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Graphical models for hierarchical computations in the analysis and design of replications. (English) Zbl 1058.65013

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.

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
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