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Density estimation with quadratic loss: a confidence intervals method

Pierre Alquier (2008)

ESAIM: Probability and Statistics

We propose a feature selection method for density estimation with quadratic loss. This method relies on the study of unidimensional approximation models and on the definition of confidence regions for the density thanks to these models. It is quite general and includes cases of interest like detection of relevant wavelets coefficients or selection of support vectors in SVM. In the general case, we prove that every selected feature actually improves the performance of the estimator. In the case...

Diffusion Monte Carlo method: Numerical Analysis in a Simple Case

Mohamed El Makrini, Benjamin Jourdain, Tony Lelièvre (2007)

ESAIM: Mathematical Modelling and Numerical Analysis


The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a fixed number of random walkers evolving according to a stochastic differential equation discretized in time. We allow stochastic reconfigurations of the walkers to reduce the discrepancy between the weights that they carry. On a simple one-dimensional example, we prove...

Directed forests with application to algorithms related to Markov chains

Piotr Pokarowski (1999)

Applicationes Mathematicae

This paper is devoted to computational problems related to Markov chains (MC) on a finite state space. We present formulas and bounds for characteristics of MCs using directed forest expansions given by the Matrix Tree Theorem. These results are applied to analysis of direct methods for solving systems of linear equations, aggregation algorithms for nearly completely decomposable MCs and the Markov chain Monte Carlo procedures.

Directional quantile regression in Octave (and MATLAB)

Pavel Boček, Miroslav Šiman (2016)

Kybernetika

Although many words have been written about two recent directional (regression) quantile concepts, their applications, and the algorithms for computing associated (regression) quantile regions, their software implementation is still not widely available, which, of course, severely hinders the dissemination of both methods. Wanting to partly fill in the gap here, we provide all the codes needed for computing and plotting the multivariate (regression) quantile regions in Octave and MATLAB, describe...

Directional quantile regression in R

Pavel Boček, Miroslav Šiman (2017)

Kybernetika

Recently, the eminently popular standard quantile regression has been generalized to the multiple-output regression setup by means of directional regression quantiles in two rather interrelated ways. Unfortunately, they lead to complicated optimization problems involving parametric programming, and this may be the main obstacle standing in the way of their wide dissemination. The presented R package modQR is intended to address this issue. It originates as a quite faithful translation of the authors'...

Discrete approximations of generalized RBSDE with random terminal time

Katarzyna Jańczak-Borkowska (2012)

Discussiones Mathematicae Probability and Statistics

The convergence of discrete approximations of generalized reflected backward stochastic differential equations with random terminal time in a general convex domain is studied. Applications to investigation obstacle elliptic problem with Neumann boundary condition for partial differential equations are given.

Discrete Approximations of Strong Solutions of Reflecting SDEs with Discontinuous Coefficients

Alina Semrau (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We study L p convergence for the Euler scheme for stochastic differential equations reflecting on the boundary of a general convex domain D ⊆ ℝd. We assume that the equation has the pathwise uniqueness property and its coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. In the case D=[0,∞) new sufficient conditions ensuring pathwise uniqueness for equations with possibly discontinuous coefficients are given.

Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification

Kamaljit Chowdhary, Paul Dupuis (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the system when the distributions of some variables are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all.The main tool used is the duality between risk-sensitive integrals and relative entropy, and we...

Do Demographic and Disease Structures Affect the Recurrence of Epidemics ?

A. Castellazzo, A. Mauro, C. Volpe, E. Venturino (2012)

Mathematical Modelling of Natural Phenomena

In this paper we present an epidemic model affecting an age-structured population. We show by numerical simulations that this demographic structure can induce persistent oscillations in the epidemic. The model is then extended to encompass a stage-structured disease within an age-dependent population. In this case as well, persistent oscillations are observed in the infected as well as in the whole population.

Doubly reflected BSDEs with call protection and their approximation

Jean-François Chassagneux, Stéphane Crépey (2014)

ESAIM: Probability and Statistics

We study the numerical approximation of doubly reflected backward stochastic differential equations with intermittent upper barrier (RIBSDEs). These denote reflected BSDEs in which the upper barrier is only active on certain random time intervals. From the point of view of financial interpretation, RIBSDEs arise as pricing equations of game options with constrained callability. In a Markovian set-up we prove a convergence rate for a time-discretization scheme by simulation to an RIBSDE. We also...

Dyadic diaphony of digital sequences

Friedrich Pillichshammer (2007)

Journal de Théorie des Nombres de Bordeaux

The dyadic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this paper we give formulae for the dyadic diaphony of digital ( 0 , s ) -sequences over ℤ 2 , s = 1 , 2 . These formulae show that for fixed s ∈ { 1 , 2 } , the dyadic diaphony has the same values for any digital ( 0 , s ) -sequence. For s = 1 , it follows that the dyadic diaphony and the diaphony of special digital ( 0 , 1 ) -sequences are up to a constant the same. We give the exact asymptotic order of the dyadic diaphony of digital...

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