Projects per year
Abstract
Optimizationbased samplers such as randomizethenoptimize (RTO) [J. M. Bardsley et al., SIAM J. Sci. Comput., 36 (2014), pp. A1895A1910] provide an efficient and parallellizable approach to solving largescale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw samples from an approximate posterior distribution. "Correcting" these samples, either by Metropolization or importance sampling, enables characterization of the original posterior distribution. This paper focuses on the scalability of RTO to problems with highor infinitedimensional parameters. In particular, we introduce a new subspace strategy to reformulate RTO. For problems with intrinsic lowrank structures, this subspace acceleration makes the computational complexity of RTO scale linearly with the parameter dimension. Furthermore, this subspace perspective suggests a natural extension of RTO to a function space setting. We thus formalize a function space version of RTO and establish sufficient conditions for it to produce a valid MetropolisHastings proposal, yielding dimensionindependent sampling performance. Numerical examples corroborate the dimension independence of RTO and demonstrate sampling performance that is also robust to small observational noise.
Original language  English 

Pages (fromto)  A1317A1347 
Number of pages  31 
Journal  SIAM Journal on Scientific Computing 
Volume  42 
Issue number  2 
DOIs  
Publication status  Published  27 Apr 2020 
Keywords
 Bayesian inference
 Infinitedimensional inverse problems
 Markov chain Monte Carlo
 Metropolis independence sampling
 Transport maps
Projects
 1 Finished

ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights
Hall, P., Bartlett, P., Bean, N., Burrage, K., DeGier, J., Delaigle, A., Forrester, P., Geweke, J., Kohn, R., Kroese, D., Mengersen, K. L., Pettit, A., Pollett, P., Roughan, M., Ryan, L., Taylor, P., Turner, I., Wand, M., Garoni, T., SmithMiles, K. A., Caley, M., Churches, T., Elazar, D., Gupta, A., Harch, B., Tam, S., Weegberg, K., Willinger, W. & Hyndman, R.
Australian Research Council (ARC), Monash University – Internal Department Contribution, University of Melbourne, Queensland University of Technology , University of Adelaide, University of New South Wales, University of Queensland , University of Technology Sydney, Monash University – Internal University Contribution, Monash University – Internal Faculty Contribution, Monash University – Internal School Contribution, Roads Corporation (trading as VicRoads) (Victoria)
1/01/17 → 31/12/21
Project: Research