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dc.contributor.authorJasra, Ajay
dc.contributor.authorLaw, Kody J H
dc.contributor.authorLu, Deng
dc.identifier.citationJasra, A., Law, K. J. H., & Lu, D. (2021). Unbiased estimation of the gradient of the log-likelihood in inverse problems. Statistics and Computing, 31(3). doi:10.1007/s11222-021-09994-6
dc.description.abstractWe consider the problem of estimating a parameter θ∈Θ⊆Rdθ associated with a Bayesian inverse problem. Typically one must resort to a numerical approximation of gradient of the log-likelihood and also adopt a discretization of the problem in space and/or time. We develop a new methodology to unbiasedly estimate the gradient of the log-likelihood with respect to the unknown parameter, i.e. the expectation of the estimate has no discretization bias. Such a property is not only useful for estimation in terms of the original stochastic model of interest, but can be used in stochastic gradient algorithms which benefit from unbiased estimates. Under appropriate assumptions, we prove that our estimator is not only unbiased but of finite variance. In addition, when implemented on a single processor, we show that the cost to achieve a given level of error is comparable to multilevel Monte Carlo methods, both practically and theoretically. However, the new algorithm is highly amenable to parallel computation.
dc.description.sponsorshipAJ was supported by KAUST baseline funding. Some of this research was supported by Singapore MOE tier 1 grant R-155-000-182-114. KJHL was supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1. We thank two referees for their comments which have greatly improved the article.
dc.publisherSpringer Nature
dc.rightsThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
dc.titleUnbiased estimation of the gradient of the log-likelihood in inverse problems
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalStatistics and Computing
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionDepartment of Mathematics, University of Manchester, Manchester, M13 9PL, UK
dc.contributor.institutionDepartment of Statistics & Applied Probability, National University of Singapore, Singapore, 117546, Singapore
kaust.personJasra, Ajay
kaust.acknowledged.supportUnitKAUST baseline funding

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