knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

This demo shows how to use the malt function from the malt library to sample from the Banana distribution.

library(malt)

Banana distribution $\theta=(\theta_1,\theta_2)$ given by $$ \begin{align} \theta_1~&\sim~\mathcal{N}(0,10)\,, \ \theta_2~&\sim~\mathcal{N}(0.03(\theta_1^2-100),1)\,. \end{align} $$ It is a simple modification of a two dimensional Gaussian target with level sets that are highly non-convex.

The potential and its gradient are specified as follows:

U=function(theta){
(theta[1]^2/10+(theta[2]-0.03*(theta[1]^2-100))^2)/2
}
grad=function(theta){
c(theta[1]/10+0.06*theta[1]*(0.03*(theta[1]^2-100)-theta[2]),theta[2]-0.03*(theta[1]^2-100))
}
d=2
init=rep(5,d)
n_steps=5000
g=0.1
h=1.5
L=6
output=malt(init, U, grad, n_steps, g, h, L)
chain=output$samples
apply(chain,2,mean)
output$acceptance
plot(chain[,1],type="l")
plot(chain[,2],type="l")

plot(chain[,1],chain[,2])
library(coda)
effectiveSize(chain)
effectiveSize(chain^2)


lrioudurand/malt documentation built on July 28, 2022, 11:06 p.m.