h: Calculate the probability one random beta variable is greater...
In dgrtwo/ebbinom: Empirical Bayes on binomial data

Description Usage Arguments Details Source Examples

Find the probability that Beta(a, b) > Beta(c, d), using either an exact solution or a normal approximation. Vectorized across a, b, c and d.

1	h(a, b, c, d, approx = FALSE, log_h = FALSE)

`a`	alpha parameter for first Beta
`b`	beta parameter for second Beta
`c`	alpha parameter for first Beta
`d`	beta parameter for second Beta
`approx`	whether to use a normal approximation to the beta
`log_h`	whether to return `log(h(a, b, c, d))` rather than `h(a, b, c, d)`

The "exact" solution is exact only for integer values of c.

The exact version comes from Evan Miller and Chris Stucchio: https://www.chrisstucchio.com/blog/2014/bayesian_ab_decision_rule.html

John D. Cook lays out the normal approximation here: http://www.johndcook.com/fast_beta_inequality.pdf.

h(60, 40, 50, 50)
h(60, 40, 50, 50, approx = TRUE)

# compare against random simulation:
mean(rbeta(1e5, 60, 40) > rbeta(1e5, 50, 50))

# it is vectorized across one or multiple arguments
a <- 1:19
h(a, 20 - a, 10, 10)
plot(a, h(a, 20 - a, 10, 10))