Numerical Bayesian Inference

Ruanaidh, Joseph J. K. Ó; Fitzgerald, William J.

doi:10.1007/978-1-4612-0717-7_3

Cited by 34 publications

(55 citation statements)

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“…Alternatively, the posterior can be assumed to be of a particular parametric form. In the Laplace approximation, which is employed, for example, in the "evidence framework," the posterior is assumed to be Gaussian [16]. This procedure is quick but is often inaccurate.…”

Section: Variational Bayes Learningmentioning

confidence: 99%

“…For the Gamma distributions, we use vague priors (see, e.g., [16]); for , we set , , and for , we set and . It is noted that we do not find particular sensitivity to these values.…”

Section: E Practicalitiesmentioning

confidence: 99%

“…For Gaussian noise models, the negative free energy simplifies to (62) where (63) and (64) where is the digamma function. An alternative Bayesian approach is that offered by the evidence framework [16]. Given that the observation noise is zero-mean Gaussian with precision and that the weights are drawn from a prior distribution with zero mean and isotropic covariance having precision , the posterior distribution is Gaussian with mean and covariance, which is also given by (59).…”

Section: Gaussian Autoregressive Modelmentioning

confidence: 99%

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Variational Bayes for generalized autoregressive models

Roberts

Penny

2002

IEEE Trans. Signal Process.

136

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Abstract-We describe a variational Bayes (VB) learning algorithm for generalized autoregressive (GAR) models. The noise is modeled as a mixture of Gaussians rather than the usual single Gaussian. This allows different data points to be associated with different noise levels and effectively provides robust estimation of AR coefficients. The VB framework is used to prevent overfitting and provides model-order selection criteria both for AR order and noise model order. We show that for the special case of Gaussian noise and uninformative priors on the noise and weight precisions, the VB framework reduces to the Bayesian evidence framework. The algorithm is applied to synthetic and real data with encouraging results.Index Terms-Bayesian inference, generalized autoregressive models, model order selection, robust estimation.

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Section: Variational Bayes Learningmentioning

confidence: 99%

“…For the Gamma distributions, we use vague priors (see, e.g., [16]); for , we set , , and for , we set and . It is noted that we do not find particular sensitivity to these values.…”

Section: E Practicalitiesmentioning

confidence: 99%

Section: Gaussian Autoregressive Modelmentioning

confidence: 99%

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Variational Bayes for generalized autoregressive models

Roberts

Penny

2002

IEEE Trans. Signal Process.

136

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“…Assume that we want to compute an integral I = R f(x)dx. One way of computing I is using samplers [Ó Ruanaidh and Fitzgerald, 1996] after assuming x is a random variable with PDF q(x). It is possible to rewrite I in the form of an expectation:…”

Section: Basics Of Particle Filtersmentioning

confidence: 99%

“…The IS converges to the true value with diminishing error variance as the number of particles drawn from q(x) increases. The variance is [Ó Ruanaidh and Fitzgerald, 1996]:…”

Section: Basics Of Particle Filtersmentioning

confidence: 99%

Sequential Bayesian techniques applied to non‐volcanic tremor

Yardim

Gerstoft

2012

J. Geophys. Res.

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.[1] This paper uses sequential Bayesian techniques such as particle filters and smoothers to track in time both the non-volcanic tremor (NVT) source location on the plate interface and the angle of arrival via horizontal phase slowness. Sequential Bayesian techniques enable tracking of evolving geophysical parameters via sequential tremor observations. These techniques provide a formulation where the geophysical parameters that characterize dynamic, non-stationary processes are continuously estimated as new data become available. In addition to the optimal solution, particle filters and smoothers can calculate the underlying probability densities for the desired parameters, providing the uncertainties in the estimates. The tremor tracking has been performed using array beamforming. Here it is demonstrated that the uncertainties both in the NVT source location estimates and phase slowness estimates are reduced using a particle filter compared to just using a beamformer based inversion. Particle smoothers further reduces the uncertainty, giving the best performance out of the three methods used here.

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Consistent two‐stage multiple change‐point detection in linear models

Jin

Shi

2016

Can J Statistics

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A two‐stage procedure for simultaneously detecting multiple change‐points in linear models is developed. In the cutting stage, the change‐point problem is converted into a model selection problem so that a modern model selection method can be applied. In the refining stage, the change‐points obtained in the cutting stage are finalized via a refining method. Under mild conditions, consistency of the number of change‐point estimates is established. The new procedure is fast and accurate, as shown in simulation studies. Its applicability in real situations is demonstrated via well‐log and ozone data. The Canadian Journal of Statistics 44: 161–179; 2016 © 2016 Statistical Society of Canada

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Numerical Bayesian Inference

Cited by 34 publications

References 0 publications

Variational Bayes for generalized autoregressive models

Variational Bayes for generalized autoregressive models

Sequential Bayesian techniques applied to non‐volcanic tremor

Consistent two‐stage multiple change‐point detection in linear models

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