laplace: Summarization of a posterior density by the Laplace method

In LearnBayes: Functions for Learning Bayesian Inference

Description

For a general posterior density, computes the posterior mode, the associated variance-covariance matrix, and an estimate at the logarithm at the normalizing constant.

Usage

laplace(logpost,mode,...)

Arguments

logpost	function that defines the logarithm of the posterior density
mode	vector that is a guess at the posterior mode
...	vector or list of parameters associated with the function logpost

Value

mode	current estimate at the posterior mode
var	current estimate at the associated variance-covariance matrix
int	estimate at the logarithm of the normalizing constant
converge	indication (TRUE or FALSE) if the algorithm converged

Author(s)

Jim Albert

Examples

logpost=function(theta,data)
{
s=5
sum(-log(1+(data-theta)^2/s^2))
}
data=c(10,12,14,13,12,15)
start=10
laplace(logpost,start,data)

Example output

$mode
[1] 12.68945

$var
         [,1]
[1,] 2.685352

$int
[1] 0.8572137

$converge
[1] TRUE

LearnBayes documentation built on May 1, 2019, 7:03 p.m.