binogcp {Bolstad}  R Documentation 
Binomial sampling with a general continuous prior
Description
Evaluates and plots the posterior density for \pi
, the probability
of a success in a Bernoulli trial, with binomial sampling and a general
continuous prior on \pi
Usage
binogcp(
x,
n,
density = c("uniform", "beta", "exp", "normal", "user"),
params = c(0, 1),
n.pi = 1000,
pi = NULL,
pi.prior = NULL,
...
)
Arguments
x 
the number of observed successes in the binomial experiment. 
n 
the number of trials in the binomial experiment. 
density 
may be one of "beta", "exp", "normal", "student", "uniform" or "user" 
params 
if density is one of the parameteric forms then then a vector of parameters must be supplied. beta: a, b exp: rate normal: mean, sd uniform: min, max 
n.pi 
the number of possible 
pi 
a vector of possibilities for the probability of success in a single trial. This must be set if density = "user". 
pi.prior 
the associated prior probability mass. This must be set if density = "user". 
... 
additional arguments that are passed to 
Value
A list will be returned with the following components:
likelihood 
the scaled likelihood function for 
posterior 
the posterior probability of

pi 
the vector of possible

pi.prior 
the associated
probability mass for the values in 
See Also
Examples
## simplest call with 6 successes observed in 8 trials and a continuous
## uniform prior
binogcp(6, 8)
## 6 successes, 8 trials and a Beta(2, 2) prior
binogcp(6, 8,density = "beta", params = c(2, 2))
## 5 successes, 10 trials and a N(0.5, 0.25) prior
binogcp(5, 10, density = "normal", params = c(0.5, 0.25))
## 4 successes, 12 trials with a user specified triangular continuous prior
pi = seq(0, 1,by = 0.001)
pi.prior = rep(0, length(pi))
priorFun = createPrior(x = c(0, 0.5, 1), wt = c(0, 2, 0))
pi.prior = priorFun(pi)
results = binogcp(4, 12, "user", pi = pi, pi.prior = pi.prior)
## find the posterior CDF using the previous example and Simpson's rule
myCdf = cdf(results)
plot(myCdf, type = "l", xlab = expression(pi[0]),
ylab = expression(Pr(pi <= pi[0])))
## use the quantile function to find the 95% credible region.
qtls = quantile(results, probs = c(0.025, 0.975))
cat(paste("Approximate 95% credible interval : ["
, round(qtls[1], 4), " ", round(qtls, 4), "]\n", sep = ""))
## find the posterior mean, variance and std. deviation
## using the output from the previous example
post.mean = mean(results)
post.var = var(results)
post.sd = sd(results)
# calculate an approximate 95% credible region using the posterior mean and
# std. deviation
lb = post.mean  qnorm(0.975) * post.sd
ub = post.mean + qnorm(0.975) * post.sd
cat(paste("Approximate 95% credible interval : ["
, round(lb, 4), " ", round(ub, 4), "]\n", sep = ""))