In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level, it suffices to continue sampling until the sample sum is no less than a certain bound and then take the average of samples as an estimate for the mean of th...

Problem: Given a uniform random variable U, generate a random variable X having a prescribed distribution function F X) (⋅. We previously discussed the inversion method. While inversion is a very general method, it may be computationally expensive. In particular, computing 1 X F () − ⋅ may have to be implemented via a numerical root-finding method in many cases. Therefore, we will now describe ...

In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based on an analysis of electromagnetic scattering and the behavior of the fundamental solution. It is applicable to a few incident fields and needs only to compute...

Monte Carlo techniques are often the only practical way to evaluate difficult integrals or to sample random variables governed by complicated probability density functions. Here we describe an assortment of methods for sampling some commonly occurring probability density functions. Most Monte Carlo sampling or integration techniques assume a " random number generator, " which generates uniform ...

A novel multilevel algorithm is presented for implementing the widely used linear sampling method in inverse obstacle scattering problems. The new method is shown to possess asymptotically optimal computational complexity. For an n×n sampling mesh in R2 or an n×n×n sampling mesh in R3, the proposed algorithm requires one to solve only O(nN−1) far-field equations for a RN problem (N=2,3), and th...

Probabilistic formulation of inverse problems leads to the definition of a probability distribution in the model space. This probability distribution combines a priori information with new information obtained by measuring some observable parameters (data). As, in the general case, the theory linking data with model parameters is nonlinear, the a posteriori probability in the model space may no...

In many practical problems in applied sciences, the features of most interest cannot be observed directly, but have to be inferred from other, observable quantities. In particular, many important data acquisition devices provide an access to the measurement of the partial derivatives of a feature of interest rather than sensing its values in a direct way. In this case, the feature has to be rec...

Implicit sampling is a Monte Carlo (MC) method that focuses the computational effort on the region of high probability by first locating this region via numerical optimization and then solving random algebraic equations to explore it. Implicit sampling has been shown to be efficient in online state estimation and filtering (data assimilation) problems; we use it here to estimate a diffusion coe...

Within the online media universe there are many underlying communities. These may be defined, for example, through politics, location, health, occupation, extracurricular interests or retail habits. Government departments, charities and commercial organisations can benefit greatly from insights about the structure of these communities; the move to customer-centered practices requires knowledge ...

We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a polynomial approximation scheme using Chebyshev polynomials, Chebyshev grids, and low rank function approximation. Numerical experiments demonstrate that our ...