Adaptive approximate Bayesian computation

By MARK A. Beaumont, Jean-Marie Cornuet, Jean-Michel Marin, Christian P. Robert. 2008

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Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al. (2006), the application to approximate Bayesian computation results in a bias in the approximation to the posterior. An alternative version based on genuine importance sampling arguments bypasses this difficulty, in connection with the population Monte Carlo method of Cappe et al. (2004), and it includes an automatic scaling of the forward kernel. When applied to a population genetics example, it compares favourably with two other versions of the approximate algorithm. Copyright 2009, Oxford University Press.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e9ca41e58efd86aca0efdc83c7732c85bc6e32b9

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Citations in the corpus

Filtering via approximate Bayesian computation (2010, positive): “In addition, statistical inference from (4) can be achieved via rejection sampling (Pritchard et al. 1999), Markov chain Monte Carlo (MCMC) (Majoram et al. 2003) or SMC methods (Beaumont et al. 2009; Del Moral et al. 2009).”
Approximate Bayesian computational methods (2011, methodology): “The correction published in Sisson et al. (2009) ac-knowledges the existence of a bias and suggests a correction essentially identical to the PMC solution of Beaumont et al. (2009).”
Asymptotically exact inference in differentiable generative models (2016, methodology): “This motivates the use of a constrained variant of Hamiltonian Monte Carlo which leverages the smooth geometry of the manifold to coherently move between inputs exactly consistent with observations.”
Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology (2018, methodology): “Population Monte Carlo (pmc) and Sequential Monte Carlo (smc) abc methods (Del Moral et al. 2006; Sisson et al. 2007; Beaumont et al. 2009; Toni et al. 2009; Bonassi et al. 2015) are popular advancements on rejection abc that adaptively learn a more intelligent proposal distribution, whilst at the…”
Constructing summary statistics for approximate Bayesian computation: semi‐automatic approximate Bayesian computation (2012, methodology): “For alternative importance sampling approaches, based on sequential Monte Carlo sampling, see Beaumont et al. (2009), Sisson et al. (2007) and Toni et al. (2009).”
Kernel approximate Bayesian computation in population genetic inferences (2012, methodology): “Recent progress in ABC algorithm development also has involved the use of Markov chain Monte Carlo or sequential Monte Carlo methods (Marjoram et al. 2003; Sisson et al. 2007; Beaumont et al. 2009; Wegmann et al. 2009 ; Drovandi and Pettit 2011 ).”
Likelihood-free inference via classification (2014, methodology): “Approximate Bayesian computation (ABC) stems from research in genetics (Beaumont et al. 2002; Marjoram et al. 2003; Pritchard et al. 1999; Tavaré et al. 1997),while themethodof simulatedmoments (McFadden 1989; Pakes and Pollard 1989) and indirect inference (Gouriéroux et al. 1993; Smith 2008) come f”
Fast $\epsilon$-free Inference of Simulation Models with Bayesian Conditional Density Estimation (2016, methodology): “We compare to three ABC baselines: (a) rejection ABC [25], where parameters are proposed from the prior and are accepted if (cid:107) x − x o (cid:107) < (cid:15) ; (b) MCMC-ABC [16] with a spherical Gaussian proposal, whose variance we manually tuned separately in each case for best performance; an”
Likelihood-free Markov chain Monte Carlo (2010, methodology): “…attempts to improve sampler efficiency over MCMC-based methods have resulted in the development of likelihood-free sequential Monte Carlo and sequential importance sampling algorithms (Beaumont et al., 2009; Del Moral et al., 2008; Peters et al., 2008; Sisson et al., 2007; Toni et al., 2009).”
ABC–CDE: Toward Approximate Bayesian Computation With Complex High-Dimensional Data and Limited Simulations (2018, methodology): “, 2007) or population Monte Carlo ABC (Beaumont et al., 2009), to construct T .”
Statistical inference for stochastic simulation models--theory and application. (2011, methodology): “Particularly for the ABC approximation (Box 2), SMC algorithms may exhibit advantages over MCMCs, because they are less prone to get stuck in areas of low likelihood (Sisson et al. 2007; Beaumont et al. 2009; Toni et al. 2009, see Alg.”
Non-linear regression models for Approximate Bayesian Computation (2008, methodology): “The main SMCABC algorithm combines ideas underlying rejection methods and sequential importance sampling (Sisson et al. 2007; Beaumont et al. 2009; Toni et al. 2009).”
Efficient Acquisition Rules for Model-Based Approximate Bayesian Computation (2017, methodology): “Algorithms based on Markov Chain Monte Carlo and sequential Monte Carlo have been used to improve the efficiency of ABC as compared to the basic rejection sampler (Marjoram et al., 2003; Sisson et al., 2007; Beaumont et al., 2009; Toni et al., 2009; Marin et al., 2012; Lenormand et al., 2013).”