Journal article
The Shadow Prior
Journal of computational and graphical statistics, v 18(2), pp 368-383
01 Jun 2009
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
In this article we consider posterior simulation in models with constrained parameter or sampling spaces. Constraints on the support of sampling and prior distributions give rise to a normalization constant in the complete conditional posterior distribution for the (hyper-) parameters of the respective distribution, complicating posterior simulation.
To mitigate the problem of evaluating normalization constants, we propose a computational approach based on model augmentation. We include an additional level in the probability model to separate the (hyper-) parameter from the constrained probability model, and we refer to this additional level in the probability model as a shadow prior. This approach can significantly reduce the overall computational burden if the original (hyper-) prior includes a complicated structure, but a simple form is chosen for the shadow prior, for example, if the original prior includes a mixture model or multivariate distribution, and the shadow prior defines a set of shadow parameters that are iid given the (hyper-) parameters. Although introducing the shadow prior changes the posterior inference on the original parameters, we argue that by appropriate choices of the shadow prior, the change is minimal and posterior simulation in the augmented probability model provides a meaningful approximation to the desired inference. Data used in this article are available online.
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Details
- Title
- The Shadow Prior
- Creators
- Merrill W. Liechty - Drexel UniversityJohn C. Liechty - MarketingPeter Mueller - Univ Texas MD Anderson Canc Ctr, Dept Biostat, Houston, TX 77030 USA
- Publication Details
- Journal of computational and graphical statistics, v 18(2), pp 368-383
- Publisher
- Amer Statistical Assoc
- Number of pages
- 16
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Decision Sciences (and Management Information Systems)
- Web of Science ID
- WOS:000270063800007
- Scopus ID
- 2-s2.0-77950665001
- Other Identifier
- 991019168388504721
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InCites Highlights
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Statistics & Probability