Bayesian model of categorization

categorization_first_attempt.js

var data = {self: 1, group : [5,5,6,7,8,9]}

var model = function(){
  // uninformative prior over group beliefs
  var groupMean = uniform(0,10) //prior
  var groupSd = uniform(0,10)   //prior
  var belong = flip()           //prior


  // estimate groupmean and sd considering the group
  mapData({data: data.group}, function(datum){
    observe(Gaussian({mu: groupMean, sigma: groupSd}), datum)
  })
  
  // use group dist as true emotion prior if you belong; otherwise uninformative
  var groupDist = (belong ?
                          Gaussian({mu: groupMean, sigma: groupSd}) :
                          Uniform({a: 0, b: 10}))

   // data about self is noisy observation from group distribution
  observe(Gaussian({mu:sample(groupDist), sigma: groupSd}), data.self)

  // return beliefs about both the group and the self, so we can compare
  return (belong)

}

var posterior = Infer({method:'MCMC', samples: 1000, lag: 100, burn: 5},model)
print('probability of belong: ' + expectation(posterior))
viz(posterior)