Identification and curvature bias for shared inputs in multichannel dynamical models

Abstract

Pooling many channels with a shared unknown input can leave persistent bias when each channel retains a fixed number of observations and its own incidental parameters. For heterogeneous smooth channel manifolds under isotropic noise, the second-order bias is an information-weighted regression of mean curvature on normal input velocity. A feasible correction gives centred Gaussian inference as the noise level σ decreases with Rσ⁶→0, compared with Rσ²→0 without correction. We extend the stochastic expansion and studentization to deterministic channel arrays with densely correlated Gaussian errors of bounded covariance operator norm. General marginal covariance adds a forcing term that can bias even flat channels, while cross-channel covariance changes uncertainty. For Gaussian errors with a separable frame-by-channel covariance whose channel factor is autoregressive in a known ordering, an independent zero-mean calibration field yields a covariance estimator accurate enough for corrected inference. Boundary accumulation and fixed working population models introduce distinct bias terms; rational-multiplier and zero-count arguments connect identification to frame-integrated compartment models. Simulations test both oracle and estimated-covariance inference, including independent PET replications. Moderate-noise undercoverage, optimization ambiguity and the need to validate reconstruction covariance limit practical inference. The real-data example supports sensitivity analysis, not clinically calibrated intervals.

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BibTeX RIS

BibTeX

@misc{huang2026identification,
  title = {{Identification and curvature bias for shared inputs in multichannel dynamical models}},
  author = {Hsin-Hsiung Huang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33642},
  eprint = {2610.33642},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33642},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Identification and curvature bias for shared inputs in multichannel dynamical models
AU  - Hsin-Hsiung Huang
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33642
UR  - https://arxiv.org/abs/2610.33642
AB  - Pooling many channels with a shared unknown input can leave persistent bias when each channel retains a fixed number of observations and its own incidental parameters. For heterogeneous smooth channel manifolds under isotropic noise, the second-order bias is an information-weighted regression of mean curvature on normal input velocity. A feasible correction gives centred Gaussian inference as the noise level σ decreases with Rσ^6→0, compared with Rσ^2→0 without correction. We extend the stochastic expansion and studentization to deterministic channel arrays with densely correlated Gaussian errors of bounded covariance operator norm. General marginal covariance adds a forcing term that can bias even flat channels, while cross-channel covariance changes uncertainty. For Gaussian errors with a separable frame-by-channel covariance whose channel factor is autoregressive in a known ordering, an independent zero-mean calibration field yields a covariance estimator accurate enough for corrected inference. Boundary accumulation and fixed working population models introduce distinct bias terms; rational-multiplier and zero-count arguments connect identification to frame-integrated compartment models. Simulations test both oracle and estimated-covariance inference, including independent PET replications. Moderate-noise undercoverage, optimization ambiguity and the need to validate reconstruction covariance limit practical inference. The real-data example supports sensitivity analysis, not clinically calibrated intervals.
ER  -

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