Markov chain Monte Carlo without likelihoods

By Paul Marjoram, John Molitor, V. Plagnol, S. Tavaré. 2003

1,366 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Genetics, Probabilistic & Bayesian Methods

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Citations in the corpus

The frontier of simulation-based inference (2019, background): “(12), and highlight the combination with MCMC (13) and Sequential Monte Carlo (14).”
Gradient-free Hamiltonian Monte Carlo with Efficient Kernel Exponential Families (2015, methodology): “ABC-MCMC [5] targets an approximate posterior by constructing an unbiased Monte Carlo estimator of the approximate likelihood.”
Kernel Bayes' Rule (2010, methodology): “Approximate Bayesian Computation (ABC) is a popular sampling method in these situations [25, 12, 17].”
Learning in Implicit Generative Models (2016, methodology): “The two other approaches are: moment matching and ABC-MCMC (Marjoram et al., 2003), which has been successful for many problems with moderate dimension; and the nat-ural choice of gradient-free optimisation methods, which include familiar tools such as Bayesian optimisation (Gut-mann and Corander, 2”
Approximate Bayesian Image Interpretation using Generative Probabilistic Graphics Programs (2013, methodology): “For example, in our text application, the Sis include binary indicators for the presence or absence of each glyph, along with its identity (“A“ through ”Z”, plus digits 0-9), and parameters including location,”
Venture: a higher-order probabilistic programming platform with programmable inference (2014, background): “, 2013) and models defined in terms of complex stochastic simulation software that lack tractable likelihoods (Marjoram et al., 2003).”
Likelihood-free Markov chain Monte Carlo (2010, methodology): “…is available through Monte Carlo integration as πLF (θ|y) ≈ π(θ) S S∑ s=1 π (y|xs, θ) (1.3.3) where x1, . . . , xS are independent draws from the model π(x|θ) (Marjoram et al., 2003; Peters et al., 2008; Ratmann et al., 2009; Reeves and Pettitt, 2005; Sisson et al., 2007; Toni et al., 2009;…”
Asymptotically exact inference in differentiable generative models (2016, methodology): “Alternatively a MCMC scheme can be used to estimate the ABC posterior expectation in (3) [21].”
Bayesian Solution Uncertainty Quantification for Differential Equations (2013, methodology): “Such partially likelihood-free Markov chain Monte Carlo methods (Marjoram et al., 2003) are widely used for inference on stochastic diﬀerential equations (e.g., Golightly and Wilkinson, 2011).”
Probabilistic machine learning and artificial intelligence (2015, background): “The fact that defining such universal inference algorithms for computer programs is even possible is somewhat surprising, but it is related to the generality of certain key ideas from sampling such as rejection sampling, sequential Monte Carlo methods 25 and ‘approximate Bayesian computation’ 49 .”
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.”
Bridging the gap between GLUE and formal statistical approaches: approximate Bayesian computation (2013, methodology): “So rather than considering the data, ˜ Y , itself we consider a summary statistic of the data, S( ˜ Y ) , and use a distance function (Marjoram et al., 2003; Sisson et al., 2007) ρ S( ˜ Y ),S( Y ( θ )) ≤ (5) to decide whether to accept the parameter values, θ , or not.”
The Rate of Convergence for Approximate Bayesian Computation (2013, methodology): “Newer developments and extensions of the method include placing ABC in an MCMC context (Marjoram et al., 2003), sequential ABC (Sisson et al.”
Constructing summary statistics for approximate Bayesian computation: semi‐automatic approximate Bayesian computation (2012, methodology): “An alternative Monte Carlo procedure for implementing ABC is based on Markov chain Monte Carlo (MCMC) sampling (Marjoram et al., 2003; Bortot et al., 2007) and given in algorithm 2 (Table 2).”
Approximate Bayesian Computation in Evolution and Ecology (2010, methodology): “As noted by Becquet & Przeworski (2007), there is a close relationship between the algorithm by Marjoram et al. (2003) and another algorithm that has become known as the pseudo-marginal method (Andrieu & Roberts 2009) introduced by Beaumont (2003).”
Under Review as a Conference Paper at Iclr 2017 Learning in Implicit Generative Models (2017, methodology): “The two other approaches are: moment matching and ABC-MCMC (Marjoram et al., 2003), which has been successful for many problems with moderate dimension; and the natural choice of gradientfree optimisation methods, which include familiar tools such as Bayesian optimisation (Gutmann and Corander, 2016”
Likelihood-free MCMC with Approximate Likelihood Ratios (2019, methodology): “In recent years variants of ABC have been proposed to improve the acceptance rate by guiding simulations based on previously accepted states [20, 33, 34, 35].”
Inference for Stereological Extremes (2007, methodology): “To address this difficulty, Marjoram et al. (2003) proposed two modifications to the basic algorithm.”