Last week I defined balanced sampling and I discussed the first part of the two-part cube method for obtaining a balanced sample. In that post we identified samples with vertices of the unit cube, and we discussed the flight phase of the sampling algorithm, which converges to a point in the cube satisfying the given balance equations and inclusion probabilities. We stated that, in many cases, there are no samples which satisfy the balance equation and the flight phase won’t be able to converge to a vertex. This week I’ll describe the landing phase, the second part of the cube method which we use to obtain the final sample.
When my coworker reminded me yesterday that it was Pi Day, she also reminded me of Buffon’s Needle. This is a classic problem in probability, named after 18th century French author Georges-Louis Leclerc, Comte du Buffon. Buffon was an aristocratic scientist who once annoyed Thomas Jefferson by claiming that America was for wimps.
I recently read the chapter in Yves Tillé’s Sampling Algorithms about balanced sampling and I thought it would be useful to summarize what I’ve learned. Suppose you want to survey a population about which some data is already known. Specifically, there are auxilliary data points which are known for every individual in the population. A balanced sample is one in which the sample-based estimate for these auxilliary data conform to the true values.