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We examine a family of intrinsic performance measures in terms of probability distributions that generalize Hellinger distance and Fisher information. They are applied to quantum metrology to assess the uncertainty in the detection of…
Any physical system can be viewed from the perspective that information is implicitly represented in its state. However, the quantification of this information when it comes to complex networks has remained largely elusive. In this work, we…
What does it mean to say that, for example, the probability for rain tomorrow is between 20% and 30%? The theory for the evaluation of precise probabilistic forecasts is well-developed and is grounded in the key concepts of proper scoring…
A suitable scalar metric can help measure multi-calibration, defined as follows. When the expected values of observed responses are equal to corresponding predicted probabilities, the probabilistic predictions are known as "perfectly…
Prediction performance does not always reflect the estimation behaviour of a method. High error in estimation may necessarily not result in high prediction error, but can lead to an unreliable prediction if test data lie in a slightly…
Deep probabilistic forecasting is gaining attention in numerous applications ranging from weather prognosis, through electricity consumption estimation, to autonomous vehicle trajectory prediction. However, existing approaches focus on…
We consider finite-dimensional linear Gaussian Bayesian inverse problems with uncorrelated sensor measurements. In this setting, it is known that the expected information gain, quantified by the expected Kullback-Leibler divergence from the…
A new probabilistic post-processing method for wind vectors is presented in a distributional regression framework employing the bivariate Gaussian distribution. In contrast to previous studies all parameters of the distribution are…
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…
Extensive monitoring systems generate data that is usually compressed for network transmission. This compressed data might then be processed in the cloud for tasks such as anomaly detection. However, compression can potentially impair the…
Information generating functions have been used for generating various entropy and divergence measures. In the present work, we introduce quantile based relative information generating function and study its properties. The proposed…
Suppose we observe a geometrically ergodic semi-Markov process and have a parametric model for the transition distribution of the embedded Markov chain, for the conditional distribution of the inter-arrival times, or for both. The first two…
This paper illustrates novel methods for nonstationary time series modeling along with their applications to selected problems in neuroscience. These methods are semi-parametric in that inferences are derived by combining sequential…
We derive an information criterion to select a parametric model of complete-data distribution when only incomplete or partially observed data is available. Compared with AIC, our new criterion has an additional penalty term for missing…
We propose an adjusted likelihood ratio test of two-factor separability (Kronecker product structure) for unbalanced multivariate repeated measures data. Here we address the particular case where the within subject correlation is believed…
This work presents a comprehensive examination of the use of information theory for understanding Polarimetric Synthetic Aperture Radar (PolSAR) images by means of contrast measures that can be used as test statistics. Due to the phenomenon…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties. Indeed state-of-the-art approaches use the $L^2$ distance between kernel-based distribution…
The restricted polynomially-tilted pairwise interaction (RPPI) distribution gives a flexible model for compositional data. It is particularly well-suited to situations where some of the marginal distributions of the components of a…
Verifying probabilistic forecasts for extreme events is a highly active research area because popular media and public opinions are naturally focused on extreme events, and biased conclusions are readily made. In this context, classical…