arXiv subjects

Arianna Ceccarelli

Publications and source records attributed to Arianna Ceccarelli.

3 recordsLinked to original sources

arXiv2026

Structural identifiability of partially-observed stochastic processes: from single-particle trajectories to total particle density data

The increasing availability of experimental data has intensified interest in calibrating stochastic models, raising fundamental questions about parameter identifiability. Structural identifiability determines whether parameters can be uniquely recovered from idealised, noise-free data, a prerequisite to allow for parameter estimation in real-world scenarios. However, existing methods to assess structural identifiability are not generally applicable to stochastic processes. We develop a methodology to analyse structural identifiability for a class of stochastic processes. We investigate how structural identifiability depends on the type of available data, distinguishing between single-particle trajectories and total particle density measurements. For trajectory data, we use the particle-based model description that explicitly represents single-particle dynamics. For population-level data, we derive a partial differential equation model representation, that describes the evolution of total particle density, and apply a differential algebra approach, common to ordinary differential equation analysis. We further introduce a method to study information arising from the initial condition, based on using the characteristic equations to construct a Taylor expansion of the particle density evolution. We apply our methodology to an example model and show that it is structurally identifiable from single-particle trajectory data but not from total particle density data, demonstrating that parameter identifiability depends on the type of data available.

stat.ME↗

arXiv2025

A likelihood-based Bayesian inference framework for the calibration of and selection between stochastic velocity-jump models

Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities. These tracking data can be used to calibrate mathematical models describing the motility of individual entities. The challenges in calibrating models for single-agent motion derive from the intrinsic characteristics of experimental data, collected at discrete time steps and with measurement noise. We consider motion of individual agents that can be described by velocity-jump models in one spatial dimension. These agents transition between a network of \textit{n} states, in which each state is associated with a fixed velocity and fixed rates of switching to every other state. Exploiting approximate solutions to the resultant stochastic process, we develop a Bayesian inference framework to calibrate these models to discrete-time noisy data. We first demonstrate that the framework can be used to effectively recover the model parameters of data simulated from two-state and three-state models. Finally, we explore the question of model selection first using simulated data and then using experimental data tracking mRNA transport inside \textit{Drosophila} neurons. Overall, our results demonstrate that the framework is effective and efficient in calibrating and selecting between velocity-jump models and it can be applied to a range of motion processes.

stat.ME↗

arXiv2025

Approximate solutions of a general stochastic velocity-jump model subject to discrete-time noisy observations

Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities over time. These tracking data motivate the use of mathematical models to characterise the motion observed. In this paper, we aim to describe the solutions of velocity-jump models for single-agent motion in one spatial dimension, characterised by successive Markovian transitions within a finite network of n states, each with a specified velocity and a fixed rate of switching to every other state. In particular, we focus on obtaining the solutions of the model subject to noisy, discrete-time, observations, with no direct access to the agent state. The lack of direct observation of the hidden state makes the problem of finding the exact distributions generally intractable. Therefore, we derive a series of approximations for the data distributions. We verify the accuracy of these approximations by comparing them to the empirical distributions generated through simulations of four example model structures. These comparisons confirm that the approximations are accurate given sufficiently infrequent state switching relative to the imaging frequency. The approximate distributions computed can be used to obtain fast forwards predictions, to give guidelines on experimental design, and as likelihoods for inference and model selection.

physics.data-an↗