Trick, S. ; Rothkopf, C. A. ; Jäkel, F. (2023)
Parameter estimation for a bivariate beta distribution with arbitrary beta marginals and positive correlation.
In: Metron, 81 (1)
doi: 10.1007/s40300-023-00247-2
Article, Bibliographie
Abstract
We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma- distributed random variates. While previous work used an approximate and sometimes inaccurate method to compute the distribution’s covariance and estimate its parameters, here, we derive all product moments and the exact covariance, which can be computed numerically. Based on this analysis we present an algorithm for estimating the parameters of the distribu- tion using moment matching. We evaluate this inference method in a simulation study and demonstrate its practical use on a data set consisting of predictions from two correlated fore- casters. Furthermore, we generalize the bivariate beta distribution to a correlated Dirichlet distribution, for which the proposed parameter estimation method can be used analogously.
| Item Type: | Article |
|---|---|
| Erschienen: | 2023 |
| Creators: | Trick, S. ; Rothkopf, C. A. ; Jäkel, F. |
| Type of entry: | Bibliographie |
| Title: | Parameter estimation for a bivariate beta distribution with arbitrary beta marginals and positive correlation |
| Language: | English |
| Date: | 9 June 2023 |
| Publisher: | Springer |
| Journal or Publication Title: | Metron |
| Volume of the journal: | 81 |
| Issue Number: | 1 |
| DOI: | 10.1007/s40300-023-00247-2 |
| URL / URN: | https://link.springer.com/article/10.1007/s40300-023-00247-2 |
| Abstract: | We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma- distributed random variates. While previous work used an approximate and sometimes inaccurate method to compute the distribution’s covariance and estimate its parameters, here, we derive all product moments and the exact covariance, which can be computed numerically. Based on this analysis we present an algorithm for estimating the parameters of the distribu- tion using moment matching. We evaluate this inference method in a simulation study and demonstrate its practical use on a data set consisting of predictions from two correlated fore- casters. Furthermore, we generalize the bivariate beta distribution to a correlated Dirichlet distribution, for which the proposed parameter estimation method can be used analogously. |
| Divisions: | 03 Department of Human Sciences Forschungsfelder Forschungsfelder > Information and Intelligence Forschungsfelder > Information and Intelligence > Cognitive Science 03 Department of Human Sciences > Institute for Psychology 03 Department of Human Sciences > Institute for Psychology > Models of Higher Cognition 03 Department of Human Sciences > Institute for Psychology > Psychology of Information Processing |
| Date Deposited: | 09 Jun 2023 17:40 |
| Last Modified: | 03 Jul 2023 05:06 |
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