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
Artikel, Bibliographie
Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2023 |
| Autor(en): | Trick, S. ; Rothkopf, C. A. ; Jäkel, F. |
| Art des Eintrags: | Bibliographie |
| Titel: | Parameter estimation for a bivariate beta distribution with arbitrary beta marginals and positive correlation |
| Sprache: | Englisch |
| Publikationsjahr: | 9 Juni 2023 |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Metron |
| Jahrgang/Volume einer Zeitschrift: | 81 |
| (Heft-)Nummer: | 1 |
| DOI: | 10.1007/s40300-023-00247-2 |
| URL / URN: | https://link.springer.com/article/10.1007/s40300-023-00247-2 |
| Kurzbeschreibung (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. |
| Fachbereich(e)/-gebiet(e): | 03 Fachbereich Humanwissenschaften Forschungsfelder Forschungsfelder > Information and Intelligence Forschungsfelder > Information and Intelligence > Cognitive Science 03 Fachbereich Humanwissenschaften > Institut für Psychologie 03 Fachbereich Humanwissenschaften > Institut für Psychologie > Modelle höherer Kognition 03 Fachbereich Humanwissenschaften > Institut für Psychologie > Psychologie der Informationsverarbeitung |
| Hinterlegungsdatum: | 09 Jun 2023 17:40 |
| Letzte Änderung: | 03 Jul 2023 05:06 |
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