# Probabilistic Recalibration of Forecasts

## TL;DR

This paper introduces a recalibration method for probabilistic forecasts using Gaussian processes, improving calibration and enabling consistent betting advantages, demonstrated through experiments with nonlinear circuits and climate forecasts.

## Contribution

It proposes a novel Gaussian process-based recalibration scheme that enhances probabilistic forecast calibration and betting performance, even with dependent PIT values.

## Key findings

- Recalibrated forecasts achieve uniform PIT distribution.
- The scheme improves betting success against original forecasts.
- Effective in both laboratory and climate forecast case studies.

## Abstract

We present a scheme by which a probabilistic forecasting system whose predictions have poor probabilistic calibration may be recalibrated by incorporating past performance information to produce a new forecasting system that is demonstrably superior to the original, in that one may use it to consistently win wagers against someone using the original system. The scheme utilizes Gaussian process (GP) modeling to estimate a probability distribution over the Probability Integral Transform (PIT) of a scalar predictand. The GP density estimate gives closed-form access to information entropy measures associated with the estimated distribution, which allows prediction of winnings in wagers against the base forecasting system. A separate consequence of the procedure is that the recalibrated forecast has a uniform expected PIT distribution. A distinguishing feature of the procedure is that it is appropriate even if the PIT values are not i.i.d. The recalibration scheme is formulated in a framework that exploits the deep connections between information theory, forecasting, and betting. We demonstrate the effectiveness of the scheme in two case studies: a laboratory experiment with a nonlinear circuit and seasonal forecasts of the intensity of the El Ni\~no-Southern Oscillation phenomenon.