Journal article
Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media
- 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 825.8KB, Terms of use)
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- Publisher copy:
- 10.1098/rspa.2021.0214
Authors
- Publisher:
- The Royal Society
- Journal:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences More from this journal
- Volume:
- 447
- Issue:
- 2250
- Article number:
- 20210214
- Publication date:
- 2021-06-09
- Acceptance date:
- 2021-05-10
- DOI:
- EISSN:
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1471-2946
- ISSN:
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1364-5021
- Language:
-
English
- Keywords:
- Pubs id:
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1147859
- Local pid:
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pubs:1147859
- Deposit date:
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2021-05-27
- ARK identifier:
Terms of use
- Copyright holder:
- Simpson et al.
- Copyright date:
- 2021
- Rights statement:
- © 2021 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
- Notes:
- This is the accepted manuscript version of the article. The final version is available from The Royal Society at: https://doi.org/10.1098/rspa.2021.0214
- Licence:
- CC Attribution (CC BY)
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