Numerical Bayesian Methods Applied to Signal Processing

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

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

Cited by 316 publications

(191 citation statements)

References 0 publications

Supporting

Mentioning

189

Contrasting

Unclassified

Order By: Relevance

“…The results we obtain differ substantially from previous analyses. The posterior distribution suggests around 40 changepoints, which is roughly three times as many as assumed byÓ Ruanaidh and Fitzgerald (1996). Fearnhead and Clifford (2003) only infer 16 changepoints.…”

mentioning

confidence: 72%

“…An example of well-log data, which comes fromÓ Ruanaidh and Fitzgerald (1996), is given in Figure 1. The data consist of measurements of the nuclear-magnetic response of underground rocks.…”

Section: Well-log Datamentioning

confidence: 99%

“…The data were obtained by lowering a probe into a bore-hole. These data have been previously analysed byÓ Ruanaidh and Fitzgerald (1996), who used MCMC to fit a change-point model with a fixed number of changepoints; and by Fearnhead and Clifford (2003) who considered online analysis of the data using particle filters. We performed a batch analysis of the data, but allowed for multiple changepoints.…”

Section: Well-log Datamentioning

confidence: 99%

See 2 more Smart Citations

Exact and efficient Bayesian inference for multiple changepoint problems

2006

View full text Add to dashboard Cite

Summary We demonstrate how to perform direct simulation from the posterior distribution of a class of multiple changepoint models where the number of changepoints is unknown. The class of models assumes independence between the posterior distribution of the parameters associated with segments of data between successive changepoints. This approach is based on the use of recursions, and is related to work on product partition models. The computational complexity of the approach is quadratic in the number of observations, but an approximate version, which introduces negligible error, and whose computational cost is roughly linear in the number of observations, is also possible. Our approach can be useful, for example within an MCMC algorithm, even when the independence assumptions do not hold. We demonstrate our approach on well-log data. Our method can cope with a range of models for this data, and exact simulation from the posterior distribution is possible in a matter of minutes.

show abstract

mentioning

confidence: 72%

Section: Well-log Datamentioning

confidence: 99%

Section: Well-log Datamentioning

confidence: 99%

See 1 more Smart Citation

Exact and efficient Bayesian inference for multiple changepoint problems

2006

View full text Add to dashboard Cite

show abstract

“…We first run Gibbs sampling on the model to propose a numerical approximation of Pr(S 0 j y) (Ruanaidh and Fitzgerald, 1996;Gelman et al, 1998) and successively sample each variable given the set of remaining variables. To allow for burnin effect, we discard the first half of the samples and only keep the second half for consideration, that we note (S 0 [l] ), l = 1,. .…”

Section: Numerical Samplingmentioning

confidence: 99%

Partial correlation for functional brain interactivity investigation in functional MRI

et al. 2006

View full text Add to dashboard Cite

“…(2)) and thus presents a challenging numerical task. Standard techniques like thermodynamic integration [19] are extremely computationally expensive which makes evidence evaluation typically at least an order of magnitude more costly than parameter estimation. Some fast approximate methods have been used for evidence evaluation, such as treating the posterior as a multivariate Gaussian centred at its peak (see, for example, [20]), but this approximation is clearly a poor one for highly non-Gaussian and multi-modal posteriors.…”

Section: Bayesian Inferencementioning

confidence: 99%

Classifying LISA gravitational wave burst signals using Bayesian evidence

Feroz

Gair

Graff

et al. 2010

Class. Quantum Grav.

View full text Add to dashboard Cite

Abstract. We consider the problem of characterisation of burst sources detected with the Laser Interferometer Space Antenna (LISA) using the multi-modal nested sampling algorithm, MULTINEST. We use MULTINEST as a tool to search for modelled bursts from cosmic string cusps, and compute the Bayesian evidence associated with the cosmic string model. As an alternative burst model, we consider sine-Gaussian burst signals, and show how the evidence ratio can be used to choose between these two alternatives. We present results from an application of MULTINEST to the last round of the Mock LISA Data Challenge, in which we were able to successfully detect and characterise all three of the cosmic string burst sources present in the release data set. We also present results of independent trials and show that MULTINEST can detect cosmic string signals with signal-to-noise ratio (SNR) as low as ∼ 7 and sine-Gaussian signals with SNR as low as ∼ 8. In both cases, we show that the threshold at which the sources become detectable coincides with the SNR at which the evidence ratio begins to favour the correct model over the alternative.

show abstract

Numerical Bayesian Methods Applied to Signal Processing

Cited by 316 publications

References 0 publications

Exact and efficient Bayesian inference for multiple changepoint problems

Exact and efficient Bayesian inference for multiple changepoint problems

Partial correlation for functional brain interactivity investigation in functional MRI

Classifying LISA gravitational wave burst signals using Bayesian evidence

Contact Info

Product

Resources

About