Residual Model Criticism for Fitted SDE Implementations
Abstract
Stochastic differential equation (SDE) models can reproduce trajectories while missing temporal dependence. We compare residual-based scores from a held-out path with scores from paths simulated by a fitted implementation, keeping fitted parameters, simulation rules and the scoring rule fixed. We give conditions for Monte Carlo calibration and bound conditional rejection error by the gap between conditional score CDFs. Residuals use zero-noise centres and covariance approximations that track noise propagation over observation intervals; report residuals also include reporting variation. Residual weights affect sensitivity and the influence of fitting error. For a quadratic energy score in a linear example with singular true covariance, whitening with nonsingular fitted covariance matrices leaves a nonvanishing score-CDF gap as nonzero coefficient estimates approach the truth. A fixed positive-definite weighting matrix makes the gap vanish. In a controlled SIR experiment using reference paths simulated at fitted parameters, adding susceptible-state endpoints to training or downweighting a low-variance residual reduces null rejection. A separate comparison using reference paths simulated at the true parameter shows reduced sensitivity to added susceptible-coordinate noise after downweighting. An exploratory weekly-report application incorporates reporting and reconstruction into reference simulations, revealing excess correlation between squared residuals in Czechia and persistently negative residuals in Finland.
Related
- On the convergence of dynamic implementations of Hamiltonian Monte Carlo and no U-turn samplers
- Simulation-based Criticism of Complex Biological Models with Neural Evidence Estimation
- Risk-minimizing GUE-implementations of truthful reporting in a Dynamic Social Choice Problem
- Model Criticism via Stochastic Optimization
- Multiclass Classification with Rare Useful Features: Fundamental Limits and the Optimality of Diversity Pursuit Higher Criticism Thresholding
BibTeX
@misc{zheng2026residual,
title = {{Residual Model Criticism for Fitted SDE Implementations}},
author = {Shengda Zheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18271},
eprint = {2610.18271},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18271},
}
RIS
TY - UNPB
TI - Residual Model Criticism for Fitted SDE Implementations
AU - Shengda Zheng
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18271
UR - https://arxiv.org/abs/2610.18271
AB - Stochastic differential equation (SDE) models can reproduce trajectories while missing temporal dependence. We compare residual-based scores from a held-out path with scores from paths simulated by a fitted implementation, keeping fitted parameters, simulation rules and the scoring rule fixed. We give conditions for Monte Carlo calibration and bound conditional rejection error by the gap between conditional score CDFs. Residuals use zero-noise centres and covariance approximations that track noise propagation over observation intervals; report residuals also include reporting variation. Residual weights affect sensitivity and the influence of fitting error. For a quadratic energy score in a linear example with singular true covariance, whitening with nonsingular fitted covariance matrices leaves a nonvanishing score-CDF gap as nonzero coefficient estimates approach the truth. A fixed positive-definite weighting matrix makes the gap vanish. In a controlled SIR experiment using reference paths simulated at fitted parameters, adding susceptible-state endpoints to training or downweighting a low-variance residual reduces null rejection. A separate comparison using reference paths simulated at the true parameter shows reduced sensitivity to added susceptible-coordinate noise after downweighting. An exploratory weekly-report application incorporates reporting and reconstruction into reference simulations, revealing excess correlation between squared residuals in Czechia and persistently negative residuals in Finland.
ER -