Where Bayes tweaks Gauss: Conditionally Gaussian priors for stable multi-dipole estimation

Viani, Alessandro; Luria, Gianvittorio; Sorrentino, Alberto; Bornfleth, Harald

doi:10.3934/ipi.2021030

Cited by 6 publications

(3 citation statements)

References 36 publications

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“…a prior on the hyper-parameter σ q . This was done originally in Viani et al ( 2021 ), where we presented an updated model in which the hyper-parameter σ q is considered unknown, and treated as an additional parameter, i.e. sampled from the hyper-prior and then updated in the SMC steps.…”

Section: Methodsmentioning

confidence: 99%

“…In this subsection we provide a very brief summary of the computations behind SESAME: for more details we invite the reader to consult (Sommariva and Sorrentino, 2014 ; Sorrentino et al, 2014 ; Viani et al, 2021 ), where the mathematical model and the algorithm have been thoroughly described.…”

Section: Methodsmentioning

confidence: 99%

“…In a set of publications (Sorrentino et al, 2013 , 2014 ; Luria et al, 2019 ; Viani et al, 2021 , 2022 ) we proposed a fully Bayesian algorithm, based on the ECD source model and belonging to the class of Sequential Monte Carlo (SMC) samplers (Del Moral et al, 2006 ), to solve the M/EEG localization problem. This inverse solver, called SEquential Semi-Analytic Montecarlo Estimator (SESAME), is able to sample the whole posterior distribution for the multi-dipole configuration, thereby providing multiple alternative solutions, each with an associated quantification of its reliability.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The SESAMEEG package: a probabilistic tool for source localization and uncertainty quantification in M/EEG

Luria,

Viani,

Pascarella

et al. 2024

Front. Hum. Neurosci.

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Source localization from M/EEG data is a fundamental step in many analysis pipelines, including those aiming at clinical applications such as the pre-surgical evaluation in epilepsy. Among the many available source localization algorithms, SESAME (SEquential SemiAnalytic Montecarlo Estimator) is a Bayesian method that distinguishes itself for several good reasons: it is highly accurate in localizing focal sources with comparably little sensitivity to input parameters; it allows the quantification of the uncertainty of the reconstructed source(s); it accepts user-defined a priori high- and low-probability search regions in input; it can localize the generators of neural oscillations in the frequency domain. Both a Python and a MATLAB implementation of SESAME are available as open-source packages under the name of SESAMEEG and are well integrated with the main software packages used by the M/EEG community; moreover, the algorithm is part of the commercial software BESA Research (from version 7.0 onwards). While SESAMEEG is arguably simpler to use than other source modeling methods, it has a much richer output that deserves to be described thoroughly. In this article, after a gentle mathematical introduction to the algorithm, we provide a complete description of the available output and show several use cases on experimental M/EEG data.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The SESAMEEG package: a probabilistic tool for source localization and uncertainty quantification in M/EEG

Luria,

Viani,

Pascarella

et al. 2024

Front. Hum. Neurosci.

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Meg

Arcara,

Pellegrino,

Pascarella

et al. 2023

Neuromethods

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Cost free hyper-parameter selection/averaging for Bayesian inverse problems with vanilla and Rao-Blackwellized SMC samplers

Viani,

Johansen,

Sorrentino

2023

Stat Comput

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In Bayesian inverse problems, one aims at characterizing the posterior distribution of a set of unknowns, given indirect measurements. For non-linear/non-Gaussian problems, analytic solutions are seldom available: Sequential Monte Carlo samplers offer a powerful tool for approximating complex posteriors, by constructing an auxiliary sequence of densities that smoothly reaches the posterior. Often the posterior depends on a scalar hyper-parameter, for which limited prior information is available. In this work, we show that properly designed Sequential Monte Carlo (SMC) samplers naturally provide an approximation of the marginal likelihood associated with this hyper-parameter for free, i.e. at a negligible additional computational cost. The proposed method proceeds by constructing the auxiliary sequence of distributions in such a way that each of them can be interpreted as a posterior distribution corresponding to a different value of the hyper-parameter. This can be exploited to perform selection of the hyper-parameter in Empirical Bayes (EB) approaches, as well as averaging across values of the hyper-parameter according to some hyper-prior distribution in Fully Bayesian (FB) approaches. For FB approaches, the proposed method has the further benefit of allowing prior sensitivity analysis at a negligible computational cost. In addition, the proposed method exploits particles at all the (relevant) iterations, thus alleviating one of the known limitations of SMC samplers, i.e. the fact that all samples at intermediate iterations are typically discarded. We show numerical results for two distinct cases where the hyper-parameter affects only the likelihood: a toy example, where an SMC sampler is used to approximate the full posterior distribution; and a brain imaging example, where a Rao-Blackwellized SMC sampler is used to approximate the posterior distribution of a subset of parameters in a conditionally linear Gaussian model.

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Where Bayes tweaks Gauss: Conditionally Gaussian priors for stable multi-dipole estimation

Cited by 6 publications

References 36 publications

The SESAMEEG package: a probabilistic tool for source localization and uncertainty quantification in M/EEG

The SESAMEEG package: a probabilistic tool for source localization and uncertainty quantification in M/EEG

Meg

Cost free hyper-parameter selection/averaging for Bayesian inverse problems with vanilla and Rao-Blackwellized SMC samplers

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