On sequential Monte Carlo, partial rejection control and approximate Bayesian computation

By Gareth William Peters, Yanan Fan, Scott Anthony Sisson. 2008

74 citations recorded by the source corpus.

We present a variant of the sequential Monte Carlo sampler by incorporating the partial rejection control mechanism of Liu (2001). We show that the resulting algorithm can be considered as a sequential Monte Carlo sampler with a modified mutation kernel. We prove that the new sampler can reduce the variance of the incremental importance weights when compared with standard sequential Monte Carlo samplers, and provide a central limit theorem. Finally, the sampler is adapted for application under the challenging approximate Bayesian computation modelling framework.

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

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Paul Fearnhead
2. Scott Anthony Sisson
3. Gilles Louppe
4. Yanan Fan
5. Dennis Prangle
6. Ajay Jasra
7. Kyle Cranmer
8. J. Brehmer

In Statistics and Probability

1. Paul Fearnhead
2. Scott Anthony Sisson
3. Dennis Prangle
4. Yanan Fan
5. Michael G. B. Blum
6. Gilles Louppe
7. Pierre Del Moral
8. Kyle Cranmer

In Probabilistic & Bayesian Methods

1. Gilles Louppe
2. Kyle Cranmer
3. J. Brehmer
4. Pierre Del Moral
5. Scott Anthony Sisson
6. Arnaud Doucet
7. Dennis Prangle
8. Michael G. B. Blum

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).”
• Likelihood-free Markov chain Monte Carlo (2010, methodology): “, 2005), chain-ladder claims reserving (Peters et al., 2008), coalescent models (Tavaré et al.”
• An adaptive sequential Monte Carlo method for approximate Bayesian computation (2011, methodology): “This is why SMC methods have recently become prominent in the ABC context (Beaumont et al. 2009; Peters et al. 2008; Sisson et al. 2007; Toni et al. 2009).”
• Constructing summary statistics for approximate Bayesian computation: semi‐automatic approximate Bayesian computation (2012, methodology): “…as the rejection sampling, importance sampling and MCMC algorithms that we have mentioned, there has been work on using sequential Monte Carlo methods (Beaumont et al., 2009; Sisson et al., 2007; Peters et al., 2010) and adaptive methods (Bortot et al., 2007; Del Moral et al., 2012) among others.”
• A comparative review of dimension reduction methods in approximate Bayesian computation (2012, methodology): “These algorithms include Markov chain Monte Carlo (Marjoram et al. 2003; Bortot et al. 2007) and sequential Monte Carlo techniques (Sisson et al. 2007; Toni et al. 2009; Beaumont et al. 2009; Drovandi and Pettitt 2011; Peters et al. 2012; Del Moral et al. 2012).”