Stratified sampling

June 9, 2010
By

(This article was first published on Xi'an's Og » R, and kindly contributed to R-bloggers)

The recently arXived paper of Goldstein, Rinott and Scarsini studies the impact of refining a partition on the precision of a stratified maximising/integration Monte Carlo approach. Quite naturally, if the partition gets improved, simulating points in each set of the partition can only improve the quality of the approximation, whether the problem is in maximising or in integrating. However, the authors include an interesting (formal) counterexample where the stratification leads to a higher L1 (if not L2) error. (And they include extensions of more classical results to cases when the function is observed with errors or contains missing data.) The difficulty I have with stratification in practice is that it is really difficult to come up with a partition which is relevant for the problem at hand and whose partition weights are known exactly… Reading this nice mathematical paper also led me to ponder the possibility of doing unbiased maximisation, while wondering if stratification was eventually compelling for maximisation, since only one set in the partition is of interest. Eliminating sets from the simulation would thus be leading to higher efficiency, if this was feasible.


Filed under: R, Statistics Tagged: maximisation, Monte Carlo methods, simulation, stratification

To leave a comment for the author, please follow the link and comment on his blog: Xi'an's Og » R.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Tags: , , , , ,

Comments are closed.