Inference for Stereological Extremes

By P. Bortot, Stuart Coles, Scott Anthony Sisson. 2007

152 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/618a4d65e09525e6861d60ac2d658ccb120cabcc

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Approximate Bayesian computation via regression density estimation (2012, methodology): “The estimates (λABC , σABC , ξABC) indicate those obtained using the MCMC-based ABC method of Bortot et al. (2007) with kernel scale parameter δ = 3.3.”
Constructing summary statistics for approximate Bayesian computation: semi‐automatic approximate Bayesian computation (2012, methodology): “An alternative would be to use computational methods that try to choose h for each run; see Bortot et al. (2007) and Ratmann et al. (2007). In the following examples our method is compared with an ABC analysis with summary statistics based on the existing literature, which is referred to as the ‘com”
An adaptive sequential Monte Carlo method for approximate Bayesian computation (2011, methodology): “For comparison, we run the MCMC algorithm of Bortot et al. (2009). The artificial prior on is selected as p( ) ∝ I[0.00045,10]( )e−2000 to ‘push’ towards small values. The MCMC proposal standard deviations for the normal random walks being (0.05, 0.05, 0.7) for (φ, τ, ξ) respectively reparameterized”
Non-linear regression models for Approximate Bayesian Computation (2008, methodology): “It has also recently been suggested in the context of compositional data (Butler and Glasbey 2008), and applied in extreme value theory (Bortot et al. 2007) and Gibbs random fields (Grelaud et al.”
Adaptive approximate Bayesian computation (2008, methodology): “…either by modifying the proposal distribution of the parameter θ to increase the density of x’s within a neighbourhood of y (Marjoram et al., 2003; Bortot et al., 2007) or by viewing the problem as a conditional density estimation and developing techniques to allow for larger (Beaumont et…”
ABCtoolbox: a versatile toolkit for approximate Bayesian computations (2010, methodology): “Additional improvements have been proposed to more efficiently explore the parameter space, including several variations of likelihood-free MCMC [6-9] or Particle-based samplers [10-12].”
On the Asymptotic Efficiency of Approximate Bayesian Computation Estimators (2015, methodology): “hese methods have been popular within population genetics [4,11,43], ecology [2] and systematic biology [42,38]. More recently, there have been applications of ABC to other areas including stereology [9], stochastic dierential equations [34] and nance [33]. The basic rejection scheme is limited due ”
Likelihood-free Markov chain Monte Carlo (2010, methodology): “Bortot et al. (2007) suggested using a distribution which favours small values for accuracy, while permitting large values to improve chain acceptance rates.”
Inference on population history and model checking using DNA sequence and microsatellite data with the software DIYABC (v1.0) (2010, background): “Whereas several studies have now shown that parameter posterior distributions inferred by ABC are similar to those provided by full-likelihood Bayesian approaches [16-19], the approach is still in its infancy and continues to evolve, and to be improved (reviewed in [4,5,20,21]).”
Approximate Bayesian Computation in Evolution and Ecology (2010, methodology): “An alternative approach is to augment the simulated Markov chain with the tolerance parameter itself (Bortot et al., 2007).”
Likelihood-Based Inference for Max-Stable Processes (2009, background): “…the intractability of the multivariate density function precludes inference except in trivial cases (e.g., bivariate), or requires additional approximations and immense computational overheads (e.g., Jiang and Turnbull 2004; Bortot, Coles, and Sisson 2007; Sisson, Fan, and Tanaka 2007).”
The Rate of Convergence for Approximate Bayesian Computation (2013, background): “…are now widely used in applications as diverse as epidemiology (Tanaka et al., 2006; Blum and Tran, 2010; Walker et al., 2010), materials science (Bortot et al., 2007), parasitology (Drovandi and Pettitt, 2011), genetic evolution (Thornton and Andolfatto, 2006; Fagundes et al., 2007; Ratmann et…”
On sequential Monte Carlo, partial rejection control and approximate Bayesian computation (2008, unknown): “This severely increases the variability of Monte Carlo estimates of expectations under π .”
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].”