Related papers: Comparing the ensemble mean and the ensemble stand…
Prediction intervals are a machine- and human-interpretable way to represent predictive uncertainty in a regression analysis. In this paper, we present a method for generating prediction intervals along with point estimates from an ensemble…
We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$ in regression…
Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…
A problem of the equivalence of statistical ensembles is critically analyzed. It is shown, that although different probability distributions of statistical physics have the same behavior in the thermodynamic limit, there are physical…
The pointwise mutual information profile, or simply profile, is the distribution of pointwise mutual information for a given pair of random variables. One of its important properties is that its expected value is precisely the mutual…
Contemporary weather forecasts are typically based on ensemble prediction systems, which consist of multiple runs of numerical weather prediction models that vary with respect to in the initial conditions and/or the the parameterization of…
Standard weather forecast evaluations focus on the forecaster's perspective and on a statistical assessment comparing forecasts and observations. In practice, however, forecasts are used to make decisions, so it seems natural to take the…
Finite sample bounds on the estimation error of the mean by the empirical mean, uniform over a class of functions, can often be conveniently obtained in terms of Rademacher or Gaussian averages of the class. If a function of n variables has…
By the end of 2021, the renewable energy share of the global electricity capacity reached 38.3% and the new installations are dominated by wind and solar energy, showing global increases of 12.7% and 18.5%, respectively. However, both wind…
Regression algorithms are regularly used for improving the accuracy of satellite precipitation products. In this context, satellite precipitation and topography data are the predictor variables, and gauged-measured precipitation data are…
We evaluate the performance of two 44 year ensemble seasonal hindcast time series for the Nino3 index produced as part of the DEMETER project. We show that the ensemble mean carries useful information out to six months. The ensemble spread,…
Large ensembles of climate projections are essential for characterizing uncertainty in future climate and extreme weather events, yet computational constraints of numerical climate models limit ensemble sizes to a small number of…
Precipitation forecasts are less accurate compared to other meteorological fields because several key processes affecting precipitation distribution and intensity occur below the resolved scale of global weather prediction models. This…
Underlying the use of statistical approaches for a wide range of applications is the assumption that the probabilities obtained from a statistical model are representative of the "true" probability that event, or outcome, will occur.…
According to the concept of typicality, an ensemble average can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space. This random-vector approximation,…
Forecasts of the trajectory of an infectious agent can help guide public health decision making. A traditional approach to forecasting fits a computational model to structured data and generates a predictive distribution. However, human…
Large language models (LLMs) have achieved remarkable results in wide range of domains. However, the accuracy and robustness of one-shot LLM predictions remain highly sensitive to the examples and the diversity among ensemble members. This…
The emerge of new technologies to synthesize and analyze big data with high-performance computing, has increased our capacity to more accurately predict crop yields. Recent research has shown that Machine learning (ML) can provide…
Meta-analysis involves combining summary information for related but independent studies. It uses different relationship to combine position measure as well as dispersion measures. The objective of this study is to discuss a relationship…
Artificial intelligence (AI)-based weather prediction research is growing rapidly and has shown to be competitive with the advanced dynamic numerical weather prediction models. However, research combining AI-based weather prediction models…