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SUMMARY:Profile likelihood analysis for a stochastic model of diffusion in
  heterogeneous media - Matthew Simpson (Queensland University of Technolog
 y)
DTSTART:20230912T101500Z
DTEND:20230912T110000Z
UID:TALK203359@talks.cam.ac.uk
DESCRIPTION:We compute profile likelihoods for a stochastic model of diffu
 sive transport motivated by experimental observations of heat conduction i
 n layered skin tissues. This process is modelled as a random walk in a lay
 ered one-dimensional material\, where each layer has a distinct particle h
 opping rate. Particles are released at some location\, and the duration of
  time taken for each particle to reach an absorbing boundary is recorded. 
 Motivated by our experimental data\, we aim to explore whether these data 
 can be used to identify the hopping rates in each layer. To achieve this w
 e compute various profile likelihoods using two methods: first\, an exact 
 likelihood is evaluated using a computationally expensive Markov chain app
 roach\; and\, second\, we form an approximate likelihood by assuming the d
 istribution of exit times is given by a Gamma distribution whose first two
  moments match the moments from the continuum limit description of the sto
 chastic model. Using the exact and approximate likelihoods\, we construct 
 various profile likelihoods for a range of problems. In cases where parame
 ter values are not identifiable\, we make progress by re-interpreting thos
 e data with a reduced model with a smaller number of layers.
LOCATION:Seminar Room 1\, Newton Institute
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