poi.beta.laplace: Laplace Approximation for Posterior Density, Practical 11.2

In SMPracticals: Practicals for Use with Davison (2003) Statistical Models

Description

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).

Usage

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.

Value

int	Estimated integral of posterior density.
conv	Did the routine for the Laplace optimization converge?
x	Values of beta
y	Values of posterior density

Author(s)

Anthony Davison ([e-mail])

References

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

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)

SMPracticals documentation built on May 2, 2019, 11:12 a.m.