Sampling is the process of collecting, analysing, and interpreting data in order to test hypotheses and provide needed information for intelligent decisions. Sampling is an attractive alternative to complete enumeration. Instead of measuring or recording all members of a population of interest, one concentrates on a representative proportion, objectively selected, to estimate desired characteri...

Monte Carlo simulation methods apply a random sampling and modifications can be made of this method is by using variance reduction techniques (VRT). VRT objective is to reduce the variance due to Monte Carlo methods become more accurate with a variance approaching zero and the number of samples approaches infinity, which is not practical in the real situation (Chen, 2004). These techniques are ...

A hierarchical random graph (HRG) model combined with a maximum likelihood approach and Markov Chain Monte Carlo algorithm can not only be used to quantitatively describe the organization of many real networks, but also predict missing connections in partly known networks high accuracy. However, computational cost is very large when graphs are sampled by (MCMC), so that graphs, which characteri...

We consider statistical aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. For a LS problem with input data (X,Y ) ∈ Rn×p × R, where n and p are both large and n p, sketching algorithms use a “sketching matrix,” S ∈ Rr×n, where r n, e.g., a matrix representing the process of random sampling or random projection. Then, rather than solving the LS pro...