Monte Carlo Simulation from a Binomial Likelihood with a Beta Prior
This function generates a sample from the posterior distribution of a binomial likelihood with a Beta prior.
MCbinomialbeta(y, n, alpha = 1, beta = 1, mc = 1000, ...)
y |
The number of successes in the independent Bernoulli trials. |
n |
The number of independent Bernoulli trials. |
alpha |
Beta prior distribution alpha parameter. |
beta |
Beta prior distribution beta parameter. |
mc |
The number of Monte Carlo draws to make. |
... |
further arguments to be passed |
MCbinomialbeta directly simulates from the posterior distribution.
This model is designed primarily for instructional use. π is
the probability of success for each independent Bernoulli trial. We assume
a conjugate Beta prior:
π \sim \mathcal{B}eta(α, β)
y is the number of successes in n trials. By default, a uniform prior is used.
An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package.
## Not run:
posterior <- MCbinomialbeta(3,12,mc=5000)
summary(posterior)
plot(posterior)
grid <- seq(0,1,0.01)
plot(grid, dbeta(grid, 1, 1), type="l", col="red", lwd=3, ylim=c(0,3.6),
xlab="pi", ylab="density")
lines(density(posterior), col="blue", lwd=3)
legend(.75, 3.6, c("prior", "posterior"), lwd=3, col=c("red", "blue"))
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