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Book review: Darwinia
Reviewed: Friday, August 11, 2006

Summer reading: Spin
Reviewed: Saturday, August 5, 2006

Runner
Reviewed: Tuesday, July 18, 2006

the Omnivoire's Delimma
Reviewed: Wednesday, July 12, 2006

the Golem's Eye
Reviewed: Wednesday, May 31, 2006





tinderbox

Development of sampling plans by using sequential selection
C. T. Fan and Mervin E. Muller and Ivan Rezucha, 1962
Monday, July 11, 2005

When doing any statistical study, we start with a population (sample space), take measurements and then go from there. For example, suppose we want to learn something about the population of movie fans that have seen the Fantastic Four. For the sake of this example, assume that we further want to take a stratified sample based on the row in which the fans were sitting (maybe people closer to the screen enjoyed the movie more). The obvious way to do this is to wait until everyone is seated and then look in the rows and make selections. This, however, is a lot of work and means that you have to interrupt the picture. This ancient (1962!) paper by Fan et. al. demonstrates numerous ways to sample sequentially (item by item) without waiting for the entire group of people to arrive. Some methods are clever statistical tricks made more practical by the advent of digital computers. Others and really quite marvelous. My favorite, for example, is to turn the question of which members of the population do we want into how many members should we skip between samples. This lets us select at random an expected number of items without replacement from the population even when we don't know up front how big the population is! I won't go into the math but I do think it's a very insight. I love how problems can become solvable when viewed in the correct light.


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