Density biased sampling (DBS) has been proposed to address the limitations of Uniform sampling, by producing the desired probability distribution in the sample. The ease of producing a random sample depends on the available mechanism for accessing the elements of the dataset. Existing DBS algorithms perform sampling over flat files. In this paper, we develop a new method that exploits spatial i...

We survey some randomized search methods for global optimization that are based on sampling from an underlying probability distribution “model” on the solution space. In this approach, the probability model is updated iteratively after evaluating the performance of the samples at each iteration. Such model-based methods include estimation of distribution algorithms (EDAs), the cross-entropy met...

We consider the problem of low canonical polyadic (CP) rank tensor completion. A completion is a tensor whose entries agree with the observed entries and its rank matches the given CP rank. We analyze the manifold structure corresponding to the tensors with the given rank and define a set of polynomials based on the sampling pattern and CP decomposition. Then, we show that finite completability...

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form γ = (〈ui, vj〉)i,j=1, where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of α = m n , where the previous vectors are sampled according to the Haar measure in the unit sphere o...

Free-energy landscape is an important quantity to study large-scale motions of a biomolecular system because it maps possible pathways for the motions. When the landscape consists of thermodynamically stable states (low-energy basins), which are connected by narrow conformational pathways (i.e., bottlenecks), the narrowness slows the inter-basin round trips in conformational sampling. This resu...

This paper proposes an envelope rejection method for computer sampling from the negative binomial distribution, with index parameter α and probability parameter p, based on a simple probability distribution inequality. Comparative timings with existing methods of generating NB variates show that the proposed method is comparable or faster when α is not too large (α < 11), and it is fastest for ...

Multi-phased designs and biased sampling designs are two of the well recognized approaches to enhance study efficiency. In this paper, we propose a new and cost-effective sampling design, the two-phase probability dependent sampling design (PDS), for studies with a continuous outcome. This design will enable investigators to make efficient use of resources by targeting more informative subjects...

Density Biased Sampling (DBS) has been proposed to address the limitations of Uniform sampling, by producing the desired probability distribution in the sample. The ease of producing a random sample depends on the available mechanism for accessing the elements of the dataset. Existing DBS algorithms perform sampling over flat files. In this paper we develop a new method that exploits spatial in...

the computation of structural failure probability is vital importance in the reliability analysis and may be carried out on the basis of the first-order reliability method using various mathematical iterative approaches such as hasofer-lind and rackwitz-fiessler (hl-rf). this method may not converge in complicated problems and nonlinear limit state functions, which usually shows itself in the f...

In the thesis, high order Parzen windows are studied for understanding some algorithms in learning theory and randomized sampling in multivariate approximation. Our ideas are from Parzen window method for density estimation and sampling theory. First, we define basic window functions to construct our high order Parzen windows. We derived learning rates for the least-square regression and densit...