posterior propriety
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2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Chengyuan Song ◽  
Dongchu Sun ◽  
Kun Fan ◽  
Rongji Mu

The use of hierarchical Bayesian models in statistical practice is extensive, yet it is dangerous to implement the Gibbs sampler without checking that the posterior is proper. Formal approaches to objective Bayesian analysis, such as the Jeffreys-rule approach or reference prior approach, are only implementable in simple hierarchical settings. In this paper, we consider a 4-level multivariate normal hierarchical model. We demonstrate the posterior using our recommended prior which is proper in the 4-level normal hierarchical models. A primary advantage of the recommended prior over other proposed objective priors is that it can be used at any level of a hierarchical model.


2017 ◽  
Vol 12 (2) ◽  
pp. 533-555 ◽  
Author(s):  
Hyungsuk Tak ◽  
Carl N. Morris

2016 ◽  
Vol 11 (2) ◽  
pp. 545-571 ◽  
Author(s):  
Sarah E. Michalak ◽  
Carl N. Morris

2005 ◽  
Vol 33 (2) ◽  
pp. 606-646 ◽  
Author(s):  
James O. Berger ◽  
William Strawderman ◽  
Dejun Tang

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