Sampling from a multivariate Gaussian distribution truncated on a simplex: A review

Altmann, Yoann; McLaughlin, Stephen; Dobigeon, Nicolas

doi:10.1109/ssp.2014.6884588

Cited by 25 publications

(35 citation statements)

References 14 publications

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“…Considering these assumptions, a statistical model using Bayesian framework has been introduced by Heinonen et al [22], and a truncated multivariate normal (TMVN) posterior distribution for the fluxes has been presented. Efficient sampling from a truncated multivariate normal distribution is a challenging task, and often Gibbs sampling is applied [23]. The Bayesian metabolic flux analysis (BMFA) is implemented in the COBRA toolbox by Heinonen et al [22].…”

Section: Plos Onementioning

confidence: 99%

A comparison of Monte Carlo sampling methods for metabolic network models

2020

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Reaction rates (fluxes) in a metabolic network can be analyzed using constraint-based modeling which imposes a steady state assumption on the system. In a deterministic formulation of the problem the steady state assumption has to be fulfilled exactly, and the observed fluxes are included in the model without accounting for experimental noise. One can relax the steady state constraint, and also include experimental noise in the model, through a stochastic formulation of the problem. Uniform sampling of fluxes, feasible in both the deterministic and stochastic formulation, can provide us with statistical properties of the metabolic network, such as marginal flux probability distributions. In this study we give an overview of both the deterministic and stochastic formulation of the problem, and of available Monte Carlo sampling methods for sampling the corresponding solution space. We apply the ACHR, OPTGP, CHRR and Gibbs sampling algorithms to ten metabolic networks and evaluate their convergence, consistency and efficiency. The coordinate hit-and-run with rounding (CHRR) is found to perform best among the algorithms suitable for the deterministic formulation. A desirable property of CHRR is its guaranteed distributional convergence. Among the three other algorithms, ACHR has the largest consistency with CHRR for genome scale models. For the stochastic formulation, the Gibbs sampler is the only method appropriate for sampling at genome scale. However, our analysis ranks it as less efficient than the samplers used for the deterministic formulation.

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Section: Plos Onementioning

confidence: 99%

A comparison of Monte Carlo sampling methods for metabolic network models

2020

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“…A recent review summarizes sampling approaches for TMVNca (Altmann et al , 2014). The conditionals of TMVNhe are still TMVNs (Horrace, 2005), which has led to many Gibbs-based samplers (Emery et al , 2014; Geweke, 1991; Horrace, 2005; Kotecha and Djuric, 1999; Li and Ghosh, 2015).…”

Section: Methodsmentioning

confidence: 99%

Bayesian metabolic flux analysis reveals intracellular flux couplings

et al. 2019

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Motivation Metabolic flux balance analysis (FBA) is a standard tool in analyzing metabolic reaction rates compatible with measurements, steady-state and the metabolic reaction network stoichiometry. Flux analysis methods commonly place model assumptions on fluxes due to the convenience of formulating the problem as a linear programing model, while many methods do not consider the inherent uncertainty in flux estimates. Results We introduce a novel paradigm of Bayesian metabolic flux analysis that models the reactions of the whole genome-scale cellular system in probabilistic terms, and can infer the full flux vector distribution of genome-scale metabolic systems based on exchange and intracellular (e.g. 13C) flux measurements, steady-state assumptions, and objective function assumptions. The Bayesian model couples all fluxes jointly together in a simple truncated multivariate posterior distribution, which reveals informative flux couplings. Our model is a plug-in replacement to conventional metabolic balance methods, such as FBA. Our experiments indicate that we can characterize the genome-scale flux covariances, reveal flux couplings, and determine more intracellular unobserved fluxes in Clostridium acetobutylicum from 13C data than flux variability analysis. Availability and implementation The COBRA compatible software is available at github.com/markusheinonen/bamfa. Supplementary information Supplementary data are available at Bioinformatics online.

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“…Samples distributed according to the above truncated multivariate Gaussian distributions can be generated by a Gibbs sampler described in [45, Section IV.B.] [46], by an Hamiltonian Monte-Carlo procedure [47], [48] or by the general method recently proposed in [49]. In this work, the Gibbs sampler [45, Section IV.B.]…”

Section: B Sampling the Abundances āmentioning

confidence: 99%

A Hierarchical Bayesian Model Accounting for Endmember Variability and Abrupt Spectral Changes to Unmix Multitemporal Hyperspectral Images

Thouvenin

Dobigeon

Tourneret

2018

IEEE Trans. Comput. Imaging

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Abstract-Hyperspectral unmixing is a blind source separation problem which consists in estimating the reference spectral signatures contained in a hyperspectral image, as well as their relative contribution to each pixel according to a given mixture model. In practice, the process is further complexified by the inherent spectral variability of the observed scene and the possible presence of outliers. More specifically, multi-temporal hyperspectral images, i.e., sequences of hyperspectral images acquired over the same area at different time instants, are likely to simultaneously exhibit moderate endmember variability and abrupt spectral changes either due to outliers or to significant time intervals between consecutive acquisitions. Unless properly accounted for, these two perturbations can significantly affect the unmixing process. In this context, we propose a new unmixing model for multitemporal hyperspectral images accounting for smooth temporal variations, construed as spectral variability, and abrupt spectral changes interpreted as outliers. The proposed hierarchical Bayesian model is inferred using a Markov chain Monte-Carlo (MCMC) method allowing the posterior of interest to be sampled and Bayesian estimators to be approximated. A comparison with unmixing techniques from the literature on synthetic and real data allows the interest of the proposed approach to be appreciated.Index Terms-Hyperspectral imagery, multitemporal images, endmember variability, Markov chain Monte-Carlo (MCMC) methods.

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Sampling from a multivariate Gaussian distribution truncated on a simplex: A review

Cited by 25 publications

References 14 publications

A comparison of Monte Carlo sampling methods for metabolic network models

A comparison of Monte Carlo sampling methods for metabolic network models

Bayesian metabolic flux analysis reveals intracellular flux couplings

A Hierarchical Bayesian Model Accounting for Endmember Variability and Abrupt Spectral Changes to Unmix Multitemporal Hyperspectral Images

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