Abstract
The standard Bayesian inference scenario involves data \( \underline {\rm X} \) whose distribution is governed by a family of densities \( \left\{ {f\left( {\underline x ;\underline \theta } \right):\underline \theta \in \Theta } \right\} \) where frequently Θ is of dimension, say k, greater than 2. A Bayesian analysis of such a problem will involve identification of a prior density for \( \underline \theta \) which will be combined with the likelihood of the data to yield a posterior distribution suitable for inferences about \( \underline \theta \). The use of informative priors (obtained from knowledgable expert(s)) is usually envisioned in such settings. Considerable modern Bayesian analysis has focussed on the frequently occurring case in which prior information is sparse or absent. In this context we encounter priors associated with adjectives such as: diffuse, noninformative, convenience, reference, etc. Much early Bayesian work was focussed on so-called conjugate priors. Such priors are convenient but lack flexibility for modeling informed prior belief. The classical scenario, in which most of the issues are already clearly visible, involves a sample from a normal distribution with unknown mean and variance.
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© 1999 Springer-Verlag New York, Inc.
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(1999). Bayesian Analysis Using Conditionally Specified Models. In: Arnold, B.C., Castillo, E., Sarabia, J.M. (eds) Conditional Specification of Statistical Models. Spinger Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22588-3_13
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DOI: https://doi.org/10.1007/978-0-387-22588-3_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98761-3
Online ISBN: 978-0-387-22588-3
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