IntLik (version 1.0)

IntLik-package: Numerical Integration for Integrated Likelihood

Description

This package calculates the integrated likelihood numerically. Given the Likelihood function and the prior function, this package integrates out the nuisance parameters by Metropolis-Hastings (MCMC) Algorithm.

Details

Package:

IntLik

Type:

Package

Version:

1.0

Date:

2012-01-25

License:

GPL

References

Chib, S. and Jeliazkov, I. (2001) Marginal likelihood from the Metropolis-Hastings Output. Journal of the American Statistical Association. 96, 270-281

Severini, T.A. (2007) Integrated likelihood functions for non-Bayesian inference. Biometrika. 94 529-542

Examples

##Integrated Likelihood for Ratio of Normal Mean (Example 2 in Severini 2007)
##Generating Data
n=10
u1=4
u2=1/5
x=rnorm(1,u1,sqrt(1/n))
y=rnorm(1,u2,sqrt(1/n))

##Calculate MLE for the start value
psi_hat=x/y
lambda_hat=(x*psi_hat+y)/(psi_hat^2+1)

#Define prior function
prior=function(lambda,psi){
dnorm((psi^2+1)*lambda/(psi*psi_hat+1),mean=0,sd=1)*(psi^2+1)/(psi*psi_hat+1)
}


#Define Likelihood
L=function(psi,lambda){
L=n/2/pi*exp(-n/2*((x-psi*lambda)^2+(y-lambda)^2))
L
}

#Estimate the Integrated Likelihood evaluated at a sequence of psi 
ILik(L,prior, start=lambda_hat, seq(psi_hat-10,psi_hat+10,1), 1, "Normal")