arXiv subjects

Alexander P. Browning

Publications and source records attributed to Alexander P. Browning.

7 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↗

arXiv2026

Reliable model selection in the presence of parameter non-identifiability

Mathematical models are invaluable for understanding and predicting how biological systems behave, although their construction requires specifying mechanisms and relationships that are often not perfectly known. In the presence of multiple competing models, model uncertainty should be accounted for when performing inference based on available data. Bayesian model selection is a framework for testing mechanistic hypotheses and generating predictions under model uncertainty, which generally requires computation of the model evidence. In this work, we investigate the reliability of evidence computation methods when parameter non-identifiability -- the inability to distinguish between parameter values given available data -- is present, and find that deterministic evidence approximations can produce misleading model selection results because their underlying assumptions are violated. We propose a novel implementation of adaptive multiple importance sampling for evidence estimation, and demonstrate its robustness against non-identifiability. We use ecological case studies to demonstrate how simple model selection methods fail to produce accurate results, whereas our method yields model selection results that are comparable to those obtained by Markov chain Monte Carlo methods at substantially lower computational cost. Given the pervasiveness of parameter non-identifiability in mathematical biology, this work provides a practical approach to reliable model selection in the presence of poorly identified parameters.

stat.ME↗

arXiv2026

Framing local structural identifiability and observability in terms of parameter-state symmetries

We introduce a subclass of Lie symmetries, called parameter-state symmetries, to analyse the local structural identifiability and observability of mechanistic models consisting of state-dependent ODEs with observed outputs. These symmetries act on parameters and states while preserving observed outputs at every time point. We prove that locally structurally identifiable parameter combinations and locally structurally observable states correspond to universal invariants of all parameter-state symmetries of a given model. We illustrate the framework on four previously studied mechanistic models, confirming known identifiability results and revealing novel insights into which states are observable, providing a unified symmetry-based approach for analysing structural properties of dynamical systems.

math.DS↗

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↗

arXiv2023

Predicting radiotherapy patient outcomes with real-time clinical data using mathematical modelling

Longitudinal tumour volume data from head-and-neck cancer patients show that tumours of comparable pre-treatment size and stage may respond very differently to the same radiotherapy fractionation protocol. Mathematical models are often proposed to predict treatment outcome in this context, and have the potential to guide clinical decision-making and inform personalised fractionation protocols. Hindering effective use of models in this context is the sparsity of clinical measurements juxtaposed with the model complexity required to produce the full range of possible patient responses. In this work, we present a compartment model of tumour volume and tumour composition, which, despite relative simplicity, is capable of producing a wide range of patient responses. We then develop novel statistical methodology and leverage a cohort of existing clinical data to produce a predictive model of both tumour volume progression and the associated level of uncertainty that evolves throughout a patient's course of treatment. To capture inter-patient variability, all model parameters are patient specific, with a bootstrap particle filter-like Bayesian approach developed to model a set of training data as prior knowledge. We validate our approach against a subset of unseen data, and demonstrate both the predictive ability of our trained model and its limitations.

q-bio.TO↗

arXiv2022

Efficient inference and identifiability analysis for differential equation models with random parameters

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data. Therefore, methods for exploring the identifiability of models that explicitly incorporate heterogeneity through variability in model parameters are relatively underdeveloped. We develop a new likelihood-based framework, based on moment matching, for inference and identifiability analysis of differential equation models that capture biological heterogeneity through parameters that vary according to probability distributions. As our novel method is based on an approximate likelihood function, it is highly flexible; we demonstrate identifiability analysis using both a frequentist approach based on profile likelihood, and a Bayesian approach based on Markov-chain Monte Carlo. Through three case studies, we demonstrate our method by providing a didactic guide to inference and identifiability analysis of hyperparameters that relate to the statistical moments of model parameters from independent observed data. Our approach has a computational cost comparable to analysis of models that neglect heterogeneity, a significant improvement over many existing alternatives. We demonstrate how analysis of random parameter models can aid better understanding of the sources of heterogeneity from biological data.

stat.ME↗