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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.