One World ABC Seminar: Agnieszka Borowska

on the October 29, 2020

at 11:30 am [UK time]
For this thirteenth session of the One World ABC Seminar, Agnieszka Borowska from University of Glasgow and CLDS will talk about "Gaussian process enhanced semi-automatic ABC for inference in a stochastic differential equation system for chemotaxis".

Inspired by the "One World Probability Seminar", we decided to run The One World ABC Seminar, a weekly/fortnightly series of seminars that will take place on Blackboard Collaborate on Thursdays at 11.30am [UK time]. The idea is to gather members and disseminate results and innovation during these weeks and months under lockdown.

Agnieszka Borowska

Chemotaxis is a type of cell movement in response to a chemical stimulus which plays a keyrole in multiple biophysical processes, such as embryogenesis and wound healing, and whichis crucial for understanding metastasis in cancer research.  In the literature, chemotaxis hasbeen  modelled  using  biophysical  models  based  on  systems  of  nonlinear  stochastic  partialdifferential equations (NSPDEs), which are known to be challenging for statistical inferencedue to the intractability of the associated likelihood and the high computational costs of theirnumerical integration.  Therefore, data analysis in this context has been limited to comparingpredictions from NSPDE models to laboratory data using simple descriptive statistics.  Wepresent a statistically rigorous framework for parameter estimation in complex biophysicalsystems described by NSPDEs such as the one of chemotaxis.  We adopt a likelihood-freeapproach based on approximate Bayesian computations with sequential Monte Carlo (ABC-SMC) which allows for circumventing the intractability of the likelihood.  To find informativesummary statistics, crucial for the performance of ABC, we propose to use a Gaussian process(GP) regression model.  The interpolation provided by the GP regression turns out usefulon its own merits:  it relatively accurately estimates the parameters of the NSPDE modeland allows for uncertainty quantification, at a very low computational cost.  Our proposedmethodology allows for a considerable part of computations to be completed before havingobserved  any  data,  providing  a  practical  toolbox  to  experimental  scientists  whose  modesof  operation  frequently  involve  experiments  and  inference  taking  place  at  distinct  pointsin time.  In an application to externally provided synthetic data we demonstrate that thecorrection provided by ABC-SMC is essential for accurate estimation of some of the NSPDEmodel parameters and for more flexible uncertainty quantification.
[1]  A. Borowska, D. Giurghita, D. Husmeier. Gaussian process enhanced semi-automatic ap-proximate Bayesian computation: parameter inference in a stochastic differential equationsystem for chemotaxis. Preprint available here
Published on October 7, 2020