In this paper, we propose a new wide class of hypergeometric heavy tailed priors that is given as the convolution of a Student-t density for the location parameter and a Scaled Beta 2 prior for the squared scale parameter. These priors may have heavier tails than Student-t priors, and the variances have a sensible behaviour both at the origin and at the tail, making it suitable for objective analysis. Since the representation of our proposal is a scale mixture, it is suitable to detect sudden changes in the model. Finally, we propose a Gibbs sampler using this new family of priors for modelling outliers and structural breaks in Bayesian dynamic linear models. We demonstrate in a published example, that our proposal is more suitable than the Inverted Gamma’s assumption for the variances, which makes very hard to detect structural changes.
"An alternative to the Inverted Gamma for the variances to modelling outliers and structural breaks in dynamic models." Braz. J. Probab. Stat. 28 (2) 288 - 299, May 2014. https://doi.org/10.1214/12-BJPS207