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We compute profile likelihoods for a stochastic model of diffusive transportmotivated by experimental observations of heat conduction in layered skintissues. This process is modelled as a random walk in a layered one-dimensionalmaterial, where each layer has a distinct particle hopping rate. Particles arereleased at some location, and the duration of time taken for each particle toreach an absorbing boundary is recorded. To explore whether this data can beused to identify the hopping rates in each layer, we compute various profilelikelihoods using two methods: first, an exact likelihood is evaluated using arelatively expensive Markov chain approach; and, second we form an approximatelikelihood by assuming the distribution of exit times is given by a Gammadistribution whose first two moments match the expected moments from thecontinuum limit description of the stochastic model. Using the exact andapproximate likelihoods we construct various profile likelihoods for a range ofproblems. In cases where parameter values are not identifiable, we makeprogress by re-interpreting those data with a reduced model with a smallernumber of layers.

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