Mean Field Variational Bayes for Elaborate Distributions

Wand, M. P.; Ormerod, John T.; Padoan, Simone A.; Frühwirth, R.

doi:10.1214/11-ba631

Cited by 128 publications

(120 citation statements)

References 26 publications

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“…Moreover, some distributions can be expressed as a mixture of normal distributions, which may be useful to carry out Bayesian analysis using Monte Carlo Markov chain or variational methods; see, for example, Wand et al (2011). Some generalizations of the Birnbaum-Saunders distribution can also be represented as a mixture of normal distributions, so that these ideas on Bayesian analysis will be explored in a future work; see Balakrishnan et al (2009) and .…”

Section: Discussion Conclusion and Future Researchmentioning

confidence: 99%

Multivariate Birnbaum-Saunders Distributions: Modelling and Applications

Aykroyd

Leiva

Marchant

2018

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Abstract:Since its origins and numerous applications in material science, the Birnbaum-Saunders family of distributions has now found widespread uses in some areas of the applied sciences such as agriculture, environment and medicine, as well as in quality control, among others. It is able to model varied data behaviour and hence provides a flexible alternative to the most usual distributions. The family includes Birnbaum-Saunders and log-Birnbaum-Saunders distributions in univariate and multivariate versions. There are now well-developed methods for estimation and diagnostics that allow in-depth analyses. This paper gives a detailed review of existing methods and of relevant literature, introducing properties and theoretical results in a systematic way. To emphasise the range of suitable applications, full analyses are included of examples based on regression and diagnostics in material science, spatial data modelling in agricultural engineering and control charts for environmental monitoring. However, potential future uses in new areas such as business, economics, finance and insurance are also discussed. This work is presented to provide a full tool-kit of novel statistical models and methods to encourage other researchers to implement them in these new areas. It is expected that the methods will have the same positive impact in the new areas as they have had elsewhere.

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Section: Discussion Conclusion and Future Researchmentioning

confidence: 99%

Multivariate Birnbaum-Saunders Distributions: Modelling and Applications

Aykroyd

Leiva

Marchant

2018

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“…Simple extensions include binary response via the probit link, Berkson measurement error, semiparametric regression, non-Gaussian x i models and models where repeated w i observations are available to estimate σ 2 v . Extensions for various types of non-Gaussian response are also possible due to Wand et al (2011), however it is anticipated that these extensions of the techniques presented here would require a reasonable amount of modification.…”

Section: Discussionmentioning

confidence: 99%

“…For an introduction to such techniques see Bishop (2006), Ormerod and Wand (2010) or Wand et al (2011). We show that the transference of such technology to the measurement error setting achieves reasonable accuracy while being hundreds of times faster than MCMC.…”

Section: Introductionmentioning

confidence: 94%

Mean field variational Bayesian inference for nonparametric regression with measurement error

Pham

Ormerod

Wand

2013

Computational Statistics & Data Analysis

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A fast mean field variational Bayes (MFVB) approach to nonparametric regression when the predictors are subject to classical measurement error is investigated. It is shown that the use of such technology to the measurement error setting achieves reasonable accuracy. In tandem with the methodological development, a customized Markov chain Monte Carlo method is developed to facilitate the evaluation of accuracy of the MFVB method.

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“…We assume a discrete first-order Markovian dependence structure, therefore the current state depends only on the state occupied at the last time-point. We will follow the notation set out in [8] for specifying the HMM and we will apply the algorithm described in that article for estimation of the model. Given that the system is in state j 1 at time-point i, the transition matrix π represents the probability of moving to state j 2 at time-point i + 1.…”

Section: Variational Bayesian Inference For Hidden Markov Models mentioning

confidence: 99%

“…Within the context of finite mixture estimation, [5] proposed a new transdimensional SMC algorithm based on the idea of using the variational Bayes (VB) approach [6], [7], [8] within an SMC framework. The resulting hybrid algorithm is called SMCVB.…”

Section: Introductionmentioning

confidence: 99%

Transdimensional sequential Monte Carlo for hidden Markov models using variational Bayes - SMCVB

McGrory¹,

Ahfock²

2014

Annals of Computer Science and Information Systems

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Abstract-In this paper we outline a transdimensional sequential Monte Carlo algorithm -SMCVB -for fitting hidden Markov models. Sequential Monte Carlo (SMC) involves generating a weighted sample of particles from a sequence of probability distributions with the aim of converging to the target Bayesian posterior distribution. SMCVB makes use of variational Bayes (VB) in combination with SMC principles to create an algorithm which targets the posterior distribution more efficiently thereby saving on time and computational storage requirements. Another key feature of our methodology is that the variational-Bayesgenerated proposals can vary in dimension. We have found in our simulation studies that we are able to obtain sensible estimates of the model dimensionality in this one-step procedure. This introduces very valuable additional flexibility in the modelling approach and opens up the potential for use of the algorithm in on-line settings where efficient and reliable estimation of dimensionality and parameters is required.

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Mean Field Variational Bayes for Elaborate Distributions

Cited by 128 publications

References 26 publications

Multivariate Birnbaum-Saunders Distributions: Modelling and Applications

Multivariate Birnbaum-Saunders Distributions: Modelling and Applications

Mean field variational Bayesian inference for nonparametric regression with measurement error

Transdimensional sequential Monte Carlo for hidden Markov models using variational Bayes - SMCVB

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