[R] Gelman 2006 half-Cauchy distribution

Uwe Ligges ligges at statistik.tu-dortmund.de
Fri May 28 16:02:38 CEST 2010

Am 28.05.2010 15:29, schrieb Christopher David Desjardins:
> Hi,
> I am trying to recreate the right graph on page 524 of Gelman's 2006
> paper "Prior distributions for variance parameters in hierarchical
> models" in Bayesian Analysis, 3, 515-533. I am only interested, however,
> in recreating the portion of the graph for the overlain prior density
> for the half-Cauchy with scale 25 and not the posterior distribution.
> However, when I try:
> curve(dcauchy, from=0, to=200, location=0, scale=25)

This won't pass location and scale to dcauchy.

You need something along the lines

   dcauchy0_25 <- function(x) dcauchy(x, location=0, scale=25)
   curve(dcauchy0_25, from=0, to=200)

Uwe Ligges

> the probabilities for the half-Cauchy values seem to approach zero
> almost immediately after 0 whereas in Gelman 2006 the tail appears much
> fatter giving non-zero probabilities out to 100.
> I am interested in replicating this because I want to use half-Cauchy
> priors and want to play around with the scale values but I want to know
> what my prior looks like before using it in models.
> Please cc me as I am digest subscriber.
> Thanks!
> Chris
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