Multilevel Monte Carlo in approximate Bayesian computation

Jasra, Ajay; Jo, Seongil; Nott, David J.; Shoemaker, C. A.; Tempone, Raúl

doi:10.1080/07362994.2019.1566006

Cited by 16 publications

(22 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Guha and Tan (2017) extend the work of Efendiev et al (2015) by replacing the Metropolis-Hasting acceptance probability in a similar way to the MCMC-ABC method (Marjoram et al, 2003). The MLSMC method (Beskos et al, 2017) is exploited to achieve coupling in an ABC context by Jasra et al (2017).…”

Section: Related Workmentioning

confidence: 99%

Multilevel rejection sampling for approximate Bayesian computation

Warne

Baker

Simpson

2018

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate Bayesian computation can be effective techniques for sampling posterior distributions in an approximate Bayesian computation setting. However, without careful consideration of convergence criteria and selection of proposal kernels, such methods can lead to very biased inference or computationally inefficient sampling. In contrast, rejection sampling for approximate Bayesian computation, despite being computationally intensive, results in independent, identically distributed samples from the approximated posterior. An alternative method is proposed for the acceleration of likelihood-free Bayesian inference that applies multilevel Monte Carlo variance reduction techniques directly to rejection sampling. The resulting method retains the accuracy advantages of rejection sampling while significantly improving the computational efficiency.

show abstract

Section: Related Workmentioning

confidence: 99%

Multilevel rejection sampling for approximate Bayesian computation

Warne

Baker

Simpson

2018

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

show abstract

“…Such a benchmark would be significantly more computationally intensive than the comparison of Monte Carlo methods for the forwards problem (Figure 3). The computational statistics literature demonstrates that ABCMCMC [94], ABCSMC [11,121] and ABCMLMC [61,73,144] can be tuned to provide very competitive results on a given inference problem. However, a large number of trial computations are often required to achieve this tuning, or more complex adaptive schemes need to be exploited [30,111].…”

Section: Methodsmentioning

confidence: 99%

“…The formulation of ABCSMC using a sequence of discrepancy thresholds hints that MLMC ideas could also be applicable. Recently, a variety of MLMC methods for ABC have been proposed [61,73,144]. All of these approaches are similar in their application of the multilevel telescoping summation to compute expectations with respect to ABC posterior distributions,…”

Section: Samplers For Approximate Bayesian Computationmentioning

confidence: 99%

“…. ., L. Several approaches to this problem have been proposed: Guha & Tan [135] use a sequence of correlated ABCMCMC samplers in a similar manner to Dodwell et al [105] and Efendiev et al [106]; Jasra et al [136] apply the MLSMC estimator of Beskos et al [107] directly to equation (4.11); and Warne et al [137] develop a MLMC variant of ABC rejection sampler through the introduction of an approximation based on the empirical marginal posterior distributions.…”

Section: Samplers For Approximate Bayesian Computationmentioning

confidence: 99%

See 1 more Smart Citation

Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Warne

Baker

Simpson

2019

J. R. Soc. Interface.

112

View full text Add to dashboard Cite

Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterizing stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealizations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time-course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with Matlab ® implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community.

show abstract

“…The method of Beskos et al (2017) has been extended to the computation of normalising constants (Del Moral et al , 2017) and has been applied to other examples, such as non‐local equations (Jasra et al , 2016) and approximate Bayesian computation (Jasra et al , 2019). The method has also been extended to the case that the accuracy of the approximation improves as the dimension of the target grows, that is, infinite dimensional

sans-serifE

(see Beskos et al , 2018).…”

Section: Approaches For Multilevel Monte Carlo Estimationmentioning

confidence: 99%

Advanced Multilevel Monte Carlo Methods

Jasra

Law

Suciu

2020

Int Statistical Rev

Self Cite

View full text Add to dashboard Cite

This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the discretization of a associated probability law. The MLMC approach works with a hierarchy of biased approximations which become progressively more accurate and more expensive. Using a telescoping representation of the most accurate approximation, the method is able to reduce the computational cost for a given level of error versus i.i.d. sampling from this latter approximation. All of these ideas originated for cases where exact sampling from couples in the hierarchy is possible. This article considers the case where such exact sampling is not currently possible. We consider Markov chain Monte Carlo and sequential Monte Carlo methods which have been introduced in the literature and we describe different strategies which facilitate the application of MLMC within these methods.

show abstract

Multilevel Monte Carlo in approximate Bayesian computation

Cited by 16 publications

References 26 publications

Multilevel rejection sampling for approximate Bayesian computation

Multilevel rejection sampling for approximate Bayesian computation

Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Advanced Multilevel Monte Carlo Methods

Contact Info

Product

Resources

About