Possible, Yes; Ignorant, Perhaps: A Scorecard for Possibilistic Forecasts
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915909883396096 |
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| author | Lawson, John R. |
| author_facet | Lawson, John R. |
| contents | Probabilistic forecasts must sum to unity and cannot express ``I don't know.'' Possibility theory relaxes this constraint: a subnormal distribution explicitly measures how much of the plausibility budget remains unassigned, ignorance signal that probability cannot represent. This paper develops a verification framework for such forecasts, centred on a five-number scorecard that separately diagnoses whether the forecast pointed at the right outcome (depth-of-truth), how sharply (diffuseness, support margin), how confidently (ignorance), and how dominantly (conditional necessity). A possibility-to-probability conversion preserves ignorance for familiar frequency-based scoring; categorical threshold scores (POD, FAR, CSI, etc.) connect to operational practice. Together, these three complementary facets -- possibilistic, probabilistic, and categorical -- expose failure modes invisible to any single metric. Storm Prediction Center convective outlook categories serve as the running example throughout; a synthetic reforecast demonstrates diagnostic visualisations and scorecard interpretation. Ignorance is better expressed than repressed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02187 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Possible, Yes; Ignorant, Perhaps: A Scorecard for Possibilistic Forecasts Lawson, John R. Applications Atmospheric and Oceanic Physics Probabilistic forecasts must sum to unity and cannot express ``I don't know.'' Possibility theory relaxes this constraint: a subnormal distribution explicitly measures how much of the plausibility budget remains unassigned, ignorance signal that probability cannot represent. This paper develops a verification framework for such forecasts, centred on a five-number scorecard that separately diagnoses whether the forecast pointed at the right outcome (depth-of-truth), how sharply (diffuseness, support margin), how confidently (ignorance), and how dominantly (conditional necessity). A possibility-to-probability conversion preserves ignorance for familiar frequency-based scoring; categorical threshold scores (POD, FAR, CSI, etc.) connect to operational practice. Together, these three complementary facets -- possibilistic, probabilistic, and categorical -- expose failure modes invisible to any single metric. Storm Prediction Center convective outlook categories serve as the running example throughout; a synthetic reforecast demonstrates diagnostic visualisations and scorecard interpretation. Ignorance is better expressed than repressed. |
| title | Possible, Yes; Ignorant, Perhaps: A Scorecard for Possibilistic Forecasts |
| topic | Applications Atmospheric and Oceanic Physics |
| url | https://arxiv.org/abs/2604.02187 |