The pseudo-marginal approach for efficient Monte Carlo computations

By Christophe Andrieu, Gareth O. Roberts. 2009

946 citations recorded by the source corpus.

We introduce a powerful and flexible MCMC algorithm for stochastic simulation. The method builds on a pseudo-marginal method originally introduced in [Genetics 164 (2003) 1139--1160], showing how algorithms which are approximations to an idealized marginal algorithm, can share the same marginal stationary distribution as the idealized method. Theoretical results are given describing the convergence properties of the proposed method, and simple numerical examples are given to illustrate the promising empirical characteristics of the technique. Interesting comparisons with a more obvious, but inexact, Monte Carlo approximation to the marginal algorithm, are also given.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families (2015, methodology): “Note that this also involves ‘recycling’ the estimates of H from previous iterations to ensure anyymptotic correctness, c.f. [3, Table 1].”
Kernel Adaptive Metropolis-Hastings (2013, background): “This shows that the trends observed in the main text persist alongthe evolution of the whole chain.”
Edward: A library for probabilistic modeling, inference, and criticism (2016, methodology): “This extends to many algorithms: for example, exact EM for exponential families; contrastive divergence (Hinton, 2002); pseudo-marginal and ABC methods (Andrieu and Roberts, 2009); Gibbs sampling within variational inference (Wang and Blei, 2012); Laplace variational inference (Wang and Blei, 2013);”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, methodology): “The latter uses in addition an importance sampling function and retrospectively can be reinterpreted as Grouped Inde-pendence Metropolis-Hastings (GIMH of Andrieu and Roberts (2009), see below) with sample size 1.”
Austerity in MCMC Land: Cutting the Metropolis-Hastings Budget (2013, methodology): “For example, the pseudo marginal MCMC method [Andrieu and Roberts, 2009] and the method developed by Lin et al. [2000] provide a way to conduct exact accept/reject tests using unbiased estimators of the likelihood.”
Toward a general, scaleable framework for Bayesian teaching with applications to topic models (2016, methodology): “To generate documents from the teaching distribution, we employ pseudo-marginal sampling [18, 19], which allows exact Metropolis-Hasting to be performed using approximated functions.”
A Spectral Approach to Gradient Estimation for Implicit Distributions (2018, background): “One way to address this problem is the pseudo-marginal MCMC (Andrieu et al., 2009), through which a markov chain can be simulated to directly sample from p ( θ y ) .”
Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (2012, methodology): “We follow the terminology of [4] and call this method the marginal algorithm.”
Robust generalised Bayesian inference for intractable likelihoods (2021, neutral): “Existing approaches to Bayesian inference for intractable likelihood fall into three categories: (1) likelihood-free methods such as approximate Bayesian computation and Bayesian synthetic likelihood ; Beaumont et al., 2002; Cherief-Abdellatif & Alquier, 2020; Frazier, 2020; Marin et al., 2012; Pric”
Nested Sequential Monte Carlo Methods (2015, background): “Algorithm 1 is an example of what is referred to as an exact approximation ; see e.g., Andrieu & Roberts (2009); Andrieu et al. (2010).”
GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation (2014, methodology): “We will call this the marginal LF MCMC method [2].”
Uniform ergodicity of the iterated conditional SMC and geometric ergodicity of particle Gibbs samplers (2013, methodology): “While PMMH methods have been studied in a series of papers [4, 5, 16, 28, 11], a theoretical study of the PGibbs is still missing.”
Statistical inference for stochastic simulation models--theory and application. (2011, background): “…sense, we also view Monte Carlo within Metropolis Approximation and grouped independence Metropolis-Hastings (O’Neill et al. 2000; Beaumont 2003; Andrieu & Roberts 2009) as parametric approximations, although we see their prime concern not in the approximation of p(D|/) as such, but rather in…”
Bayesian forecasting in economics and finance: A modern review (2022, background): “, 1993; Chopin and Papaspiliopoulos, 2020) and pseudo-marginal MCMC (Beaumont, 2003; Andrieu and Roberts, 2009; Andrieu et al., 2011) – discussed briefly in Section 3.”
Approximate Bayesian Computation in Evolution and Ecology (2010, methodology): “Andrieu & Roberts (2009) show that, more generally, Monte Carlo estimates of the likelihood based on any size of sample (including ABC approximations) can be used in place of the true likelihood in the Metropolis-Hasting accept-reject step provided their expectation corresponds to the true…”
Likelihood-Free Inference by Ratio Estimation (2016, methodology): “(11) In case samples from the posterior are needed, we can use standard sampling schemes with ˆ p ( θ | x 0 ) as the target pdf (Andrieu and Roberts, 2009), for instance MCMC (Her-mans et al., 2020).”
On Markov chain Monte Carlo methods for tall data (2015, methodology): “Exact subsampling approaches: Pseudo-marginal MH Pseudo-marginal MH (Lin et al., 2000; Beaumont, 2003; Andrieu and Roberts, 2009) is a variant of MH, which relies on unbiased estimators of an unnormalized version of the target.”
On Nesting Monte Carlo Estimators (2017, methodology): “Certain nested estimation problems can be tackled by pseudo-marginal methods (Beaumont, 2003; Andrieu and Roberts, 2009; Andrieu et al., 2010).”
The correlated pseudomarginal method (2015, methodology): “Contrary to these approaches, the pseudo-marginal (PM) algorithm directly mimicks the MH scheme targeting the marginal π (θ) by substituting an estimator of the likelihood ratio p(y | θ′)/p(y | θ) for the true likelihood ratio in the MH acceptance probability [36], [5], [3].”