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

Area of Science:

• Computational physics
• Biophysics
• Mathematical modeling

Background:

• Heat conduction in layered skin tissues is complex.
• Stochastic models offer insights into diffusive transport.
• Understanding particle hopping rates is crucial for accurate modeling.

Purpose of the Study:

• To compute profile likelihoods for a stochastic diffusive transport model.
• To assess the identifiability of hopping rates in layered tissues.
• To develop methods for parameter estimation in complex systems.

Main Methods:

• A stochastic random walk model simulating particle transport in layered materials.
• Exact likelihood evaluation using a Markov chain approach.
• Approximate likelihood formation using a Gamma distribution fitted to model moments.

Main Results:

• Profile likelihoods were computed using both exact and approximate methods.
• Parameter identifiability was assessed for various model configurations.
• Model reduction by decreasing the number of layers improved parameter identification in challenging cases.

Conclusions:

• The study demonstrates the utility of profile likelihoods for parameter estimation in stochastic transport models.
• Both exact and approximate methods provide valuable insights.
• Model simplification is an effective strategy for addressing parameter non-identifiability.