Friday, October 23, 2009

Frequentist vs Bayesian

Layfolks hoping to sound sophisticated often ask their statistician aquaintences the following buzz-question: "Are you a frequentist or a bayesian?" I have always been terrified by this question. As an imposter in the field of statistics, I am terrified by almost any question having to do with data.

Suppose I want to know the average height of people in the US. This average I will call hpop. To estimate hpop, I randomly choose 100 people and take their heights, and compute the average height. Call this sample average hsamp. For most people and I, saying "hpop is probably somewhere near hsamp" is good enough. But a statistician wants to know exactly how close hpop is to hsamp, and with what probability.

At this point, a frequentist (not to be confused with a Freakwentest), creates a "confidence interval." This involves estimating the variance of heights, and then applying some theoretical crap having to do with "normal" distributions to come up with a minimum number, say 5.5 ft, and a maximum number, say 5.7 feet, such that we can be "95% confident" that hpop is between 5.5 and 5.7 feet.

A bayesian, on the other hand, does something weird and ends up with a statement like "the probability that hpop is between 5.5 and 5.7 is approximately 0.95." This sounds a lot like being 95% confident that hpop is between 5.5 and 5.7, but it's not.

Someday I will have a better answer for the question, but until then I am an opportunist, picking between frequentist or bayesian methods on the basis of convenience instead of ideology.

4 Comments:

Anonymous goodbadi said...

Me, too!

12:19 PM  
Anonymous mountaineer said...

I'll guess: the frequentist's analysis is the chi-square test.

12:46 PM  
Anonymous Anonymous said...

I just know I'm short

8:09 AM  
Blogger Alex Zorach said...

I don't like it when people talk about frequentist or bayesian perspectives as if they were two competing fundamentalist religions.

They're different ways of looking at things, that's all. Often, in certain situations, one way may make a lot more sense or be a lot more practical than the other.

2:46 PM  

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