poi.beta.laplace function

Laplace Approximation for Posterior Density, Practical 11.2

This function computes the Laplace approximation to the posterior density of the parameter beta in a Poisson regression model. For more details see Practical 11.2 of Davison (2003).

poi.beta.laplace(data, alpha = get.alpha(data), phi = 1, nu = 0.1, 
                 beta = seq(from = 0, to = 7, length = 1000))

Arguments

• data: A data frame with vector components y and x of the same length. y contains the numbers of counts, and x the corresponding time intervals.
• alpha: Prior value of a parameter, estimated from the data by default.
• phi: Prior value of a parameter.
• nu: Prior value of a parameter.
• beta: Values for which posterior density of beta should be provided.

Details

This is provided simply so that readers spend less time typing. It is not intended to be robust and general code.

Returns

• int: Estimated integral of posterior density.

• conv: Did the routine for the Laplace optimization converge?

• x: Values of beta

• y: Values of posterior density

References

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Practical 11.2.

Author(s)

Anthony Davison (anthony.davison@epfl.ch)

Examples

## From Practical 11.2:
get.alpha <- function(d)
{  # estimate alpha from data
  rho <- d$y/d$x
  n <- length(d$y)
  mean(rho)^2/( (n-1)*var(rho)/n - mean(rho)*mean(1/d$x) )
}
data(cloth)
attach(cloth)
plot(x,y)
beta <- seq(from=0,to=10,length=1000)
beta.post <- poi.beta.laplace(cloth,beta=beta,nu=1)
plot(beta.post,type="l",xlab="beta",ylab="Posterior density")
beta.post <- poi.beta.laplace(cloth,beta=beta,nu=5)
lines(beta.post,lty=2)