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A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations of functions of the corresponding output variables. The advantage of the proposed method over the existing methods is that it preserves the exact form of the joint distribution on the input variables. The asymptotic distribution of the new estimator is derived. Asymptotically, the variance of the estimator using the proposed method is less than that obtained using the simple random sampling, with the degree of variance reduction depending on the degree of additivity in the function being integrated. This technique is applied to a practical example related to the performance of the river flood inundation model., Comment: 27 pages, 4 figures

Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling problem with relatively simple univariate regressions. In this paper, we begin to characterize the stationary distributions of iterative imputations and their statistical properties. More precisely, when the conditional models are compatible (defined in the text), we give a set of sufficient conditions under which the imputation distribution converges in total variation to the posterior distribution of a Bayesian model. When the conditional models are incompatible but are valid, we show that the combined imputation estimator is consistent., Comment: 38 pages and 5 figures