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Search Results: 1 - 10 of 23826 matches for " Paul Dupuis "
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The Impact of Criminal Code Training on Eyewitness Identification Accuracy  [PDF]
Michael Storozuk, Paul Dupuis
Psychology (PSYCH) , 2013, DOI: 10.4236/psych.2013.412149

Eyewitness identification accuracy of offenders (persons who committed a crime) is generally unreliable. In this study, we implemented a training approach to examine the impact of a brief criminal law training session on the identification accuracy of eyewitnesses viewing a simulated violent altercation between two males. Participants provided with prior training on how to appropriately apply specific criminal law definitions relevant to a violent altercation (assault and self-defense provisions) were more accurate in their identifications of the offender when compared to participants provided with irrelevant training (a riot and the unlawful assembly of a riot), and participants provided with no training, when observing the same violent altercation. Potential implications and limitations are discussed.

Splitting for Rare Event Simulation: A Large Deviation Approach to Design and Analysis
Thomas Dean,Paul Dupuis
Mathematics , 2007,
Abstract: Particle splitting methods are considered for the estimation of rare events. The probability of interest is that a Markov process first enters a set $B$ before another set $A$, and it is assumed that this probability satisfies a large deviation scaling. A notion of subsolution is defined for the related calculus of variations problem, and two main results are proved under mild conditions. The first is that the number of particles generated by the algorithm grows subexponentially if and only if a certain scalar multiple of the importance function is a subsolution. The second is that, under the same condition, the variance of the algorithm is characterized (asymptotically) in terms of the subsolution. The design of asymptotically optimal schemes is discussed, and numerical examples are presented.
Large Deviations for Multiscale Diffusions via Weak Convergence Methods
Paul Dupuis,Konstantinos Spiliopoulos
Mathematics , 2010, DOI: 10.1016/j.spa.2011.12.006
Abstract: We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to zero relative to the homogenization parameter. We use weak convergence methods which provide convenient representations for the action functional for all three regimes. Along the way we study weak limits of related controlled SDEs with fast oscillating coefficients and derive, in some cases, a control that nearly achieves the large deviations lower bound at the prelimit level. This control is useful for designing efficient importance sampling schemes for multiscale diffusions driven by small noise.
Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification
Kamaljit Chowdhary,Paul Dupuis
Mathematics , 2011,
Abstract: 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 obtain explicit bounds on standard performance measures (variances, exceedance probabilities) over families of distributions whose distance from a nominal distribution is measured by relative entropy. The evaluation of the risk-sensitive expectations is based on polynomial chaos expansions, which help keep the computational aspects tractable.
A differential game with constrained dynamics and viscosity solutions of a related HJB equation
Rami Atar,Paul Dupuis
Mathematics , 1999,
Abstract: This paper considers a formulation of a differential game with constrained dynamics, where one player selects the dynamics and the other selects the applicable cost. When the game is considered on a finite time horizon, its value satisfies an HJB equation with oblique Neumann boundary conditions. The first main result is uniqueness for viscosity solutions to this equation. This uniqueness is applied to obtain the second main result,i which is a unique characterization of the value function for a corresponding infinite time problem. The motivation comes from problems associated with queueing networks, where the games appear in several contexts, including a robust approach to network modeling and optimization and risk-sensitive control.
Correction. SDEs with oblique reflections on nonsmooth domains
Paul Dupuis,Hitoshi Ishii
Mathematics , 2008, DOI: 10.1214/07-AOP374
Abstract: Correction to The Annals of Probability 21 (1993) 554--580 [http://projecteuclid.org/euclid.aop/1176989415]
On the large deviation rate function for the empirical measures of reversible jump Markov processes
Paul Dupuis,Yufei Liu
Mathematics , 2013, DOI: 10.1214/13-AOP883
Abstract: The large deviations principle for the empirical measure for both continuous and discrete time Markov processes is well known. Various expressions are available for the rate function, but these expressions are usually as the solution to a variational problem, and in this sense not explicit. An interesting class of continuous time, reversible processes was identified in the original work of Donsker and Varadhan for which an explicit expression is possible. While this class includes many (reversible) processes of interest, it excludes the case of continuous time pure jump processes, such as a reversible finite state Markov chain. In this paper, we study the large deviations principle for the empirical measure of pure jump Markov processes and provide an explicit formula of the rate function under reversibility.
Large deviations and queueing networks: methods for rate function identification
Rami Atar,Paul Dupuis
Mathematics , 1998,
Abstract: This paper considers the problem of rate function identification for multidimensional queueing models with feedback. A set of techniques are introduced which allow this identification when the model possesses certain structural properties. The main tools used are representation formulas for exponential integrals, weak convergence methods, and the regularity properties of associated Skorokhod Problems. Two examples are treated as special cases of the general theory: the classical Jackson network and a model for processor sharing.
Dynamic importance sampling for uniformly recurrent markov chains
Paul Dupuis,Hui Wang
Mathematics , 2005, DOI: 10.1214/105051604000001016
Abstract: Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. In standard importance sampling schemes, the system is simulated using an a priori fixed change of measure suggested by a large deviation lower bound analysis. Recent work, however, has suggested that such schemes do not work well in many situations. In this paper we consider dynamic importance sampling in the setting of uniformly recurrent Markov chains. By ``dynamic'' we mean that in the course of a single simulation, the change of measure can depend on the outcome of the simulation up till that time. Based on a control-theoretic approach to large deviations, the existence of asymptotically optimal dynamic schemes is demonstrated in great generality. The implementation of the dynamic schemes is carried out with the help of a limiting Bellman equation. Numerical examples are presented to contrast the dynamic and standard schemes.
On the convergence from discrete to continuous time in an optimal stopping problem
Paul Dupuis,Hui Wang
Mathematics , 2005, DOI: 10.1214/105051605000000034
Abstract: We consider the problem of optimal stopping for a one-dimensional diffusion process. Two classes of admissible stopping times are considered. The first class consists of all nonanticipating stopping times that take values in [0,\infty], while the second class further restricts the set of allowed values to the discrete grid {nh:n=0,1,2,...,\infty} for some parameter h>0. The value functions for the two problems are denoted by V(x) and V^h(x), respectively. We identify the rate of convergence of V^h(x) to V(x) and the rate of convergence of the stopping regions, and provide simple formulas for the rate coefficients.
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