Bayesian computation: a summary of the current state, and samples backwards and forwards

Green, Peter J.; Łatuszyński, Krzysztof; Pereyra, Marcelo; Robert, Christian P.

doi:10.1007/s11222-015-9574-5

Cited by 164 publications

(138 citation statements)

References 236 publications

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“…As discussed in [48], some asymptotic analysis of these algorithms shows that, in the stationary regime, the random-walk As for the MALA, the authors in [41] proposed a generalization of this HMC algorithm by considering Hamiltonian dynamics on a manifold in order to be able to take into account the local structure of the target distribution. The…”

Section: B On Hamiltonian Based Mcmc Kernelmentioning

confidence: 99%

Langevin and Hamiltonian Based Sequential MCMC for Efficient Bayesian Filtering in High-Dimensional Spaces

Septier

Peters²

2016

IEEE J. Sel. Top. Signal Process.

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Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm, also known as particle filtering. Nevertheless, this method tends to be inefficient when applied to high dimensional problems.In this paper, we focus on another class of sequential inference methods, namely the Sequential Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising alternative to SMC methods. After providing a unifying framework for the class of SMCMC approaches, we propose novel efficient strategies based on the principle of Langevin diffusion andHamiltonian dynamics in order to cope with the increasing number of high-dimensional applications. Simulation results show that the proposed algorithms achieve significantly better performance compared to existing algorithms.

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Section: B On Hamiltonian Based Mcmc Kernelmentioning

confidence: 99%

Langevin and Hamiltonian Based Sequential MCMC for Efficient Bayesian Filtering in High-Dimensional Spaces

Septier

Peters²

2016

IEEE J. Sel. Top. Signal Process.

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“…However, these methods often struggle to detect multiple divergence times across pairs of populations (Oaks et al, 2013 or have little information to update a priori expectations (Oaks, 2014). More fundamentally, the loss of information inherent to ABC approaches can prevent them from discriminating among models (Robert et al, 2011;Marin et al, 2013;Green et al, 2015). Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Full Bayesian Comparative Phylogeography from Genomic Data

Oaks

2018

Preprint

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A challenge to understanding biological diversification is accounting for community-scale processes that cause multiple, co-distributed lineages to co-speciate. Such processes predict nonindependent, temporally clustered divergences across taxa. Approximate-likelihood Bayesian computation (ABC) approaches to inferring such patterns from comparative genetic data are very sensitive to prior assumptions and often biased toward estimating shared divergences. We introduce a full-likelihood Bayesian approach, ecoevolity, which takes full advantage of information in genomic data. By analytically integrating over gene trees, we are able to directly calculate the likelihood of the population history from genomic data, and efficiently sample the model-averaged posterior via Markov chain Monte Carlo algorithms. Using simulations, we find that the new method is much more accurate and precise at estimating the number and timing of divergence events across pairs of populations than existing approximatelikelihood methods. Our full Bayesian approach also requires several orders of magnitude less computational time than existing ABC approaches. We find that despite assuming unlinked characters (e.g., unlinked single-nucleotide polymorphisms), the new method performs better if this assumption is violated in order to retain the constant characters of whole linked loci. In fact, retaining constant characters allows the new method to robustly estimate the correct number of divergence events with high posterior probability in the face of character-acquisition biases, which commonly plague loci assembled from reduced-representation genomic libraries. We apply our method to genomic data from four pairs of insular populations of Gekko lizards from the Philippines that are not expected to have co-diverged. Despite all four pairs diverging very recently, our method strongly supports that they diverged independently, and these results are robust to very disparate prior assumptions.

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“…A main computational advantage of the MAP estimator (3) is that it can be computed very efficiently, even in high dimensions, by using convex optimisation algorithms (e.g. [10], [9], [19]). However, since MAP estimation results in a single point estimator, we lose uncertainty information that sampling approaches like MCMC methods can provide [5].…”

Section: Problem Formulationmentioning

confidence: 99%

Quantifying Uncertainty in High Dimensional Inverse Problems by Convex Optimisation

Cai

Pereyra

McEwen

2019

2019 27th European Signal Processing Conference (EUSIPCO)

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Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems and problems with non-smooth objective functionals (e.g. sparsity-promoting priors). In this article, a series of strategies to visualise this uncertainty are presented, e.g. highest posterior density credible regions, and local credible intervals (cf. error bars) for individual pixels and superpixels. Our methods support non-smooth priors for inverse problems and can be scaled to high-dimensional settings. Moreover, we present strategies to automatically set regularisation parameters so that the proposed uncertainty quantification (UQ) strategies become much easier to use. Also, different kinds of dictionaries (complete and over-complete) are used to represent the image/signal and their performance in the proposed UQ methodology is investigated.

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Bayesian computation: a summary of the current state, and samples backwards and forwards

Cited by 164 publications

References 236 publications

Langevin and Hamiltonian Based Sequential MCMC for Efficient Bayesian Filtering in High-Dimensional Spaces

Langevin and Hamiltonian Based Sequential MCMC for Efficient Bayesian Filtering in High-Dimensional Spaces

Full Bayesian Comparative Phylogeography from Genomic Data

Quantifying Uncertainty in High Dimensional Inverse Problems by Convex Optimisation

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