[R] Comparing posterior and likelihood estimates for proportions (off topic)

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[R] Comparing posterior and likelihood estimates for proportions (off topic)

 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]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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Re: [R] Comparing posterior and likelihood estimates for proportions (off topic)

 You are not comparing estimates of the population proportion. Giovanni > Date: Tue, 05 Dec 2006 17:08:27 -0500 > From: "Doran, Harold" <[hidden email]> > Sender: [hidden email] > 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]] > > ______________________________________________ > [hidden email] 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  <[hidden email]> Associate Professor Department of Mathematical Sciences University of Arkansas - Fayetteville, AR 72701 Ph: (479) 575-6324, 575-8630 (fax) http://definetti.uark.edu/~gpetris/______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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[R] dynamic panel data estimation

 In reply to this post by Doran, Harold Hello every one, is there an R package that can handle dynamic panel data model aviablable ? thank you for help chen ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.