We study the problem of making calibrated probabilistic forecasts for a binary sequence generated by an adversarial nature. Following the seminal paper of Foster and Vohra (1998), nature is often modeled as an adaptive adversary who sees all activity of the forecaster except the randomization that the forecaster may deploy. A number of papers have proposed randomized forecasting strategies that achieve an ϵ-calibration error rate of O(1/sqrt T), which we prove is tight in general. On the other hand, it is well known that it is not possible to be calibrated without randomization, or if nature also sees the forecaster's randomization; in both cases the calibration error could be Ω(1). Inspired by the equally seminal works on the "power of two choices" and imprecise probability theory, we study a small variant of the standard online calibration problem. The adversary gives the forecaster the option of making two nearby probabilistic forecasts, or equivalently an interval forecast of small width, and the endpoint closest to the revealed outcome is used to judge calibration. This power of two choices, or imprecise forecast, accords the forecaster with significant power -- we show that a faster ϵ-calibration rate of O(1/T) can be achieved even without deploying any randomization.
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On the Comparison of Interval Forecasts: ON THE COMPARISON OF INTERVAL FORECASTS
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null (Ed.)Abstract Ensemble forecasts using the WRF Model at 20-km grid spacing with varying parameterizations are used to investigate and compare precipitation and atmospheric profile forecast biases in North and South America. By verifying a 19-member ensemble against NCEP Stage IV precipitation analyses, it is shown that the cumulus parameterization (CP), in addition to precipitation amount and season, had the largest influence on precipitation forecast skill in North America during 2016-2017. Verification of an ensemble subset against operational radiosondes in North and South America finds that forecasts in both continents feature a substantial mid-level dry bias, particularly at 700 hPa, during the warm season. Case-by-case analysis suggests that large mid-level error is associated with mesoscale convective systems (MCSs) east of the high terrain and westerly subsident flow from the Rocky and Andes Mountains in North and South America. However, error in South America is consistently greater than North America. This is likely attributed to the complex terrain and higher average altitude of the Andes relative to the Rockies, which allow for a deeper low-level jet and long-lasting MCSs, both of which 20-km simulations struggle to resolve. In the wake of data availability from the RELAMPAGO field campaign, the authors hope that this work motivates further comparison of large precipitating systems in North and South America, given their high impact in both continents.more » « less
