I read this sentence in a book:
"... therefore this method is particularly useful for Bayesian inference since it doesn't require a normalization constant"
The method is a computational algorithm that takes a density (possibly un-normalized) and does some stuff with it.
I've seen this sentiment elsewhere too, that in Bayesian stats, we need methods that don't require normalization constants ... but I don't understand what the big deal is??
If we have a density $f$ on $R$ but we don't know the normalization constant ... give me two seconds to type this in R:
integrate(f, -Inf, Inf)
and out pops the (inverse of the) normalization constant.
So what is the big deal? Why do we care whether or not a method needs normalization constants when it takes 2 seconds to calculate them in R?