Description Details Author(s) References Examples
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.
Package: | IntLik |
Type: | Package |
Version: | 1.0 |
Date: | 2012-01-25 |
License: | GPL |
Zhenyu Zhao zhenyuzhao2014@u.northwestern.edu
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ##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")
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