Sequential Monte Carlo without likelihoods

By Scott Anthony Sisson, Yanan Fan, Mark M. Tanaka. 2007

974 citations recorded by the source corpus.

Recent new methods in Bayesian simulation have provided ways of evaluating posterior distributions in the presence of analytically or computationally intractable likelihood functions. Despite representing a substantial methodological advance, existing methods based on rejection sampling or Markov chain Monte Carlo can be highly inefficient and accordingly require far more iterations than may be practical to implement. Here we propose a sequential Monte Carlo sampler that convincingly overcomes these inefficiencies. We demonstrate its implementation through an epidemiological study of the transmission rate of tuberculosis.

Subfields: Artificial Intelligence, Epidemiology, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

The frontier of simulation-based inference (2019, background): “This approach abstracts the capabilities needed to implement particle filters and SMC (41).”
Kernel Bayes' Rule (2010, methodology): “Approximate Bayesian Computation (ABC) is a popular sampling method in these situations [25, 12, 17].”
Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks (2012, methodology): “(14) MCMC (Marjoram et al. 2003) and SMC samplers (Sisson, Fan, and Tanaka 2007; Del Moral, Doucet, and Jasra 2011; Robert et al. 2011) have been introduced to enable efficient exploration of the θ space when using an ABC approximation to the likelihood.”
Likelihood-Based Inference for Max-Stable Processes (2009, background): “bivariate), or requires additional approximations and immense computational overheads (Jiang and Turnbull, 2004; Sisson et al., 2007; Peters et al., 2008).”
Optimization Monte Carlo: Efficient and Embarrassingly Parallel Likelihood-Free Inference (2015, neutral): “2 Normal Mixture A standard illustrative ABC problem is the inference of the mean θ of a mixture of two normals [19, 3, 5]: p(x|θ) = ρN (θ, σ(2) 1)+ (1− ρ)N (θ, σ(2) 2), with π(θ) = U(θa, θb) where hyperparameters are ρ = 1/2, σ(2) 1 = 1, σ 2 2 = 1/100, θa = −10, θb = 10, and a single observation sc”
abc: an R package for approximate Bayesian computation (ABC) (2011, methodology): “Third, ABC is subject to intensive research and many new algorithms have been published in the past few years [18–21].”
Statistical Inference for Partially Observed Markov Processes via the R Package pomp (2015, methodology): “…al. 1998), iterated ﬁltering (Ionides et al. 2006, 2015), ensemble Kalman ﬁltering (Shaman and Karspeck 2012), approximate Bayesian computation (ABC; Sisson et al. 2007), particle Markov chain Monte Carlo (PMCMC; Andrieu et al. 2010), probe matching (Kendall et al. 1999), and synthetic likelihood…”
Likelihood-Free Inference of Population Structure and Local Adaptation in a Bayesian Hierarchical Model (2010, methodology): “However, we note that the algorithms described in this article are particularly amenable to sequential ABC approaches (Sisson et al. 2007; Beaumont et al. 2009; Toni et al. 2009) and improved conditional density estimation (Blum and Francxois 2009).”
On sequential Monte Carlo, partial rejection control and approximate Bayesian computation (2008, positive): “Setting q = 0 for the uniform kernel corresponds to existing SMCtype ABC samplers (Sisson et al. 2007; Toni et al. 2009; Beaumont et al. 2009).”
Kernel Bayes' rule: Bayesian inference with positive definite kernels (2013, methodology): “In this case, Approximate Bayesian Computation (ABC) is a popular method for Bayesian inference.”
Non-linear regression models for Approximate Bayesian Computation (2008, methodology): “Iterated importance sampling A second change to the LocL ABC algorithm converts the single-stage regression based ABC method into a multi-stage algorithm in which estimations are improved iteratively (Liu 2001; Sisson et al. 2007).”
GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation (2014, methodology): “Besides the marginal and pseudo-marginal approaches to ABC, there is a large body of work using sequential Monte Carlo sampling to approach this problem [21, 4, 26].”
Likelihood-free Markov chain Monte Carlo (2010, methodology): “The classes of algorithms and methods developed to perform Bayesian inference in this setting have become known as likelihood-free computation or approximate Bayesian computation (Beaumont et al., 2002; Marjoram et al., 2003; Ratmann et al., 2009; Sisson et al., 2007; Tavaré et al., 1997).”
Toward diagnostic model calibration and evaluation: Approximate Bayesian computation (2013, methodology): “The premise behind ABC is that should be a sample from the posterior distribution as long as the distance between the observed and simulated data, hereafter referred to as ~ Y;Y ð Þ is less than some small positive value, [Marjoram et al., 2003; Sisson et al., 2007].”
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.”
Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models (2015, methodology): “Related sequential Monte Carlo (SMC) ABC algorithms were proposed by Sisson et al. (2007); Toni et al. (2009).”
Statistical inference for dynamical systems: A review (2012, methodology): “ as a philosophical argument in [107] and introduced to population genetics in [117]. Since then these methods have become extremely popular in many applied elds. A partial list of references include [23, 25, 80, 96, 101, 103, 111, 119, 125]. A good review with applications to ltering is [46]. Brie ”