Convergence and Asymptotic Normality of Variational Bayesian Approximations for Expon

By D. M. Titterington. 2004

69 citations recorded by the source corpus.

A ceramic green arc tube for a metal vapor discharge lamp wherein an outer diameter of the arc discharging portion is larger than that of the end portions holding the discharging electrodes is produced by preparing a stiff plastic body consisting mainly of a ceramic material or which main component is alumina, and a binder of which main component is thermal geltinizing organic substance; forming the prepared body into a straight tubular body by means of an extruder; placing the tubular body into an inner cavity of molding die having the above described ceramic arc tube shape wherein the molding die has been previously heated; closing one end portion of the tubular body; applying a compressed fluid from another opened end portion of the tubular body into the inside of said tubular body to inflate the central portion of tubular body until contacting to the inner cavity surface of the molding die,; hardening and drying the inflated body with the heat of previously heated molding die; and ejecting the dried body from the die. This production is characterized in that the forming is effected by using a die comprising two halves of die divided by a plane parallel to an axial direction of the tube, said two halves forming an inner circumferential cavity conforming to the shape of the tube when the two halves are engaged, vents provided at the cavity portion and perforating from the inner surface of the cavity to the outside, and heating means.

Subfields: Artificial Intelligence, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

An Introduction to Bayesian Inference via Variational Approximations (2011, methodology): “Wang and Titterington (2004) demonstrate that, given a sufficient number of observations, this family of approximating distributions will correctly characterize the posterior mean, a guarantee not possible for sampling-based approaches to inference.1 Following Bishop (2006), we call this a…”
Variational Bayesian Multinomial Probit Regression with Gaussian Process Priors (2006, background): “Finally,wehavethateach Q ( ψ kd ) = (cid:7) ψ kd ( σ k + 1 , τ k + (cid:19) ϕ kd ), and the associated posterior mean is simply (cid:19) ψ kd = ( σ k + 1) / ( τ k + (cid:19) ϕ kd ).”
Bounded Approximations for Marginal Likelihoods (2010, methodology): “L4: L4 is the estimate of lower bound of log marginal likelihood using the traditional variational method (Corduneanu and Bishop, 2001; Wang and Titterington, 2004).”
On Smoothing and Inference for Topic Models (2009, methodology): “Variational methods like VB are known to underestimate posterior variance [Wang and Titterington, 2004].”
Inadequacy of interval estimates corresponding to variational Bayesian approximations (2005, background): “Some initial investigations have been implemented by the authors in Wang and Titterington (2003) and Wang and Titterington (2004b).”
Variational learning for rectified factor analysis (2007, background): “There are some general results for the exponential family of models, regarding the asymptotic properties [19] of such approximations.”