webppl/src/dists/cauchy.js

Probabilistic programming for the web

'use strict';
var ad = require('../ad');
var base = require('./base');
var types = require('../types');
var util = require('../util');
var numeric = require('../math/numeric');
var Uniform = require('./uniform').Uniform;
var LOG_PI = numeric.LOG_PI;
var Cauchy = base.makeDistributionType({
    name: 'Cauchy',
    desc: 'Distribution over ``[-Infinity, Infinity]``',
    params: [
        {
            name: 'location',
            desc: '',
            type: types.unboundedReal
        },
        {
            name: 'scale',
            desc: '',
            type: types.positiveReal
        }
    ],
    wikipedia: true,
    mixins: [base.continuousSupport],
    sample: function () {
        var u = util.random();
        return ad.value(this.params.location) + ad.value(this.params.scale) * Math.tan(Math.PI * (u - 0.5));
    },
    score: function (x) {
        var scale = this.params.scale;
        var location = this.params.location;
        return ad.scalar.sub(ad.scalar.sub(ad.scalar.neg(LOG_PI), ad.scalar.log(scale)), ad.scalar.log(ad.scalar.add(1, ad.scalar.pow(ad.scalar.div(ad.scalar.sub(x, location), scale), 2))));
    },
    base: function () {
        return new Uniform({
            a: 0,
            b: 1
        });
    },
    transform: function (x) {
        var location = this.params.location;
        var scale = this.params.scale;
        return ad.scalar.add(location, ad.scalar.mul(scale, ad.scalar.tan(ad.scalar.mul(ad.scalar.PI, ad.scalar.sub(x, 0.5)))));
    }
});
module.exports = { Cauchy: Cauchy };