The correlated pseudomarginal method
By George Deligiannidis, Arnaud Doucet, Michael K. Pitt. Journal of The Royal Statistical Society Series B-statistical Methodology, 2015
106 citations recorded by the source corpus.
The pseudomarginal algorithm is a Metropolis–Hastings‐type scheme which samples asymptotically from a target probability density when we can only estimate unbiasedly an unnormalized version of it. In a Bayesian context, it is a state of the art posterior simulation technique when the likelihood function is intractable but can be estimated unbiasedly by using Monte Carlo samples. However, for the performance of this scheme not to degrade as the number T of data points increases, it is typically necessary for the number N of Monte Carlo samples to be proportional to T to control the relative variance of the likelihood ratio estimator appearing in the acceptance probability of this algorithm. The correlated pseudomarginal method is a modification of the pseudomarginal method using a likelihood ratio estimator computed by using two correlated likelihood estimators. For random‐effects models, we show under regularity conditions that the parameters of this scheme can be selected such that the relative variance of this likelihood ratio estimator is controlled when N increases sublinearly with T and we provide guidelines on how to optimize the algorithm on the basis of a non‐standard weak convergence analysis. The efficiency of computations for Bayesian inference relative to the pseudomarginal method empirically increases with T and exceeds two orders of magnitude in some examples.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/f130bc1faf8da808759c32666c1783c8361f6190
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In Artificial Intelligence
- Ruben Loaiza-Maya
- Gary Koop
- Amos J. Storkey
- Gael M. Martin
- John M. Maheu
- Anastasios Panagiotelis
- Didier Nibbering
- David T. Frazier
In Statistics and Probability
- Ruben Loaiza-Maya
- Gary Koop
- Amos J. Storkey
- Gael M. Martin
- John M. Maheu
- Anastasios Panagiotelis
- Didier Nibbering
- David T. Frazier
Citations in the corpus
- Asymptotically exact inference in differentiable generative models (2016, methodology): “Related approaches using Metropolis updates instead have also been proposed [24, 25].”
- Bayesian forecasting in economics and finance: A modern review (2022, methodology): “For the purpose of this review, the most pertinent development is the melding of particle filtering with MCMC in state space settings to produce a particle marginal MH (PMMH) algorithm (Andrieu et al., 2011; Flury and Shephard, 2011; Pitt et al., 2012; Doucet et al., 2015; Deligiannidis et al., 2018”