Just want to say that I've worked this out fairly well, using Bayesian inference and an ad-hoc mechanism to deal with the observations that are strongly connected.
(Again, mathematical rigor is not so important here so long as the algorithm "behaves" well for most cases. )
Basically, for two pairs of tests, I know that if the first test contributes, say, a multiplier of 1.05 to the probability, then the second test will be "influenced" by about 1.025. I suppose I could simply divide the running product by the square root of the first test's multiplier, but I'm...
I don't suppose you have any suggestions as to how to "fudge" non-independent measurements, so they don't muck up an estimate too much? The vast majority of discussions I can find on the topic of non-independence just deal with the obvious cases analogous to drawing cards from a deck.
I mean each of the four colors has a different correlation to the diagnosis of foot fungus, and if one color is present the others are not. And since they're mutually exclusive they're obviously not "independent".
What about mutually exclusive tests?
What if I have mutually exclusive tests? Eg, I can test for red, green, blue, and yellow, and only one of those four can be true. How do I factor that into Bayesian inference?
If I were testing just red or not red and correlating that with my "gold...
One point about the scenario is that people taking these tests have a "high suspicion" of a positive -- probably in the neighborhood of 10-20% (though of course it will tend to vary perversely -- the more accurate & accessible the tests become the more likely they are to be applied to lower...
Like I said, I've got the 4 quantities true positive/false positive/true negative/false negative -- it's just a matter of figuring out how to use them.
Looking at Bayesian inference again, it seems like maybe I can work something out. I'll give it a shot.
Of course, the "population" is people referred for testing, so there's already a suspicion of the disorder that upsets the validity of any frequency measurement over the general population. But we can probably come up with an approximate frequency in the referred population. (It would be on...
(I asked this question in the Stack Exchange http://stats.stackexchange.com/questions/13014/how-to-combine-the-results-of-several-binary-tests" , but didn't get anything that was helpful to me.)
I'm a programmer (former EE) working on a medical application. My last stats course was in...