Related papers: A new criterion based on Kullback-Leibler informat…

Multi-dimensional distributions whose marginal distributions are uniform are called copulas. Among them, the one that satisfies given constraints on expectation and is closest to the independent distribution in the sense of Kullback-Leibler…

The analysis of observed time series from nonlinear systems is usually done by making a time-delay reconstruction to unfold the dynamics on a multi-dimensional state space. An important aspect of the analysis is the choice of the correct…

This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in…

Space-filling designs are important in computer experiments, which are critical for building a cheap surrogate model that adequately approximates an expensive computer code. Many design construction techniques in the existing literature are…

Meta-analytic methods tend to take all-or-nothing approaches to study-level heterogeneity, assuming all studies are heterogeneous or homogeneous, leading to inefficiency and/or bias in estimation and inference. In this paper, we develop a…

Small area estimation methods are used in surveys, where sample sizes are too small to get reliable direct estimates of parameters in some population domains. We consider design-based linear combinations of direct and synthetic estimators…

Designing experiments that systematically gather data from complex physical systems is central to accelerating scientific discovery. While Bayesian experimental design (BED) provides a principled, information-based framework that integrates…

To shed light on the fundamental problems posed by Dark Energy and Dark Matter, a large number of experiments have been performed and combined to constrain cosmological models. We propose a novel way of quantifying the information gained by…

Experimental design is crucial for inference where limitations in the data collection procedure are present due to cost or other restrictions. Optimal experimental designs determine parameters that in some appropriate sense make the data…

The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…

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…

For biological experiments aiming at calibrating models with unknown parameters, a good experimental design is crucial, especially for those subject to various constraints, such as financial limitations, time consumption and physical…

The Kullback-Leibler inequality is a way of comparing any two density matrices. A technique to set up the density matrix for a physical system is to use the maximum entropy principle, given the entropy as a functional of the density matrix,…

We analyze a contrasting dynamical behavior of Gibbs-Shannon and conditional Kullback-Leibler entropies, induced by time-evolution of continuous probability distributions. The question of predominantly purpose-dependent entropy definition…

Modern machine learning approaches excel in static settings where a large amount of i.i.d. training data are available for a given task. In a dynamic environment, though, an intelligent agent needs to be able to transfer knowledge and…

Physics, chemistry, biology or finance are just some examples out of the many fields where complex Ornstein-Uhlenbeck (OU) processes have various applications in statistical modelling. They play role e.g. in the description of the motion of…

Obtaining an accurate estimate of the underlying covariance matrix from finite sample size data is challenging due to sample size noise. In recent years, sophisticated covariance-cleaning techniques based on random matrix theory have been…

Group sequential designs enable interim analyses and potential early stopping for efficacy or futility. While these adaptations improve trial efficiency and ethical considerations, they also introduce bias into the adapted analyses. We…

The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…

In data assimilation, the model may be subject to uncertainties and errors. The weak-constraint data assimilation framework enables incorporating model uncertainty in the dynamics of the governing equations. We propose a new framework for…