Related papers: Copula Calibration
When providing probabilistic forecasts for uncertain future events, it is common to strive for calibrated forecasts, that is, the predictive distribution should be compatible with the observed outcomes. Several notions of calibration are…
In conditional copula models, the copula parameter is deterministically linked to a covariate via the calibration function. The latter is of central interest for inference and is usually estimated nonparametrically. However, when a…
In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. In this paper, we introduce the concept of multivariate discrete copulas, discuss their…
Rank and PIT histograms are established tools to assess the calibration of probabilistic forecasts. They not only check whether an ensemble forecast is calibrated, but they also reveal what systematic biases (if any) are present in the…
This paper lays out a principled approach to compare copula forecasts via strictly consistent scores. We first establish the negative result that, in general, copulas fail to be elicitable, implying that copula predictions cannot sensibly…
Risk evaluation is a forecast, and its validity must be backtested. Probability distribution forecasts are used in this work and allow for more powerful validations compared to point forecasts. Our aim is to use bivariate copulas in order…
Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…
Any decision making process that relies on a probabilistic forecast of future events necessarily requires a calibrated forecast. This paper proposes new methods for empirically assessing forecast calibration in a multivariate setting where…
In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. We introduce the concept of multivariate discrete copulas, discuss their equivalence to…
Calibration is a pivotal aspect in predictive modeling, as it ensures that the predictions closely correspond with what we observe empirically. The contemporary calibration framework, however, is predominantly focused on prediction models…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
Calibration tests based on the probability integral transform (PIT) are routinely used to assess the quality of univariate distributional forecasts. However, PIT-based calibration tests for multivariate distributional forecasts face various…
Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…
A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…
We propose a new copula model that can be used with replicated spatial data. Unlike the multivariate normal copula, the proposed copula is based on the assumption that a common factor exists and affects the joint dependence of all…
Accurate uncertainty measurement is a key step to building robust and reliable machine learning systems. Conformal prediction is a distribution-free uncertainty quantification algorithm popular for its ease of implementation, statistical…
We propose a new copula model for replicated multivariate spatial data. Unlike classical models that assume multivariate normality of the data, the proposed copula is based on the assumption that some factors exist that affect the joint…
Forecasts for uncertain future events should be probabilistic. Probabilistic forecasts are commonly issued as prediction intervals, which provide a measure of uncertainty in the unknown outcome whilst being easier to understand and…
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…
A probabilistic model is said to be calibrated if its predicted probabilities match the corresponding empirical frequencies. Calibration is important for uncertainty quantification and decision making in safety-critical applications. While…