# R/Bayes: Why is a wildly different prior not affecting the posterior in bayesglm{arm}?

I am trying to see how different priors affect the posterior estimates in bayesglm{arm}. But no matter what the prior is, why is the posterior hardly changing?

library(Zelig); data(turnout) #Using the "turnout" data from the "Zelig" package

model.1 = bayesglm(vote ~ race + age, family=binomial(link=logit),
prior.df=1, prior.scale=2.5,
data=turnout) #This is the default specificication with a weakly informative prior


summary(model.1) yields:

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.042320   0.176567   0.240  0.81058
racewhite   0.641959   0.134136   4.786  1.7e-06 ***
age         0.011222   0.003046   3.683  0.00023 ***


Now compare this to:

model.2 = bayesglm(vote ~ race + age, family=binomial(link=logit),
prior.df=1, prior.scale=2.5, prior.mean=c(-100,0), #Specifying a crazy prior
data=turnout)


Summary(model.2) yields:

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.039891   0.176720   0.226 0.821410
racewhite   0.645076   0.134465   4.797 1.61e-06 ***
age         0.011219   0.003047   3.682 0.000231 ***


What's going on here? Surely a prior which is so different would influence the maximum likelihood estimates enough to sharply change the posterior?

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what is your sample size? I'm not familiar with this R package but the prior becomes less and less important as the sample size increases - here is a question and two answers related to that. – Macro Aug 1 '12 at 14:10
Your data has 2000 points. If the data has high precision and large N this is what I would expect. If you sample the data down to just 50 observations, the estimates change more with different priors. – Seth Aug 1 '12 at 14:12