Abstract:
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Sparsity inducing priors have been widely used for Bayesian modeling of Gaussian data. However, the use of these priors in skewed and heavy-tailed data settings is less developed. In this paper, motivated by the horseshoe prior, we propose a new continuous global-local shrinkage prior suitable for the case that the data model is non-symmetric. Specifically, we consider modeling the data according to the multivariate logit-beta distribution, which is a special case of the conjugate multivariate distribution. We show that this new specification can be considered as an extension of the horseshoe model. Furthermore, our approach involves an easy-to-implement Gibbs sampler. The simulation study suggests a superior performance of our proposed prior in a standard design setting against the horseshoe prior. Additionally, we conduct a statistical analysis of cloud fraction data from NASA’s Moderate Resolution Imaging Spectroradiometer (MODIS) instrument to demonstrate the effectiveness of the proposed prior.
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