Abstract Bayesian models for data grouped into distinct samples are typically defined within the framework of partial exchangeability. All currently known nonparametrics priors for partially exchangeable data induce positive correlation both between observations coming from different samples as well as between the underlying random probability measures. However, such property is not implied by partial exchangeability and may not be appropriate in some applications. Using σ-stable completely random measures and Clayton-Levy copulas, we propose a nonpara- ´ metric prior that may induce either negative or positive correlation. The contents of these pages summarize some of the results derived in [1].
Ascolani, F., Franzolini, B., Lijoi, A., Pruenster, I. (2021). On the dependence structure in Bayesian nonparametric priors. In C. Perna, N. Salvati, F. Schirripa Spagnolo (a cura di), Book of Short Papers SIS 2021 Part 2 (pp. 1219-1225). Pearson.
On the dependence structure in Bayesian nonparametric priors
Franzolini, Beatrice;
2021
Abstract
Abstract Bayesian models for data grouped into distinct samples are typically defined within the framework of partial exchangeability. All currently known nonparametrics priors for partially exchangeable data induce positive correlation both between observations coming from different samples as well as between the underlying random probability measures. However, such property is not implied by partial exchangeability and may not be appropriate in some applications. Using σ-stable completely random measures and Clayton-Levy copulas, we propose a nonpara- ´ metric prior that may induce either negative or positive correlation. The contents of these pages summarize some of the results derived in [1].
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