binodp {Bolstad}  R Documentation 
Evaluates and plots the posterior density for \pi
, the probability
of a success in a Bernoulli trial, with binomial sampling and a discrete
prior on \pi
binodp(x, n, pi = NULL, pi.prior = NULL, n.pi = 10, ...)
x 
the number of observed successes in the binomial experiment. 
n 
the number of trials in the binomial experiment. 
pi 
a vector of possibilities for the probability of success in a
single trial. if 
pi.prior 
the associated prior probability mass. 
n.pi 
the number of possible 
... 
additional arguments that are passed to 
A list will be returned with the following components:
pi 
the
vector of possible 
pi.prior 
the associated probability mass for the values in

likelihood 
the scaled likelihood function for

posterior 
the posterior
probability of 
f.cond 
the
conditional distribution of 
f.joint 
the joint distribution of 
f.marg 
the marginal distribution of 
## simplest call with 6 successes observed in 8 trials and a uniform prior
binodp(6,8)
## same as previous example but with more possibilities for pi
binodp(6, 8, n.pi = 100)
## 6 successes, 8 trials and a nonuniform discrete prior
pi = seq(0, 1, by = 0.01)
pi.prior = runif(101)
pi.prior = sort(pi.prior / sum(pi.prior))
binodp(6, 8, pi, pi.prior)
## 5 successes, 6 trials, nonuniform prior
pi = c(0.3, 0.4, 0.5)
pi.prior = c(0.2, 0.3, 0.5)
results = binodp(5, 6, pi, pi.prior)
## plot the results from the previous example using a sidebyside barplot
results.matrix = rbind(results$pi.prior,results$posterior)
colnames(results.matrix) = pi
barplot(results.matrix, col = c("red", "blue"), beside = TRUE,
xlab = expression(pi), ylab=expression(Probability(pi)))
box()
legend("topleft", bty = "n", cex = 0.7,
legend = c("Prior", "Posterior"), fill = c("red", "blue"))