Why balloons are better than balls (in urn schemes)

November 18, 2011

(This article was first published on BioStatMatt » R, and kindly contributed to R-bloggers)

The below is taken from a work in progress:

The Polya urn is a heuristic associated with Dirichlet process mixtures. We present the scheme in a modified format, using balloons instead of balls, where the probability of drawing a balloon from the urn is proportional to its volume. Balloons are preferred because their volume may be adjusted by fractional amounts, whereas a ball count may be adjusted only in whole amounts.

The Polya urn initially contains n uniquely colored baloons, each filled with the same volume of air. At each draw, a single baloon is selected at random from the collection of balloons within the urn, and its color is recorded. If the recorded color had been observed in previous draws, the baloon is inflated by an amount equal to its original volume. Finally, the balloon is returned to the urn. Hence, a balloon drawn from the Polya urn is more likely be observed in subsequent draws. ‘The rich get richer’ is a fitting mnemonic for the Polya urn scheme.

To leave a comment for the author, please follow the link and comment on their blog: BioStatMatt » R.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, 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.

Search R-bloggers


Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)