On the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post-correction

Vihola, Matti; Franks, Jordan

doi:10.1093/biomet/asz078

Cited by 14 publications

(9 citation statements)

References 31 publications

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“…In a diffusion context, a proper weighting can be constructed based on randomized multilevel Monte Carlo, as recently described in Franks et al (2018), and ABC postcorrection may be seen as IS‐type correction (Vihola & Franks, 2020). Laplace approximations are available for a wider class of Gaussian latent variable models beyond SSMs (cf.…”

Section: Discussionmentioning

confidence: 99%

Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo

Vihola

Helske

Franks

2020

Scandinavian J Statistics

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We consider importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution. In the context of Bayesian latent variable models, the MCMC typically operates on the hyperparameters, and the subsequent weighting may be based on IS or sequential Monte Carlo (SMC), but allows for multilevel techniques as well. The IS approach provides a natural alternative to delayed acceptance (DA) pseudo-marginal/particle MCMC, and has many advantages over DA, including a straightforward parallelization and additional flexibility in MCMC implementation. We detail minimal conditions which ensure strong consistency of the suggested estimators, and provide central limit theorems with expressions for asymptotic variances. We demonstrate how our method can make use of SMC in the state space models context, using Laplace approximations and time-discretized diffusions. Our experimental results are promising and show that the IS-type approach can provide substantial

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Section: Discussionmentioning

confidence: 99%

Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo

Vihola

Helske

Franks

2020

Scandinavian J Statistics

Self Cite

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“…MCMC procedures can also used to generate samples from the approximate posterior distributions [Marjoram et al, 2003, Marjoram, 2013, Vihola and Franks, 2020, and improving their applicability to high-dimensional problems is an on-going research problem [Rodrigues et al, 2020, Clarté et al, 2020.…”

Section: Recent Progress In Methods Developmentmentioning

confidence: 99%

ABC of the Future

Pesonen¹,

Simola²,

Köhn‐Luque³

et al. 2021

Preprint

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Approximate Bayesian computation (ABC) has advanced in two decades from a seminal idea to a practically applicable inference tool for simulator-based statistical models, which are becoming increasingly popular in many research domains. The computational feasibility of ABC for practical applications has been recently boosted by adopting techniques from machine learning to build surrogate models for the approximate likelihood or posterior and by the introduction of a general-purpose software platform with several advanced features, including automated parallelization. Here we demonstrate the strengths of the advances in ABC by going beyond the typical benchmark examples and considering real applications in astronomy, infectious disease epidemiology, personalised cancer therapy and financial prediction. We anticipate that the emerging success of ABC in producing actual added value and quantitative insights in the real world will continue to inspire a plethora of further applications across different fields of science, social science and technology.

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“…We also run the random-walk Metropolis-Hastings kernel directly as an ABC-MCMC algorithm. As described in [23] we use a Robbins-Monro schedule to adaptively tune the stepsize, preconditioner combination to 2.38 2 d −1…”

Section: Numerical Experimentsmentioning

confidence: 99%

Ensemble Kalman Inversion for General Likelihoods

Duffield,

Singh

2021

Preprint

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Ensemble Kalman inversion represents a powerful technique for inference in statistical models with likelihoods of the form y | x ∼ N(y | H(x), R) where the forward operator H and covariance R are known. In this article, we generalise ensemble Kalman inversion to models with general likelihoods, y | x ∼ p(y | x) where the likelihood can be sampled from, but its density not necessarily evaluated. We examine the ensemble Kalman performance for both optimisation and uncertainty quantification against fully adaptive approximate Bayesian computation techniques.

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On the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post-correction

Cited by 14 publications

References 31 publications

Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo

Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo

ABC of the Future

Ensemble Kalman Inversion for General Likelihoods

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