Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

In answering yet another question on X validated about the numerical approximation of the marginal likelihood, I suggested using an harmonic mean estimate as a simple but worthless solution based on an MCMC posterior sample. This was on a toy example with a uniform prior on (0,π) and a “likelihood” equal to sin(θ) [really a toy problem!]. Simulating an MCMC chain by a random walk Metropolis-Hastings algorithm is straightforward, as is returning the harmonic mean of the sin(θ)’s.

f <- function(x){
if ((0
However, the outcome looks remarkably stable and close to the expected value 2/π, despite 1/sin(θ) having an infinite integral on (0,π). Meaning that the average of the 1/sin(θ)’s has no variance. Hence I wonder why this specific example does not lead to an unreliable output… But re-running the chain with a smaller scale σ starts producing values of sin(θ) regularly closer to zero, which leads to an estimate of I both farther away from 2 and much more variable. No miracle, in the end!Filed under: Books, Kids, Mountains, pictures, R, Running, Statistics, Travel Tagged: Gaussian random walk, harmonic mean estimator, Metropolis-Hastings algorithm, Monte Carlo Statistical Methods, numerical integration, simulation

var vglnk = {key: '949efb41171ac6ec1bf7f206d57e90b8'};
(function(d, t) {
var s = d.createElement(t);
s.type = 'text/javascript';
s.async = true;
// s.defer = true;
var r = d.getElementsByTagName(t)[0];
r.parentNode.insertBefore(s, r);
}(document, 'script'));

Related
ShareTweet