/*
Credible interval for difference between binomial proportions, approximated by Normal distribution
Bolstad 2007 (2e): 248, eq. 13.13
post_diff_mu = binom_diff_prop_norm_approx_mu()
post_diff_sigma = sqrt(binom_diff_prop_norm_approx_var())
untested ...
*/
func BinomDiffPropCrI(post_diff_mu, post_diff_sigma, alpha float64) (float64, float64) {
/*
post_diff_mu posterior mean for difference of normal means
post_diff_sigma posterior standard deviation for difference of normal means
alpha posterior probability that the true mean lies outside the credible interval
*/
var z float64
z = s.ZInv_CDF_For(alpha / 2)
low = post_diff_mu - z*post_diff_sigma
high = post_diff_mu + z*post_diff_sigma
return low, high
}
func BinomBetaPriCrIApprox(α, β, alpha float64, n, k int64) (float64, float64) {
/*
k observed successes
n total number of observations
a beta prior a
b beta prior b
alpha posterior probability that the true proportion lies outside the credible interval
*/
var post_mean, post_var, post_α, post_β, z, low, upp float64
post_α = α + float64(k)
post_β = β + float64(n-k)
post_mean = post_α / (post_α + post_β)
post_var = (post_α * post_β) / ((post_α + post_β) * (post_α + post_β) * (post_α + post_β + 1.0))
z = s.ZInv_CDF_For(alpha / 2)
low = post_mean - z*math.Sqrt(post_var)
upp = post_mean + z*math.Sqrt(post_var)
return low, upp
}