Description Usage Arguments Details Value Author(s) References See Also Examples
Uses a beta prior on the probability of success for a binomial distribution, determines a two-sided confidence interval from a beta posterior. A plotting function is also provided to show the probability regions defined by each confidence interval.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | 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, ...)
binom.bayes.densityplot(bayes,
npoints = 500,
fill.central = "lightgray",
fill.lower = "steelblue",
fill.upper = fill.lower,
alpha = 0.8, ...)
|
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. |
bayes |
The output |
npoints |
The number of points to use to draw the density curves. Higher numbers give smoother densities. |
fill.central |
The color for the central density. |
fill.lower,fill.upper |
The color(s) for the upper and lower density. |
alpha |
The alpha value for controlling transparency. |
... |
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.
For binom.bayes
, a data.frame
containing the observed
proportions and the lower and upper bounds of the confidence interval.
For binom.bayes.densityplot
, a ggplot
object that can
printed to a graphics device, or have additional layers added.
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | # Example using highest probability density.
hpd <- binom.bayes(
x = 0:10, n = 10, type = "highest", conf.level = 0.8, tol = 1e-9)
print(hpd)
binom.bayes.densityplot(hpd)
# Remove the extremes from the plot since they make things hard
# to see.
binom.bayes.densityplot(hpd[hpd$x != 0 & hpd$x != 10, ])
# Example using central probability.
central <- binom.bayes(
x = 0:10, n = 10, type = "central", conf.level = 0.8, tol = 1e-9)
print(central)
binom.bayes.densityplot(central)
# Remove the extremes from the plot since they make things hard
# to see.
binom.bayes.densityplot(central[central$x != 0 & central$x != 10, ])
|
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