Related papers: Solution to Banff 2 Challenge Based on Likelihood …
The likelihood ratio is a crucial quantity for statistical inference in science that enables hypothesis testing, construction of confidence intervals, reweighting of distributions, and more. Many modern scientific applications, however,…
This paper is devoted to the complexity of the Boolean satisfiability problem. We consider a version of this problem, where the Boolean formula is specified in the conjunctive normal form. We prove an unexpected result that the…
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
We give a definition for Obstacle Problems with measure data and general obstacles. For such problems we prove existence and uniqueness of solutions and consistency with the classical theory of Variational Inequalities. Continuous…
A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large-dimensional, nonparametric double cone alternative. For example, the test against a constant function uses the…
In this work we consider the numerical resolution of the bilateral obstacle optimal control problem given in Bergounioux et al. Where the main feature of this problem is that the control and the obstacle are the same.
Suppose an interval is put on a horizontal line with random roughness. With probability one it is supported at two points, one from the left, and another from the right from its center. We compute probability distribution of support points…
Many scientific questions rely on determining whether two sequences of event times are associated. This article introduces a likelihood ratio test which can be parameterised in several ways to detect different forms of dependence. A common…
In this article we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy approach. Unlike standard procedures that require equating at zero the score function of the maximum-likelihood…
In this paper, we will solve the Reifenberg Plateau Problem in Hilbert space.
Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness,…
We consider a system of seminlinear parabolic variational inequalities with time-dependent convex obstacles. We prove the existence and uniqueness of its solution. We also provide a stochastic representation of the solution and show that it…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
We provide infinitely many solutions of a Dirichlet problem on balls.
The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the…
We treat success runs of independent identically distributed Bernoulli trials (with success parameter $p$) distributed according to the Type II binomial distribution of order $k$. However, the success runs are separated by a gap $g\ge1$ (a…
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…
We propose a new approximate method for counting the number of the solutions for constraint satisfaction problem (CSP). The method derives from the partition function based on introducing the free energy and capturing the relationship of…
We study approximation algorithms for the forest cover and bounded forest cover problems. A probabilistic $2+\epsilon$ approximation algorithm for the forest cover problem is given using the method of dual fitting. A deterministic algorithm…
A detailed presentation of hypothesis testing is given. The "look elsewhere" effect is illustrated, and a treatment of the trials factor is proposed with the introduction of hypothesis hypertests. An example of such a hypertest is…