Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media
arXiv:2011.03638 · doi:10.1098/rspa.2021.0214
Abstract
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 this data can be used to identify the hopping rates in each layer, we compute various profile likelihoods using two methods: first, an exact likelihood is evaluated using a relatively expensive Markov chain approach; and, second we form an approximate likelihood by assuming the distribution of exit times is given by a Gamma distribution whose first two moments match the expected moments from the continuum limit description of the stochastic model. Using the exact and approximate likelihoods we construct various profile likelihoods for a range of problems. In cases where parameter values are not identifiable, we make progress by re-interpreting those data with a reduced model with a smaller number of layers.
arXiv comment41 pages, 11 figures
References in corpus (6)
- Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems
- Joining Forces of Bayesian and Frequentist Methodology: A Study for Inference in the Presence of Non-Identifiability
- A Paradox of State-Dependent Diffusion and How to Resolve It
- New homogenization approaches for stochastic transport through heterogeneous media
- Diffusion in heterogeneous discs and spheres: new closed-form expressions for exit times and homogenization formulae
- Mean exit time for diffusion on irregular domains