Population Monte Carlo

By Olivier Capp'e, Arnaud Guillin, Jean-Michel Marin, Christian P. Robert. 2004

510 citations recorded by the source corpus.

Importance sampling methods can be iterated like MCMC algorithms, while being more robust against dependence and starting values. The population Monte Carlo principle consists of iterated generations of importance samples, with importance functions depending on the previously generated importance samples. The advantage over MCMC algorithms is that the scheme is unbiased at any iteration and can thus be stopped at any time, while iterations improve the performances of the importance function, thus leading to an adaptive importance sampling. We illustrate this method on a mixture example with multiscale importance functions. A second example reanalyzes the ion channel model using an importance sampling scheme based on a hidden Markov representation, and compares population Monte Carlo with a corresponding MCMC algorithm.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

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Citations in the corpus

Kernel Sequential Monte Carlo (2015, methodology): “The original PMC paper introduces re-sampling in order to deal with un-weighted instead of weighted samples [2], though at the cost of an increased variance.”
Optimal Proposal Distributions and Adaptive MCMC (2008, methodology): “For example, particle filters (e.g. Pitt and Sheppard, 1999), population Monte Carlo (e.g. Cappé et al., 2004), and sequential Monte Carlo (e.g. Del Moral et al., 2006), can all be considered as methods which attempt to “learn” faster convergence as they go.”
Model choice using reversible jump Markov chain Monte Carlo (2012, unknown): “Extending population MCMC (Cappé et al., 2004) to the trans-dimensional case, and drawing on the ideas of evolutionary Monte Carlo (Liang and Wong, 2000), this algorithm also employs tempered distributions (again to encourage mixing) but this time in parallel.”
Adaptive approximate Bayesian computation (2008, methodology): “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.”
Adaptive importance sampling in general mixture classes (2007, methodology): “While the method proposed here can be traced back to authors such as West (1992) or Oh and Berger (1993), it is closely related to the so-called Population Monte Carlo (henceforth abbreviated to PMC) approach—in the sense of an iterated simulation of importance samples and in opposition to Markov Ch”
Generalized Multiple Importance Sampling (2015, methodology): “MIS scheme Sampling w(xn) Used in R1 S1 π(xn) qjn (xn) Novel R2 S1 π(xn) 1 N ∑N k=1 jk (xn) Novel R3 S1 π(xn) ψ(xn) [9] N1 S3 π(xn) qn(xn) [8] N2 S2 π(xn) 1 |In| ∑ ∀k∈In qk(xn) Novel N3 S3 π(xn) ψ(xn) [10, 11]”
Likelihood-Free Inference by Ratio Estimation (2016, methodology): “We used an importance sampling scheme (Ripley, 1987, IS) by sampling 10,000 samples from the prior distribution and computed their weights using Algorithm 1, which is equivalent to one generation of the SMC algorithm (Capp´e et al., 2004; Del Moral et al., 2006, SMC).”
Sequential Monte Carlo samplers (2002, methodology): “However, it is possible to design kernels whose parameters are a function of the whole set of current particles as suggested in Crisan and Doucet (2000), Cappé et al. (2004), Chopin (2002) or West (1993). This allows the algorithm to scale a proposal distribution automatically. This idea is develope”
Convergence of adaptive mixtures of importance sampling schemes (2007, unknown): “In their generalization of importance sampling, Capp´e et al. [3] introduce an iterative dimension in the production of importance samples, aimed at adapting the importance distribution ν to the target distribution π .”
Efficient MCMC for Climate Model Parameter Estimation: Parallel Adaptive Chains and Early Rejection (2012, methodology): “Some Monte Carlo estimation methods are trivially parallelizable, or ‘embarrassingly parallel’, such as independent Metropolis-Hastings samplers and importance sampling based methods, like population Monte Carlo methods (e.g. Cappe et al. 2004) where importance sampling is performed iteratively.”
Bayesian Modelling and Inference on Mixtures of Distributions (2005, methodology): “As an alternative to MCMC, Cappé et al. (2003) have shown that the importance sampling technique (Robert and Casella 2004, Chapter 3) can be generalised to encompass much more adaptive and local schemes than thought previously, without relaxing its essential justification of providing a correct disc”
SMC2: an efficient algorithm for sequential analysis of state space models (2011, methodology): “Even in batch estimation scenarios SMC(2) may offer several advantages over PMCMC, in the same way that SMC approaches may be advantageous over MCMC methods (Neal, 2001; Chopin, 2002; Cappé et al., 2004; Del Moral et al., 2006; Jasra et al., 2007). Under certain conditions (which relate to the asymp”
Diagnostics of prior-data agreement in applied Bayesian analysis (2008, methodology): “Notorious MCMC algorithms [52] can be used but importance sampling methods [19] are more appropriate since the instrumental sampling function and the importance weights can be reused, provided π (θ |yn(li)) stays not far from π (θ |yn(lj )) (i = j ).”
Minimum variance importance sampling via Population Monte Carlo (2007, methodology): “We recall that [7] introduced this method, following the denomination of Iba [14], to advertise the availability of universal adaptive sampling machines that do not encounter the formidable difficulties of designing adaptive MCMC algorithms.”
Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Models (2015, methodology): “les iterative adaptive algorithms where the accepted (m ) of one iteration are used to dene the auxiliary distribution q( ) of the next iteration (population or sequential Monte Carlo algorithms, Cappé et al., 2004; Del Moral et al., 2006). 3.2 Parametric Approximation of the Likelihood The pdf p j”