Related papers: On Method of Statistical Differentials
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many…
Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows…
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.
The existence and uniqueness of the stationary distribution of the numerical solution generated by the stochastic theta method is studied. When the parameter theta takes different values, the requirements on the drift and diffusion…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…
In this paper we improve some existing results concerning the approximation of the distribution of extremes of a 1-dependent and stationary sequence of random variables. We enlarge the range of applicability and improve the approximation…
The coefficient of variation is a useful indicator for comparing the spread of values between dataset with different units or widely different means. In this paper we address the problem of investigating the equality of the coefficients of…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the…
We study one-dimensional nearest neighbour random walk in site-random environment. We establish precise (sharp) large deviations in the so-called ballistic regime, when the random walk drifts to the right with linear speed. In the…
Using methods of statistical mechanics, we analyse the effect of outliers on the supervised learning of a classification problem. The learning strategy aims at selecting informative examples and discarding outliers. We compare two…
We review the application of Statistical Mechanics methods to the study of online learning of a drifting concept in the limit of large systems. The model where a feed-forward network learns from examples generated by a time dependent…
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…
Stein's method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric Binomial distribution. Under appropriate smoothness properties of the summands, the same order of accuracy as in the…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…