Bayarri, M. J.; Mayoral, A. M. Graphical models for hierarchical computations in the analysis and design of replications. (English) Zbl 1058.65013 Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 93, No. 3, 281-293 (1999). Summary: Graphical models are frequently used to model dependencies in large, complex stochastic systems. Bayesians often use them to characterize propagation of learning in expert systems. Also, the properties of directed acyclic graphs greatly simplify the derivations of full conditionals in Gibbs sampling schemes. In this paper, we use them to clarify and simplify usual analytical computations in Bayesian hierarchical models. The scenario is that of designing and analyzing the replication of a performed experiment. Cited in 1 Document MSC: 65C60 Computational problems in statistics (MSC2010) 62C10 Bayesian problems; characterization of Bayes procedures 62D05 Sampling theory, sample surveys 68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence 68T05 Learning and adaptive systems in artificial intelligence Keywords:Graphical models; large, complex stochastic systems; expert systems; Gibbs sampling schemes; acceptance-rejection; Bayesian hierarchical models; exact replications; metropolis-Hastings algorithm; non-central \(t\); stochastic EM algorithm PDFBibTeX XMLCite \textit{M. J. Bayarri} and \textit{A. M. Mayoral}, Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 93, No. 3, 281--293 (1999; Zbl 1058.65013) Full Text: EuDML