Continued fraction enhancement of Bayesian computing
@article{Wand2012ContinuedFE, title={Continued fraction enhancement of Bayesian computing}, author={Matt P. Wand and John Thomas Ormerod}, journal={Stat}, year={2012}, volume={1}, url={https://api.semanticscholar.org/CorpusID:119636237} }
The agéd number theoretic concept of continued fractions can enhance certain Bayesian computations. The crux of this claim is due to continued fraction representations of numerically challenging special function ratios that arise in Bayesian computing. Continued fraction approximation via Lentz's Algorithm often leads to efficient and stable computation of such quantities. Copyright © 2012 John Wiley & Sons, Ltd.
8 Citations
Mean field variational Bayes for continuous sparse signal shrinkage: Pitfalls and remedies
- 2014
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The principal finding is that the most natural, and simplest, mean field variational Bayes algorithm can perform quite poorly due to post- rior dependence among auxiliary variables, so more sophisticated algorithms are shown to be superior.
Fast and Accurate Binary Response Mixed Model Analysis via Expectation Propagation
- 2020
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On the Computation of Gauss Hypergeometric Functions
- 2015
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The pioneering study undertaken by Liang et al. in 2008 (Journal of the American Statistical Association, 103, 410–423) and the hundreds of papers citing that work make use of certain hypergeometric…
Variational Message Passing for Elaborate Response Regression Models
- 2019
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A factor graph fragment approach means the requisite calculations only need to be done once for a particular elaborate response distribution family, which means the modularity of variational message passing extends to elaborate response regression models.
Moment Propagation
- 2022
Mathematics, Computer Science
It is proved that the moment propagation algorithm recovers the exact marginal posterior distributions for all parameters, and for probit regression it is shown that moment propagation provides asymptotically correct posterior means and covariance estimates.
Variational approximations in geoadditive latent Gaussian regression: mean and quantile regression
- 2014
Computer Science, Mathematics
Variational approximations for Bayesian inference in geoadditive regression models are developed to provide a computationally attractive, fast alternative to Markov chain Monte Carlo simulations.
Statistical Methods for Estimating the Effects of Multi-Pollutant Exposures in Children's Health Research
- 2016
Environmental Science, Medicine
23 References
Mixtures of g Priors for Bayesian Variable Selection
- 2008
Mathematics, Computer Science
This article studies mixtures of g priors as an alternative to default gpriors that resolve many of the problems with the original formulation while maintaining the computational tractability that has made the g prior so popular.
Mean field variational Bayes for continuous sparse signal shrinkage: Pitfalls and remedies
- 2014
Computer Science, Mathematics
The principal finding is that the most natural, and simplest, mean field variational Bayes algorithm can perform quite poorly due to post- rior dependence among auxiliary variables, so more sophisticated algorithms are shown to be superior.
Generalized Beta Mixtures of Gaussians
- 2011
Mathematics, Computer Science
A new class of normal scale mixtures is proposed through a novel generalized beta distribution that encompasses many interesting priors as special cases and develops a class of variational Bayes approximations that will scale more efficiently to the types of truly massive data sets that are now encountered routinely.
Bayesian Core: A Practical Approach to Computational Bayesian Statistics
- 2007
Computer Science, Mathematics
Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications.
Explaining Variational Approximations
- 2010
Mathematics, Computer Science
The ideas of variational approximation are illustrated using examples that are familiar to statisticians using terminology, notation, and examples from the former field.
Mean-field variational approximate Bayesian inference for latent variable models
- 2007
Computer Science, Mathematics
The horseshoe estimator for sparse signals
- 2010
Mathematics
This paper proposes a new approach to sparsity, called the horseshoe estimator, which arises from a prior based on multivariate-normal scale mixtures. We describe the estimator's advantages over…
Variational Bayesian Multinomial Probit Regression with Gaussian Process Priors
- 2006
Computer Science, Mathematics
This is the first time that a fully variational Bayesian treatment for multiclass GP classification has been developed without having to resort to additional explicit approximations to the nongaussian likelihood term.
Generating bessel functions in mie scattering calculations using continued fractions.
- 1976
Physics
The algorithm uses a new technique of evaluating continued fractions that starts at the beginning rather than the tail and has a built-in error check.