Sequential updating of conditional probabilities on directed graphical structures

By David J. Spiegelhalter, Steffen L. Lauritzen. 1990

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Citations in the corpus

Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks (2020, background): “One such approximation (Spiegelhalter & Lauritzen, 1990; MacKay, 1992a) is constructed by scaling the input of the probit function2 Φ by a constant λ = √ π/8 .”
Discrete Variational Autoencoders (2016, methodology): “…further restrict the neural network deﬁning the distribution over the observed variables x given the smoothing variables ζ to consist of a linear transformation followed by a pointwise logistic nonlinearity, analogous to a sigmoid belief network (SBN; Spiegelhalter & Lauritzen, 1990; Neal, 1992).”
Bayesian parameter estimation via variational methods (2000, methodology): “Our methods can be compared to the Laplace approximation for logistic regression (cf. Spiegelhalter and Lauritzen 1990), a closely related method which also utilizes a Gaussian approximation to the posterior.”
Bayesian Graphical Models for Discrete Data (1995, background): “1 Introduction The use of graphs to represent statistical models dates back to Wright (1921) and has been the focus of considerable activity in recent years.”
Bayesian Networks and Decision Graphs (2001, background): “The relation to Bayesian networks was established through work in the early 1990s ((Fung and Crawford 1990), (Spiegelhalter and Lauritzen 1990), (Dawid and Lauritzen 1993), (Cooper and Herskovits 1992)).”
The dropout learning algorithm (2014, background): “If necessary, it is also possible to derive better and more general estimates of E(O), under the assumption that S is Gaussian by approximating the logistic function with the cumulative distribution of a Gaussian, as described in Appendix F (see also [41]).”
Learning Bayesian Networks: Search Methods and Experimental Results (1995, methodology): “We say that a metric is prior equiualent when the prior probabilities of any two isomorphic network structures are equal. We say a metric is score equiaalent if it is both prior equivalent and likelihood equivalent. The parametric formula given in the previous paragraph is not prior equivalent. HGC ”
Bayesian graphical modelling: a case‐study in monitoring health outcomes (2002, background): “…on undirected graphs (Whittaker, 1990), in which undirected associations between variables are explored, and chain graphs (Frydenberg, 1990; Wermuth and Lauritzen, 1990; Cox and Wermuth, 1996), which mix directed and undirected links: these models have their own conditional independence…”
Bayesian Networks for Data Mining (2004, background): “That is, p(θ s | S h ) = n i=1 q i j=1 p(θ i j | S h ) We refer to this assumption, which was introduced by Spiegelhalter and Lauritzen (1990), as parameter independence.”
Bayesian Networks in Reliability: Some Recent Developments (2004, background): “Spiegelhalter and Lauritzen (1990) , see also Lauritzen (1995).”