# Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media

@article{Simpson2021ProfileLA, title={Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media}, author={Matthew J. Simpson and Alexander P. Browning and Christopher C. Drovandi and Elliot J. Carr and Oliver J. Maclaren and Ruth E. Baker}, journal={Proceedings. Mathematical, Physical, and Engineering Sciences}, year={2021}, volume={477} }

We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material, where each layer has a distinct particle hopping rate. Particles are released at some location, and the duration of time taken for each particle to reach an absorbing boundary is recorded. To explore whether these data can be used to identify the hopping…

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## References

SHOWING 1-10 OF 53 REFERENCES

New homogenization approaches for stochastic transport through heterogeneous media.

- MathematicsThe Journal of chemical physics
- 2019

This work presents a new class of homogenization approximations by considering a stochastic diffusive transport model on a one-dimensional domain containing an arbitrary number of layers with different jump rates, and finds that differentjump rates in the layers give rise to a net bias, leading to a non-zero advection, for the entire homogenized system.

A paradox of state-dependent diffusion and how to resolve it

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2012

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region, the diffusion coefficient is twice the value of the diffusion coefficient in the other…

Mean exit time for diffusion on irregular domains

- MathematicsNew Journal of Physics
- 2021

Many problems in physics, biology, and economics depend upon the duration of time required for a diffusing particle to cross a boundary. As such, calculations of the distribution of first passage…

Moments of action provide insight into critical times for advection-diffusion-reaction processes.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

This work generalizes Berezhkovskii's approach by presenting a framework to calculate the MAT, as well as the higher moments, which are called the moments of action, and indicates that it is possible to solve for the Moments of action exactly without requiring the transient solution of the PDE.

Bayesian estimation for percolation models of disease spread in plant populations

- MathematicsStat. Comput.
- 2006

Bayesian methods for fitting the model to observations of disease spread through space and time in replicate populations are developed and they confirm the findings of earlier non-spatial analyses regarding the dynamics of disease transmission and yield new evidence of environmental heterogeneity in the replicate experiments.

Practical parameter identifiability for spatio-temporal models of cell invasion

- BiologyJournal of the Royal Society Interface
- 2020

The profile likelihood ought to be adopted as a screening tool to assess practical identifiability before MCMC computations are performed, providing similar results to MCMC with the advantage of being an order of magnitude faster to compute.

Critical time scales for advection-diffusion-reaction processes.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

It is shown that MAT and MPLT are equivalent for certain uniform-to-uniform transitions; these results provide a practical interpretation for MAT by directly linking the stochastic microscopic processes to a meaningful macroscopic time scale.

Random walk models in biology

- BiologyJournal of The Royal Society Interface
- 2008

The mathematical theory behind the simple random walk is introduced and how this relates to Brownian motion and diffusive processes in general and a reinforced random walk can be used to model movement where the individual changes its environment.

Modeling of reaction-diffusion transport into a core-shell geometry.

- Environmental ScienceJournal of theoretical biology
- 2019