{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/comparing-sequential-forecasters","title":"Comparing Sequential Forecasters","arxiv_id":"2110.00115","date":"2021-09-30","proceeding":null,"authors":["Yo Joong Choe","Aaditya Ramdas"],"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.","url_abs":"https://arxiv.org/abs/2110.00115v6","url_pdf":"https://arxiv.org/pdf/2110.00115v6.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"comparing-sequential-forecasters","repo_url":"https://github.com/yjchoe/ComparingForecasters","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":null,"task_name":"valid"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2110.00115","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}