binobp {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 continous beta(a,b) prior.
binobp(x, n, a = 1, b = 1, pi = seq(0, 1, by = 0.001), ...)
x |
the number of observed successes in the binomial experiment. |
n |
the number of trials in the binomial experiment. |
a |
parameter for the beta prior - must be greater than zero |
b |
parameter for the beta prior - must be greater than zero |
pi |
A range of values for the prior to be calculated over. |
... |
additional arguments that are passed to |
An object of class 'Bolstad' is returned. This is a list with the following components:
prior |
the prior density of pi, i.e. the beta(a,b) density |
likelihood |
the likelihood of x given pi and n, i.e. the binomial(n,pi) density |
posterior |
the posterior density of pi given x and n - i.e. the beta(a+x,b+n-x) density |
pi |
the values of pi for which the posterior density was evaluated |
mean |
the posterior mean |
var |
the posterior variance |
sd |
the posterior std. deviation |
quantiles |
a set of quantiles from the posterior |
cdf |
a cumulative distribution function for the posterior |
quantileFun |
a quantile function for the posterior |
## simplest call with 6 successes observed in 8 trials and a beta(1,1) uniform ## prior binobp(6,8) ## 6 successes observed in 8 trials and a non-uniform beta(0.5,6) prior binobp(6,8,0.5,6) ## 4 successes observed in 12 trials with a non uniform beta(3,3) prior ## plot the stored prior, likelihood and posterior results = binobp(4, 12, 3, 3) decomp(results)