{"ID":5438878,"CreatedAt":"2026-07-01T01:17:58.482524686Z","UpdatedAt":"2026-07-03T13:00:35.913618206Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.31621","arxiv_id":"2606.31621","title":"Calibrated Probability Forecast Sequences and Measure-Valued Martingales","abstract":"We consider the calibration of probability forecasts. Several notions of calibration exist when the forecaster issues a single forecast for each of the observations that is to be predicted. We extend one of these notions, auto-calibration, to the common situation in which the forecaster issues a sequence of forecasts for each observation, repeatedly updating their prediction as they receive additional information. For observations that sit in any Borel space, we show that auto-calibration is equivalent to a certain sequence of random probability measures satisfying the martingale property, and we propose a simple, statistical approach to testing this property. This provides, for the first time, a way of testing the calibration of such sequences of probability forecasts.","short_abstract":"We consider the calibration of probability forecasts. Several notions of calibration exist when the forecaster issues a single forecast for each of the observations that is to be predicted. We extend one of these notions, auto-calibration, to the common situation in which the forecaster issues a sequence of forecasts f...","url_abs":"https://arxiv.org/abs/2606.31621","url_pdf":"https://arxiv.org/pdf/2606.31621v1","authors":"[\"Thomas Wilkinson\",\"Christopher Ferro\"]","published":"2026-06-30T13:09:09Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}