// The heights of the last ten American presidents in cm, from Kennedy to Obama 
var heights = [183, 192, 182, 183, 177, 185, 188, 188, 182, 185];

… and that you would like to fit a Bayesian model assuming a Normal distribution to this data. Well, you can do that right now by clicking “Start sampling” below! This will run an MCMC sampler in your browser implemented in JavaScript.

Start sampling Stop sampling and plot histograms Clear samples

If this doesn’t seem to work in your browser, for some reason, then try this version of the demo.

Here is the model you just sampled from…

$$mu sim text{Normal}(0, 1000) \ sigma sim text{Uniform}(0, 1000) \ text{heights}_i sim text{Normal}(mu, sigma) ~~~ text{for} ~ i ~ text{in} 1..n$$

… and this is how it is implemented in JavaScript:

/* The code below assumes that you have loaded the two modules of bayes.js:
 * - mcmc.js which implements the sampler and creates the global 
 *   object mcmc.
 * - distributions.js which implements a number of log density functions
 *   for common probability distributions and that creates the global object
 *   ld (as in log density).
 */

// The data
var heights = [183, 192, 182, 183, 177, 185, 188, 188, 182, 185];

// Parameter definitions
var params = {
  mu: {type: "real"},
  sigma: {type: "real", lower: 0}};

// Model definition
var log_post = function(state, heights) {
  var log_post = 0;
  // Priors (here sloppy and vague...)
  log_post += ld.norm(state.mu, 0, 1000);
  log_post += ld.unif(state.sigma, 0, 1000);
  // Likelihood
  for(var i = 0; i < heights.length; i++) {
    log_post += ld.norm(heights[i], state.mu, state.sigma);
  }
  return log_post;
};

// Initializing the sampler, burning some draws to the MCMC gods,
// and generating a sample of size 1000.
var sampler =  new mcmc.AmwgSampler(params, log_post, heights);
sampler.burn(1000);
var samples = sampler.sample(1000);