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arXiv · 1603.00393

On the Design and use of Ensembles of Multi-model Simulations for Forecasting

Sarah Higgins·Hailiang Du·Leonard A. Smith
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Abstract

Probability forecasting is common in the geosciences, the finance sector, and elsewhere. It is sometimes the case that one has multiple probability-forecasts for the same target. How is the information in these multiple forecast systems best "combined"? Assuming stationary, then in the limit of a very large forecast-outcome archive, each model-based probability density function can be weighted to form a "multi-model forecast" which will, in expectation, provide the most information. In the case that one of the forecast systems yields a probability distribution which reflects the distribution from which the outcome will be drawn, then Bayesian Model Averaging will identify this model as the number of forecast-outcome pairs goes to infinity. In many applications, like those of seasonal forecasting, data are precious: the archive is often limited to fewer than $2^6$ entries. And no perfect model is in hand. In this case, it is shown that forming a single "multi-model probability forecast" can be expected to prove misleading. These issues are investigated using probability forecasts of a simple mathematical system, which allows most limiting behaviours to be quantified.

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Sarah Higgins, Hailiang Du, Leonard A. Smith. 2016-03-01. On the Design and use of Ensembles of Multi-model Simulations for Forecasting. https://arxiv.org/abs/1603.00393

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