Related papers: Using proper divergence functions to evaluate clim…

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…

Uncertainty quantification is essential for the reliable deployment of machine learning models to high-stakes application domains. Uncertainty quantification is all the more challenging when training distribution and test distribution are…

Deep nonlinear models pose a challenge for fitting parameters due to lack of knowledge of the hidden layer and the potentially non-affine relation of the initial and observed layers. In the present work we investigate the use of information…

The classical paradigm of scoring rules is to discriminate between two different forecasts by comparing them with observations. The probability distribution of the observed record is assumed to be perfect as a verification benchmark. In…

Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient's positive response to treatment. Scoring rules have long been used…

Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as…

Dependency functions of dependent variables are relevant for i) performing uncertainty quantification and sensitivity analysis in presence of dependent variables and/or correlated variables, and ii) simulating random dependent variables. In…

A high-ranking goal of interdisciplinary modeling approaches in the natural sciences are quantitative prediction of system dynamics and model based optimization. For this purpose, mathematical modeling, numerical simulation and scientific…

Using optimal detection techniques with climate model simulations, most of the observed increase of near surface temperatures over the second half of the twentieth century is attributed to anthropogenic influences. However, the partitioning…

We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…

The Kullback-Leibler divergence or relative entropy is an information-theoretic measure between statistical models that play an important role in measuring a distance between random variables. In the study of complex systems, random fields…

Detrended fluctuation analysis is used to investigate correlations between the monthly average of the maximum daily temperatures for different locations in the continental US and the different climates these locations have. When we plot the…

The estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors.Powerful…

We quantify model risk of a financial portfolio whereby a multi-period mean-standard-deviation criterion is used as a selection criterion. In this work, model risk is defined as the loss due to uncertainty of the underlying distribution of…

An initial screening experiment may lead to ambiguous conclusions regarding the factors which are active in explaining the variation of an outcome variable: thus adding follow-up runs becomes necessary. We propose a fully Bayes objective…

Probabilistic temperature forecasts are potentially useful to the energy and weather derivatives industries. However, at present, they are little used. There are a number of reasons for this, but we believe this is in part due to…

We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…

Generative models frequently suffer miscalibration, wherein statistics of the sampling distribution, such as the fraction of generations in a given class, deviate from desired values. We frame calibration as a constrained optimization…

Common statistical measures of uncertainty such as $p$-values and confidence intervals quantify the uncertainty due to sampling, that is, the uncertainty due to not observing the full population. However, sampling is not the only source of…

Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots…