Today the junior editor has decided to design his remarks in the form of a math question. I do this for two reasons, firstly to address the many questions about “Bayesian Statistics” and secondly to point out some irony found across the country.
Ever been to a college campus? If so, you have probably heard the word “diversity” once or twice. In the wake of such a polarizing national election I thought it would be a good idea to take a deeper look at the “diversity” that universities are so proud of.
Let’s create a hypothetical university. Let’s just say this university is located in
(Aside: Isn’t diversity great!)
One day, as I am pulling into the parking lot of this hypothetical university in
Now for the bipartisan question; what is the exact probability that the student driving that car is a medical student? To answer this question you will utilize Bayesian statistical methods (see Wikipedia) whether you realize it or not. Oh, by the way, let me tell you one last integral piece of the problem; we have obtained some ‘prior’ information that there are 600 medical students at the university.
The first person to respond with the correct answer (to the 5th decimal) will receive a gift that will make all your friends jealous…..I promise.
13 comments:
I say the probability is 1, because non-medical students don't park in your lot.
.99010... booyeah?
Don't reverse the above numbers unless you want the answer...
The answer is 0. It cannot be displayed to the 5th decimal because there are not sufficient significant digits in the inputs to the problem. (and someone beat me to the answer)
(...furthermore, because I lost) Also...I have to ask: why bayesian methods? It is not respected by true statisticians.
In the old days, Bayesian methods at least had the virtue of being mathematically clean. Nowadays, they all seem to be computed using Markov chain Monte Carlo, which means that, not only can you not realistically evaluate the statistical properties of the method, you can't even be sure it's converged, just adding one more item to the list of unverifiable assumptions.
Bayesian inference is a coherent mathematical theory but I wouldn't trust it in scientific applications. Subjective prior distributions don't inspire confidence, and there's no good objective principle for choosing a noninformative prior (even if that concept were mathematically defined, which it's not). Where do prior distributions come from, anyway? I don't trust them and I see no reason to recommend that other people do, just so that I can have the warm feeling of philosophical coherence.
Bayesianism assumes: (a) Either a weak or uniform prior, in which case why bother?, (b) Or a strong prior, in which case why collect new data?, (c) Or more realistically, something in between, in which case Bayesianism always seems to duck the issue.
Wow, them's fightin words.
I will not comment further here, but know that the arguments my brother-in-law has given (though they are important to consider if you are ever to assess a situation under a Baysian paradigm) are not new. In fact, they are old, tired, and played--and we will discuss them at length mano-a-mano
I'm sorry, you are wrong.
You have made an egregious error. You have assumed there are only two parties. Simply stating you are too poor to vote Republican means you either a) did not vote at all or b) did not vote Republican. The solution space is definitely not a single population. Since you asked for "exact", I am ashamed of you all. Since Bayesian analysis requires you to know the P(voting for X|med student), and you don't even know what X is, how on earth can you answer the question?
This is an embarrassment. Think of an analogous problem: A guy has a bumper sticker that says "Whoppers are nasty!" and you pose a question stating that 1% of the population is a medical student, but that 99% of med students eat at McDonalds, and 90% of non-med students eat at McDonalds.
And we are supposed to do an exact Bayesian analysis of whether the driver of the car is from med school from that information?
Is this what they taught you in Statistics graduate school????
Which school did you go to? Just curious, for future reference (you know, like accepting students to my lab, that sort of thing...)
I cracked a book that has not been opened since 1999 for this one. A "book". One of those things with paper in them, that Script Kiddies cannot de-edit overnight.
I like donuts
You guys are hilarious.
Assuming that Ryan's reversed answer above is the one you were looking for, I'm feeling pretty proud of myself--that's the answer I got, and I haven't studied statistics of any sort (come to think of it, I haven't studied math of any sort) since High School...
The only person too poor to vote Republican, who parks in a med school parking lot is not a student-they don't realize how poor they are because they live on loans, and expect to make mega bucks after graduating---I think it is either a person on a fellowship and trying to pay back loans while living on the fellowship; or a junior level faculty member who doesn't have faculty parking rights. Therefore, forget Bayesian, there is not information because you gave no numbers for fellowship and assistant level professors.
The only person too poor to vote Republican, who parks in a med school parking lot is not a student-they don't realize how poor they are because they live on loans, and expect to make mega bucks after graduating---I think it is either a person on a fellowship and trying to pay back loans while living on the fellowship; or a junior level faculty member who doesn't have faculty parking rights. Therefore, forget Bayesian, there is not information because you gave no numbers for fellowship and assistant level professors.
Is this just a long of way of again whining about how little medical doctors get paid?
Post a Comment