Saturday, March 20, 2010

Odds Are, It's Wrong

During the past century...a mutant form of math has deflected science’s heart from the modes of calculation that had long served so faithfully. To find out more about this mutant, read more here.

1 comment:

Robert said...

This article could have been a rehash of a recent meeting I attended with the National Science Foundation on Uncertainty in Manufacturing and Machining. The attendees effectively arranged themselves into frequentists and Bayesians.

I found the comments after the article insightful for many reasons. One that I found especially interesting was the following:
"The example in box 4 illustrates yet another problem. It concludes with 'So if any single player’s test is positive, the chances that he really is a user are 50 percent, since an equal number of users and nonusers test positive.' A single player is not a random variable. In the statistics class that I teach, I flip a coin onto the floor and ask my students 'What is the probability that I got heads?' They usually answer '50%.' So I look down at the coin. If it is heads, I answer back 'No, it is 100%.' Probabilities should be applied to experimental procedures, not individual outcomes." [name removed] Mar. 18, 2010 at 12:44pm

Am I reading this correctly? He tosses the coin, doesn’t reveal the outcome, and asks the class to guess the likelihood of heads. Then he reveals the outcome. It seems odd to me that a person who teaches statistics doesn’t understand that until the outcome of the coin is revealed, the state of knowledge about the outcome being heads is still just as uncertain as before the coin was tossed. It's not until we "know" something that probabilities are resolved into certainties. Isn't this almost equivalent to declaring how much oil is in the ground within a specific reserve? The actual volume was set by nature millions of years earlier. Essentially, it’s an individual outcome that has occurred. But until we can account for every last molecule, the best we can say is that the volume falls within a range with assigned probabilities.