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Bayesian Interpolation
 Neural Computation
, 1991
"... Although Bayesian analysis has been in use since Laplace, the Bayesian method of modelcomparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and modelcomparison is demonstrated by studying the inference problem of interpolating noisy data. T ..."
Abstract

Cited by 521 (18 self)
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Although Bayesian analysis has been in use since Laplace, the Bayesian method of modelcomparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and modelcomparison is demonstrated by studying the inference problem of interpolating noisy data. The concepts and methods described are quite general and can be applied to many other problems. Regularising constants are set by examining their posterior probability distribution. Alternative regularisers (priors) and alternative basis sets are objectively compared by evaluating the evidence for them. `Occam's razor' is automatically embodied by this framework. The way in which Bayes infers the values of regularising constants and noise levels has an elegant interpretation in terms of the effective number of parameters determined by the data set. This framework is due to Gull and Skilling. 1 Data modelling and Occam's razor In science, a central task is to develop and compare models to a...
Efficient approximations for the marginal likelihood of Bayesian networks with hidden variables
 Machine Learning
, 1997
"... We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MD ..."
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Cited by 176 (11 self)
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We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MDL approximation. We also consider approximations proposed by Draper (1993) and Cheeseman and Stutz (1995). These approximations are as efficient as BIC/MDL, but their accuracy has not been studied in any depth. We compare the accuracy of these approximations under the assumption that the Laplace approximation is the most accurate. In experiments using synthetic data generated from discrete naiveBayes models having a hidden root node, we find that (1) the BIC/MDL measure is the least accurate, having a bias in favor of simple models, and (2) the Draper and CS measures are the most accurate. 1
Bayesian neural networks for internet traffic classification
 IEEE Trans. Neural Netw
, 2007
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A Molecular Ruler for Measuring Quantitative Distance Distributions
, 2008
"... We report a novel molecular ruler for measurement of distances and distance distributions with accurate external calibration. Using solution Xray scattering we determine the scattering interference between two gold nanocrystal probes attached sitespecifically to a macromolecule of interest. Fourie ..."
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Cited by 1 (0 self)
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We report a novel molecular ruler for measurement of distances and distance distributions with accurate external calibration. Using solution Xray scattering we determine the scattering interference between two gold nanocrystal probes attached sitespecifically to a macromolecule of interest. Fourier transformation of the interference pattern provides a modelindependent probability distribution for the distances between the probe centersofmass. To test the approach, we measure endtoend distances for a variety of DNA structures. We demonstrate that measurements with independently prepared samples and using different Xray sources are highly reproducible, we demonstrate the quantitative accuracy of the first and second moments of the distance distributions, and we demonstrate that the technique recovers complex distribution shapes. Distances measured with the solution scatteringinterference ruler match the corresponding crystallographic values, but differ from distances measured previously with alternate ruler techniques. The Xray scattering interference ruler should be a powerful tool for relating crystal structures to solution structures and for studying molecular fluctuations.