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Simulated annealing - moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions - has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers.…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
The Shannon sampling theorem for bandlimited wide sense stationary random processes was established in 1957, which and its extensions to various random processes have been widely studied since then. However, truncation of the Shannon series…
This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…
In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent results have demonstrated that appropriate reversible and…
We introduce a consistent estimator of the extreme value index under random truncation based on a single sample fraction of top observations from truncated and truncation data. We establish the asymptotic normality of the proposed estimator…
One aspect of Poisson approximation is that the support of the random variable of interest is often finite while the support of the Poisson distribution is not. In this paper we will remedy this by examining truncated negative binomial (of…
The problems of optimal recovery of unbounded operators are studied. Optimality means the highest possible accuracy and the minimal amount of discrete information involved. It is established that the truncation method, when certain…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
The truncation and approximation errors for the set of numerical solutions computed by methods based on the algorithms of different structure are calculated and analyzed for the case of the two-dimensional steady inviscid compressible flow.…
The article is devoted to the resampling approach application to the reliability problems. This approach to reliability problems was first proposed by Ivnitsky (1967). Resampling is intensive statistical computer method, which is…
Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not…
We prove that a class of randomized integration methods, including averages based on $(t,d)$-sequences, Latin hypercube sampling, Frolov points as well as Cranley-Patterson rotations, consistently estimates expectations of integrable…
Stochastic programming models can lead to very large-scale optimization problems for which it may be impossible to enumerate all possible scenarios. In such cases, one adopts a sampling-based solution methodology in which case the…
In this paper, we have established a new framework of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hyper-geometrical, and bounded variables. We have derived explicit…
Clipping or saturation in audio signals is a very common problem in signal processing, for which, in the severe case, there is still no satisfactory solution. In such case, there is a tremendous loss of information, and traditional methods…
Stochastic iterative methods are useful in a variety of large-scale numerical linear algebraic, machine learning, and statistical problems, in part due to their low-memory footprint. They are frequently used in a variety of applications,…
The Harmonic Balance method provides a heuristic approach for finding truncated Fourier series as an approximation to the periodic solutions of ordinary differential equations. Another natural way for obtaining these type of approximations…
Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…
This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…