func BinomBetaPriCrI(α, β, alpha float64, n, k int64) (float64, float64) {
/*
k observed successes
n total number of observations
α beta prior a
β beta prior b
alpha posterior probability that the true proportion lies outside the credible interval
*/
var low, upp float64
low = s.BetaInv_CDF_For(alpha/2.0, α+float64(k), β+float64(n-k))
upp = s.BetaInv_CDF_For(1.0-alpha/2.0, α+float64(k), β+float64(n-k))
return low, upp
}
// Quantile, Jeffrey's prior
func BinomJeffPriQtl(k, n int64, p float64) float64 {
var α, β float64
α = 0.5
β = 0.5
if k > n {
panic(fmt.Sprintf("The number of observed successes (k) must be <= number of trials (n)"))
}
return s.BetaInv_CDF_For(α+float64(k), β+float64(n-k), p)
}
// Quantile, Beta prior
func BinomBetaPriQtl(k, n int64, α, β, p float64) float64 {
if k > n {
panic(fmt.Sprintf("The number of observed successes (k) must be <= number of trials (n)"))
}
if α <= 0 || β <= 0 {
panic(fmt.Sprintf("The parameters of the prior must be greater than zero"))
}
return s.BetaInv_CDF_For(α+float64(k), β+float64(n-k), p)
}
// Quantile, Flat prior
func BinomFlatPriQtl(k, n int64, p float64) float64 {
var α, β float64
if k > n {
panic(fmt.Sprintf("The number of observed successes (k) must be <= number of trials (n)"))
}
α = float64(k + 1)
β = float64(n - k + 1)
if α <= 0 || β <= 0 {
panic(fmt.Sprintf("The parameters of the prior must be greater than zero"))
}
return s.BetaInv_CDF_For(α, β, p)
}