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Simulation-based inference using splitting schemes for partially observed diffusions in chemical reaction networks

P Jovanovski, A Golightly, U Picchini… - arXiv preprint arXiv …, 2025 - arxiv.org
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… To evaluate the performance of the proposed splitting integrator in comparison with the classical EuM method, we consider a simulation-based inference scenario using …

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@article{2508.11438v1,
Author        = {Petar Jovanovski and Andrew Golightly and Umberto Picchini and Massimiliano Tamborrino},
Title         = {Simulation-based inference using splitting schemes for partially
  observed diffusions in chemical reaction networks},
Eprint        = {2508.11438v1},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.ME},
Abstract      = {We address the problem of simulation and parameter inference for chemical
reaction networks described by the chemical Langevin equation, a stochastic
differential equation (SDE) representation of the dynamics of the chemical
species. This is challenging for two main reasons. First, the
(multi-dimensional) SDEs cannot be explicitly solved and are driven by
multiplicative and non-commutative noise, requiring the development of advanced
numerical schemes for their approximation and simulation. Second, not all
components of the SDEs are directly observed, as the available discrete-time
data are typically incomplete and/or perturbed with measurement error. We
tackle these issues via three contributions. First, we show that these models
can be rewritten as perturbed conditionally Cox-Ingersoll-Ross-type SDEs, i.e.,
each coordinate, conditioned on all other coordinates being fixed, follows an
SDE with linear drift and square root diffusion coefficient perturbed by
additional Brownian motions. Second, for this class of SDEs, we develop a
numerical splitting scheme that preserves structural properties of the model,
such as oscillations, state space and invariant distributions, unlike the
commonly used Euler-Maruyama scheme. Our numerical method is robust for large
integration time steps. Third, we propose a sequential Monte Carlo approximate
Bayesian computation algorithm incorporating "data-conditional" simulation and
sequential learning of summary statistics, allowing inference for
multidimensional partially observed systems, further developing previous
results on fully observed systems based on the Euler-Maruyama scheme. We
validate our approach on models of interest in chemical reaction networks, such
as the stochastic Repressilator, Lotka-Volterra, and two-pool systems,
demonstrating its effectiveness, in terms of both numerical and inferential
accuracy, and reduced computational cost.},
Year          = {2025},
Month         = {Aug},
Url           = {http://arxiv.org/abs/2508.11438v1},
File          = {2508.11438v1.pdf}
}

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