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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.

Original languageEnglish
Article numbere614
JournalStat
Volume12
Issue number1
DOIs
Publication statusPublished - 18 Sept 2023
MoE publication typeA1 Journal article-refereed

Keywords

  • Bayesian methods
  • computationally intensive methods
  • Markov chain Monte Carlo
  • statistical computing
  • statistical inference

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