# Stratified Random Sampling for Dependent Inputs

## TL;DR

This paper introduces a stratified random sampling method for dependent variables that preserves the joint distribution and reduces variance in estimations, demonstrated through a flood model example.

## Contribution

It presents a novel stratified sampling approach for dependent inputs that maintains the joint distribution and improves estimation efficiency.

## Key findings

- Variance of the estimator is reduced compared to simple random sampling.
- The method preserves the exact joint distribution of dependent variables.
- Application to flood inundation model demonstrates practical effectiveness.

## Abstract

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.