binogcp: Binomial sampling with a general continuous prior

In Bolstad: Functions for Elementary Bayesian Inference

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 values in the prior
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 Bolstad.control

Value

A list will be returned with the following components:

likelihood	the scaled likelihood function for pi given x and n
posterior	the posterior probability of pi given x and n
pi	the vector of possible pi values used in the prior
pi.prior	the associated probability mass for the values in pi

See Also

binobp binodp

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 = ""))

Bolstad documentation built on Jan. 8, 2021, 2:03 a.m.