A casualty of cut-and-paste in Chapter 3 of Introducing Monte Carlo Methods with R. Brad McNeney from Simon Fraser sent me a nice email about the end of Example 3.6 missing a marginal estimate. Indeed, it does. And it should have been obvious from the “estimates” we derived, 19 and 16, which are not even on the support of the posterior distribution represented on Figure 3.5… The R code is given as

> mean(y[,1]*apply(y,1,f)/den)/mean(apply(y,1,h)/den)
[1] 19.33745
> mean(y[,2]*apply(y,1,f)/den)/mean(apply(y,1,h)/den)
[1] 16.54468

and should have been

> mean(y[,1]*f(y)/den)/mean(f(y)/den)
[1] 94.08314
> mean(y[,2]*f(y)/den)/mean(f(y)/den)
[1] 80.42832

As also suggested by Brad, a similar modification applies to the remark after eqn. (3.7):

mean(apply(y,1,h)/den)

should be

mean(f(y)/den)