Related papers: Numerical Estimation of Limiting Large-Deviation R…
Rare events play a key role in many applications and numerous algorithms have been proposed for estimating the probability of a rare event. However, relatively little is known on how to quantify the sensitivity of the probability with…
In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
This paper considers the classical problem of sampling with Monte Carlo methods a target rare event distribution defined by a score function that is very expensive to compute. We assume we can build using evaluations of the true score, an…
Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
In the last fifteen the subset sampling method has often been used in reliability problems as a tool for calculating small probabilities. This method is extrapolating from an initial Monte Carlo estimate for the probability content of a…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
Supervised classifying of biological samples based on genetic information, (e.g. gene expression profiles) is an important problem in biostatistics. In order to find both accurate and interpretable classification rules variable selection is…
In recent years, bootstrap methods have drawn attention for their ability to approximate the laws of "max statistics" in high-dimensional problems. A leading example of such a statistic is the coordinate-wise maximum of a sample average of…
Importance sampling (IS) is a variance reduction method for simulating rare events. A recent paper by Dupuis, Wang and Sezer (Ann. App. Probab. 17(4):1306- 1346, 2007) exploits connections between IS and stochastic games and optimal control…
We establish a large deviation principle for the trajectories of Wiener processes subject to random resets to the origin occurring according to a Poisson process. In addition to the pathwise large deviation principle, we identify the rate…
The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
We calculate the large deviations for the length of the longest alternating subsequence and for the length of the longest increasing subsequence in a uniformly random permutation that avoids a pattern of length three. We treat all six…
In this paper, we consider the problem of numerical investigation of the counting statistics for a class of one-dimensional systems. Importance sampling, the cornerstone technique usually implemented for such problems, critically hinges on…
We study the greedy independent set algorithm on sparse Erd\H{o}s-R\'enyi random graphs ${\mathcal G}(n,c/n)$. This range of $p$ is of interest due to the threshold at $c=e$, beyond which it appears that greedy algorithms are affected by a…
We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…
In analyzing big data for finite population inference, it is critical to adjust for the selection bias in the big data. In this paper, we propose two methods of reducing the selection bias associated with the big data sample. The first…
In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and…
The ubiquitous time-delay estimation (TDE) problem becomes nontrivial when sensors are non-co-located and communication between them is limited. Building on the recently proposed "extremum encoding" compression-estimation scheme, we address…