scholarly journals Conditionally Conjugate Mean-Field Variational Bayes for Logistic Models

2019 ◽  
Vol 34 (3) ◽  
pp. 472-485 ◽  
Author(s):  
Daniele Durante ◽  
Tommaso Rigon
Keyword(s):  
Mean Field ◽  
Logistic Models ◽  
Variational Bayes ◽  
Conjugate Mean

scholarly journals Modeling the health effects of time-varying complex environmental mixtures: Mean field variational Bayes for lagged kernel machine regression

2018 ◽  
Vol 29 (4) ◽  
pp. e2504 ◽  
Author(s):  
Shelley H. Liu ◽  
Jennifer F. Bobb ◽  
Birgit Claus Henn ◽  
Lourdes Schnaas ◽  
Martha M. Tellez-Rojo ◽  
...  
Keyword(s):  
Health Effects ◽  
Mean Field ◽  
Variational Bayes ◽  
Time Varying ◽  
Kernel Machine ◽  
Kernel Machine Regression ◽  
Environmental Mixtures

scholarly journals Mean Field Variational Bayes for Elaborate Distributions

2011 ◽  
Vol 6 (4) ◽  
pp. 847-900 ◽  
Author(s):  
Matthew P. Wand ◽  
John T. Ormerod ◽  
Simone A. Padoan ◽  
Rudolf Frühwirth
Keyword(s):  
Mean Field ◽  
Variational Bayes

scholarly journals Mean field variational Bayes for continuous sparse signal shrinkage: Pitfalls and remedies

2014 ◽  
Vol 8 (1) ◽  
pp. 1113-1151 ◽  
Author(s):  
Sarah E. Neville ◽  
John T. Ormerod ◽  
M. P. Wand
Keyword(s):  
Mean Field ◽  
Variational Bayes ◽  
Sparse Signal

scholarly journals Seemingly unrelated regression with measurement error: estimation via Markov Chain Monte Carlo and mean field variational Bayes approximation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Georges Bresson ◽  
Anoop Chaturvedi ◽  
Mohammad Arshad Rahman ◽  
Shalabh
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Measurement Error ◽  
Mean Field ◽  
Variational Bayes ◽  
Seemingly Unrelated Regression ◽  
Estimation Methods ◽  
Unrelated Regression ◽  
The Impact

Abstract Linear regression with measurement error in the covariates is a heavily studied topic, however, the statistics/econometrics literature is almost silent to estimating a multi-equation model with measurement error. This paper considers a seemingly unrelated regression model with measurement error in the covariates and introduces two novel estimation methods: a pure Bayesian algorithm (based on Markov chain Monte Carlo techniques) and its mean field variational Bayes (MFVB) approximation. The MFVB method has the added advantage of being computationally fast and can handle big data. An issue pertinent to measurement error models is parameter identification, and this is resolved by employing a prior distribution on the measurement error variance. The methods are shown to perform well in multiple simulation studies, where we analyze the impact on posterior estimates for different values of reliability ratio or variance of the true unobserved quantity used in the data generating process. The paper further implements the proposed algorithms in an application drawn from the health literature and shows that modeling measurement error in the data can improve model fitting.

The Use of Variational Bayes Compared to Markov Chain Monte Carlo in The Estimation of Thermal Properties

2021 ◽  
Author(s):  
Ashley F. Emery
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Mean Field Theory ◽  
Mean Field ◽  
Local Heat ◽  
Variational Bayes ◽  
Radiative Properties ◽  
Prior Probabilities ◽  
Bayes Statistics

Abstract Estimating the parameters that describe a thermal problem using Bayes statistics requires the specification of appropriate prior probabilities. That is p(P|D) = p(D|P)p(P)/p(D) where P = parameters, D = data and p(P) is the prior probability. For thermal problems this requires prior probabilities for density, specific heat, thermal conductivities, surface convective coefficients, radiative properties, and local heat release, Q. For many problems it is common to choose Gaussian probabilities to represent the errors. If the standard deviation is large, then the predictions can lead to negative values — a result that is not possible except for Q. Variational Bayes (VB) is an alternative to Markov Chain Monte Carlo (MCMC) and assumes that complex distributions p(a,b) can be replaced by factorization, p(a,b) = p(a)p(b), the mean field theory of physics. Overall Variational Bayes is particularly important for posterior probabilities, p(a|D), that have multiple maxima distributions.

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