binom.bayes {binom} | R Documentation |
Uses a beta prior on the probability of success for a binomial distribution, determines a two-sided confidence interval from a beta posterior.
binom.bayes(x, n, conf.level = 0.95, type = c("highest", "central"), prior.shape1 = 0.5, prior.shape2 = 0.5, tol = .Machine$double.eps^0.5, maxit = 1000, ...)
x |
Vector of number of successes in the binomial experiment. |
n |
Vector of number of independent trials in the binomial experiment. |
conf.level |
The level of confidence to be used in the confidence interval. |
type |
The type of confidence interval (see Details). |
prior.shape1 |
The value of the first shape parameter to be used in the prior beta. |
prior.shape2 |
The value of the second shape parameter to be used in the prior beta. |
tol |
A tolerance to be used in determining the highest probability density interval. |
maxit |
Maximum number of iterations to be used in determining the highest probability interval. |
... |
Ignored. |
Using the conjugate beta prior on the distribution of p (the probability of success) in a binomial experiment, constructs a confidence interval from the beta posterior. From Bayes theorem the posterior distribution of p given the data x is:
p|x ~ Beta(x + prior.shape1, n - x + prior.shape2)
The default prior is Jeffrey's prior which is a Beta(0.5, 0.5)
distribution. Thus the posterior mean is (x + 0.5)/(n + 1)
.
The default type of interval constructed is "highest" which computes the highest probability density (hpd) interval which assures the shortest interval possible. The hpd intervals will achieve a probability that is within tol of the specified conf.level. Setting type to "central" constructs intervals that have equal tail probabilities.
If 0 or n successes are observed, a one-sided confidence interval is returned.
A data.frame containing the observed proportions and the lower and upper bounds of the confidence interval.
Sundar Dorai-Raj (sdorairaj@gmail.com)
Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (1997) Bayesian Data Analysis, London, U.K.: Chapman and Hall.
binom.confint
, binom.cloglog
,
binom.logit
, binom.probit
binom.bayes(x = 0:10, n = 10, tol = 1e-9)