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An importance sampling approach for reliable and efficient inference in Bayesian ordinary differential equation models
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Stat, Volume 12, issue 1
Abstract
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation error inherently biases statistical inference results, but the amount of this bias is generally unknown and often ignored in Bayesian parameter inference. We propose a computationally efficient method for verifying the reliability of posterior inference for such models, when the inference is performed using Markov chain Monte Carlo methods. We validate the efficiency and reliability of our workflow in experiments using simulated and real data and different ODE solvers. We highlight problems that arise with commonly used adaptive ODE solvers and propose robust and effective alternatives, which, accompanied by our workflow, can now be taken into use without losing reliability of the inferences.
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Funding Information: We would like to acknowledge the computational resources provided by Aalto Science‐IT, Finland. This work was supported by the Academy of Finland Flagship program: Finnish Center for Artificial Intelligence, and the Academy of Finland projects 340721, 311584, and 328401. Publisher Copyright: © 2023 The Authors. Stat published by John Wiley & Sons Ltd.
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Timonen, J, Siccha, N, Bales, B, Lähdesmäki, H & Vehtari, A 2023, 'An importance sampling approach for reliable and efficient inference in Bayesian ordinary differential equation models', Stat, vol. 12, no. 1, e614. https://doi.org/10.1002/sta4.614