You are not comparing estimates of the population proportion. Giovanni
> Date: Tue, 05 Dec 2006 17:08:27 -0500 > From: "Doran, Harold" <[EMAIL PROTECTED]> > Sender: [EMAIL PROTECTED] > Precedence: list > Thread-topic: Comparing posterior and likelihood estimates for proportions > (off > topic) > Thread-index: AccYuQPSLwIrLya5T4ivem8lVU99aQ== > > This question is slightly off topic, but I'll use R to try and make it > as relevant as possible. I'm working on a problem where I want to > compare estimates from a posterior distribution with a uniform prior > with those obtained from a frequentist approach. Under these conditions > the estimates should agree. > > Specifically, I am asking the question, "What is the probability that > the true proportion of students passing a test is 50% when the observed > proportion for that school is only 38%?" > > For my example, there are 100 students in the school and 38 of them > passed an exam. For conjugacy, if we choose a beta prior, then posterior > in this case is also a beta distribution. Now, I believe the a and b > parameters for a beta with a uniform prior is a=1 and b=1, or 1/(1+1) > > Here is my R code for the posterior with a flat prior > > n <- 100 # Total number of individuals > y <- 38 # Number of successes > a <- 1 # Parameter 1 for Beta prior > b <- 1 # Parameter 2 for Beta prior > theta <- .38 # Proportion passing > > pbeta(.50, a + y, b+n-y, lower.tail=FALSE) > [1] 0.008253 > > Now, the binomial distribution gives > > > dbinom(50, 100, .38) > [1] 0.0040984 > > Obviously, the results don't agree. So, I'm wondering if I have > > A) made a computational error > B) have an error in my assumption that the results should agree in this > case > > Thanks for any reactions > Harold > > Windows XP > > version > _ > platform i386-pc-mingw32 > arch i386 > os mingw32 > system i386, mingw32 > status > major 2 > minor 4.0 > year 2006 > month 10 > day 03 > svn rev 39566 > language R > version.string R version 2.4.0 (2006-10-03) > > > > > > > > [[alternative HTML version deleted]] > > ______________________________________________ > [email protected] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > -- Giovanni Petris <[EMAIL PROTECTED]> Associate Professor Department of Mathematical Sciences University of Arkansas - Fayetteville, AR 72701 Ph: (479) 575-6324, 575-8630 (fax) http://definetti.uark.edu/~gpetris/ ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
