Error in Replications 4

[uasolo]

The contour plots are wrong because of the way alpha and beta are defined in your code:
beta = exp(v2)/(exp(v1)+1)
alpha = exp(v2+v1)/(exp(v1)+1)
this does not produce a grid of values, which is what you want.
Taking inspiration form:
http://avehtari.github.io/BDA_R_demos/demos_ch5/demo5_1.html
you can modify that code, which does not operate the coordinate transformation, with:
cv1 <- rep(v1, each = length(v2))
cv2 <- rep(v2, length(v1))
cA = exp(cv2+cv1)/(exp(cv1)+1)
cB = exp(cv2)/(exp(cv1)+1)
Add the Jacobian to lpfun:
lpfun <- function(a, b, y, n) log(a) + log(b) + log(a+b)*(-5/2) +
sum(lgamma(a+b)-lgamma(a)-lgamma(b)+lgamma(a+y)+lgamma(b+n-y)-lgamma(a+b+n))
lp <- mapply(lpfun, cA, cB, MoreArgs = list(y, n))
df_marg <- data.frame(x = cv1, y = cv2, p = exp(lp - max(lp)))
and plot as in that code, which will give the correct result.

Btw, it is not true that the Jacobian is applied only to the prior. In fact, when applied to the posterior it looks the same as if applied to the prior only: J * post = J * prior * likelihood = (J * prior) * likelihood.