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An alternative to the inverted gamma for the variances to modelling outliers and structural breaks in dynamic models. (English) Zbl 1319.62031
Summary: 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.

MSC:
62E15 Exact distribution theory in statistics
62E20 Asymptotic distribution theory in statistics
62F15 Bayesian inference
Software:
dlm
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References:
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