binodp {Bolstad} | R Documentation |
Binomial sampling with a discrete prior
Description
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
Usage
binodp(x,n, pi = NULL, pi.prior = NULL, n.pi = 10, ret = FALSE)
Arguments
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 is NULL then a discrete
uniform prior for pi will be used. |
pi.prior |
the associated prior probability mass. |
n.pi |
the number of possible pi values in the prior |
ret |
this argument is deprecated. |
Value
A list will be returned with the following components:
pi |
the vector of possible pi values used in the prior |
pi.prior |
the associated probability mass for the values in
pi |
likelihood |
the scaled likelihood function for pi given
x and n |
posterior |
the posterior probability of pi given
x and n |
f.cond |
the conditional distribution of x given
pi and n |
f.joint |
the joint distribution of x and pi
given n |
f.marg |
the marginal distribution of x |
See Also
binobp
binogcp
Examples
## 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 non-uniform 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, non-uniform 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 side-by-side 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(pin)))
box()
legend(1,0.65,legend=c("Prior","Posterior"),fill=c("red","blue"))
[Package
Bolstad version 0.2-17
Index]