Comparing Sequential Forecasters

• URL: http://arxiv.org/abs/2110.00115v6
• Date: Thu, 9 Nov 2023 05:09:52 GMT
• Title: Comparing Sequential Forecasters
• Authors: Yo Joong Choe and Aaditya Ramdas
• Abstract summary: Consider two forecasters, each making a single prediction for a sequence of events over time. How might we compare these forecasters, either online or post-hoc, while avoiding unverifiable assumptions on how the forecasts and outcomes were generated? We present novel sequential inference procedures for estimating the time-varying difference in forecast scores. We empirically validate our approaches by comparing real-world baseball and weather forecasters.
• Score: 35.38264087676121
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Consider two forecasters, each making a single prediction for a sequence of events over time. We ask a relatively basic question: how might we compare these forecasters, either online or post-hoc, while avoiding unverifiable assumptions on how the forecasts and outcomes were generated? In this paper, we present a rigorous answer to this question by designing novel sequential inference procedures for estimating the time-varying difference in forecast scores. To do this, we employ confidence sequences (CS), which are sequences of confidence intervals that can be continuously monitored and are valid at arbitrary data-dependent stopping times ("anytime-valid"). The widths of our CSs are adaptive to the underlying variance of the score differences. Underlying their construction is a game-theoretic statistical framework, in which we further identify e-processes and p-processes for sequentially testing a weak null hypothesis -- whether one forecaster outperforms another on average (rather than always). Our methods do not make distributional assumptions on the forecasts or outcomes; our main theorems apply to any bounded scores, and we later provide alternative methods for unbounded scores. We empirically validate our approaches by comparing real-world baseball and weather forecasters.

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