically differed from retrospective empirical estimates, particularly early in the observation period. Divergence was larger and more variable under uninformative priors but attenuated over time. Empirically informed priors produced more stable, lower-bias surprisal trajectories. Substantial individual variability was observed across exposure types, especially for exercise behavior. Prospective surprisal modeling is feasible but highly sensitive to prior specification, especially in sparse data contexts (e.g., a binary exposure). Incorporating empirical or individually informed priors may improve early model calibration, though individual learning remains essential. These methods offer a foundation for real-time headache forecasting and dynamic modeling of brain–environment interactions.