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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…
Best linear unbiased prediction is well known for its wide range of applications including small area estimation. While the theory is well established for mixed linear models and under normality of the error and mixing distributions, the…
Generative models that satisfy hard constraints are critical in many scientific and engineering applications, where physical laws or system requirements must be strictly respected. Many existing constrained generative models, especially…
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…
In this paper, we develop a non-asymptotic local normal approximation for multinomial probabilities. First, we use it to find non-asymptotic total variation bounds between the measures induced by uniformly jittered multinomials and the…
Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks but lack theoretical understanding with respect to their mean square error (MSE) optimality. This paper proposes a novel denoising strategy…
Ensemble forecasting systems have advanced meteorology by providing probabilistic estimates of future states. Nonetheless, systematic biases often persist, making statistical post-processing essential. Traditional parametric post-processing…
We introduce a universal diffusion-based downscaling framework that lifts deterministic low-resolution weather forecasts into probabilistic high-resolution predictions without any model-specific fine-tuning. A single conditional diffusion…
Numerical weather forecasts can exhibit systematic errors due to simplifying model assumptions and computational approximations. Statistical postprocessing is a statistical approach to correcting such biases. A statistical postprocessing…
We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be…
Recent work has suggested that in highly correlated systems, such as sandpiles, turbulent fluids, ignited trees in forest fires and magnetization in a ferromagnet close to a critical point, the probability distribution of a global quantity…
An ensemble post-processing method is developed to improve the probabilistic forecasts of extreme precipitation events across the conterminous United States (CONUS). The method combines a 3-D Vision Transformer (ViT) for bias correction…
Accumulated precipitation forecasts are of high socioeconomic importance for agriculturally dominated societies in northern tropical Africa. In this study, we analyze the performance of nine operational global ensemble prediction systems…
The classic chi-squared statistic for testing goodness-of-fit has long been a cornerstone of modern statistical practice. The statistic consists of a sum in which each summand involves division by the probability associated with the…
The derivation of Student's pdf from superstatistics is a mere coincidence due to the choice of the $\chi^2$ distribution for the inverse temperature which is actually the Maxwell distribution for the speed. The difference between the…
The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase…
An important task in the statistical analysis of inhomogeneous point processes is to investigate the influence of a set of covariates on the point-generating mechanism. In this article, we consider the nonparametric Bayesian approach to…
Ensemble prediction systems are an invaluable tool for weather forecasting. Practically, ensemble predictions are obtained by running several perturbations of the deterministic control forecast. However, ensemble prediction is associated…
This article presents a new proof of the rate of convergence to the normal distribution of sums of independent, identically distributed random variables in chi-square distance, which was also recently studied in \cite{BobkovRenyi}. Our…
The coarse spatial resolution of gridded climate models, such as general circulation models, limits their direct use in projecting socially relevant variables like extreme precipitation. Most downscaling methods estimate the conditional…