Xiaochun Meng - Scores for Multivariate Distributions and Level Sets (in person stat seminar)
| Dates: | 9 November 2022 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Xiaochun Meng |
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Xiaochun Meng, lecturer in Finance at the University of Sussex Business School is our speaker for the Statistics seminar series.
Title: Scores for Multivariate Distributions and Level Sets
Abstract: Forecasts of multivariate probability distributions are required for a variety of applications. Scoring rules enable the evaluation of forecast accuracy, and comparison between forecasting methods. We propose a theoretical framework for scoring rules for multivariate distributions, which encompasses the existing quadratic score and multivariate continuous ranked probability score. We demonstrate how this framework can be used to generate new scoring rules. In some multivariate contexts, it is a forecast of a level set that is needed, such as a density level set for anomaly detection or the level set of the cumulative distribution as a measure of risk. This motivates consideration of scoring functions for such level sets. For univariate distributions, it is well-established that the continuous ranked probability score can be expressed as the integral over a quantile score. We show that, in a similar way, scoring rules for multivariate distributions can be decomposed to obtain scoring functions for level sets. Using this, we present scoring functions for different types of level set, including density level sets and level sets for cumulative distributions. To compute the scores, we propose a simple numerical algorithm. We use a simulation study to support our proposals, and we use real data to illustrate usefulness for forecast combining and CoVaR applications.
Venue:
Frank Adams Seminar Room 2
Alan Turing Building
Manchester
M13 9PL
Speaker
Xiaochun Meng
Organisation: University of Sussex
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Frank Adams Seminar Room 2
Alan Turing Building
Upper Brook street
Manchester
