Imperial College London
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ProfessorColinCotter

Faculty of Natural Sciences, Department of Mathematics

Professor of Computational Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 3468colin.cotter

 
 
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Location

 

755Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Cotter:2019:10.1137/17M1114867,
author = {Cotter, C and Cotter, S and Russell, P},
doi = {10.1137/17M1114867},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
pages = {444--471},
title = {Ensemble transport adaptive importance sampling},
url = {http://dx.doi.org/10.1137/17M1114867},
volume = {7},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Markov chain Monte Carlo methods are a powerful and commonly used family ofnumerical  methods  for  sampling  from  complex  probability  distributions.   As  applications  of  thesemethods increase in size and complexity, the need for efficient methods increases.  In this paper, wepresent a particle ensemble algorithm.  At each iteration, an importance sampling proposal distri-bution is formed using an ensemble of particles.  A stratified sample is taken from this distributionand weighted under the posterior, a state-of-the-art ensemble transport resampling method is thenused to create an evenly weighted sample ready for the next iteration.  We demonstrate that thisensemble transport adaptive importance sampling (ETAIS) method outperforms MCMC methodswith equivalent proposal distributions for low dimensional problems, and in fact shows better thanlinear improvements in convergence rates with respect to the number of ensemble members.  We alsointroduce a new resampling strategy, multinomial transformation (MT), which while not as accurateas  the  ensemble  transport  resampler,  is  substantially  less  costly  for  large  ensemble  sizes,  and  canthen be used in conjunction with ETAIS for complex problems.  We also focus on how algorithmicparameters regarding the mixture proposal can be quickly tuned to optimise performance.  In partic-ular, we demonstrate this methodology’s superior sampling for multimodal problems, such as thosearising from inference for mixture models, and for problems with expensive likelihoods requiring thesolution  of  a  differential  equation,  for  which  speed-ups  of  orders  of  magnitude  are  demonstrated.Likelihood evaluations of the ensemble could be computed in a distributed manner, suggesting thatthis methodology is a good candidate for parallel Bayesian computations.
AU  - Cotter,C
AU  - Cotter,S
AU  - Russell,P
DO  - 10.1137/17M1114867
EP  - 471
PY  - 2019///
SN  - 2166-2525
SP  - 444
TI  - Ensemble transport adaptive importance sampling
T2  - SIAM/ASA Journal on Uncertainty Quantification
UR  - http://dx.doi.org/10.1137/17M1114867
UR  - http://hdl.handle.net/10044/1/67317
VL  - 7
ER  -
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