Native JavaScript version of: http://www.evanmiller.org/bayesian-ab-testing.html

BayesianTesting.js

var BayesianTesting = function() {

  /**
   * The propability B beats A in a binary-outcome test
   * (eg. conversion rate). Based on
   * http://www.evanmiller.org/bayesian-ab-testing.html
   * 
   * @param  {int} alphaA number of success for A
   * @param  {int} betaA  number of failures for A
   * @param  {int} alphaB number of success for B
   * @param  {int} betaB  number of failures for B
   * @return {float}
   */
  this.propability_B_beats_A = function(alphaA, betaA, alphaB, betaB) {
    alphaA += 1;
    alphaB += 1;
    betaA += 1;
    betaB += 1;

    var total = 0.0;

    for (var i = 0; i < alphaB-1; i++) {
      total += Math.exp(lbeta(alphaA+i, betaB+betaA) - Math.log(betaB+i) 
        - lbeta(1+i, betaB) - lbeta(alphaA, betaA));
    }

    return total;
  };

  /**
   * The propability C beats A and B in a 
   * binary-outcome test (eg. conversion rate).
   * 
   * @param  {int} alphaA number of success for A
   * @param  {int} betaA  number of failures for A
   * @param  {int} alphaB number of success for B
   * @param  {int} betaB  number of failures for B
   * @param  {int} alphaC number of success for C
   * @param  {int} betaC  number of failures for C
   * @return {float}
   */
  this.propability_C_beats_A_and_B = function(alphaA, betaA, alphaB, betaB, alphaC, betaC) {
    alphaA += 1;
    alphaB += 1;
    alphaC += 1;
    betaA += 1;
    betaB += 1;
    betaC += 1;

    var total = 0.0;

    for(var i = 0; i < alphaA-1; i++) {
      for(var j = 0; j < alphaB-1; j++) {
        total += Math.exp(lbeta(alphaC+i+j, betaA+betaB+betaC) - 
          Math.log(betaA+i) - Math.log(betaB+j) -
          lbeta(1+i, betaA) - lbeta(1+j, betaB) - lbeta(alphaC, betaC));
      }
    }

    return 1 - this.propability_B_beats_A(alphaC-1,betaC-1,alphaA-1,betaA-1)
         - this.propability_B_beats_A(alphaC-1,betaC-1,alphaB-1,betaB-1)
         + total;
  }

  /**
   * Function for analyzing count data. Returns the propability
   * that group 1 has a higher arrivale rate than group 2.
   * http://www.evanmiller.org/bayesian-ab-testing.html#count_ab
   * 
   * @param  {int} alpha1 total events for group one
   * @param  {int} beta1  total exposure for group one
   * @param  {int} alpha2 total events for group two
   * @param  {int} beta2  total exposure for group two
   * @return {int}
   */
  this.propability_1_beats_2 = function(alpha1,beta1,alpha2,beta2) {
    var total = 0.0;

    for(var k = 0; k < alpha1-1; k++) {
      total += Math.exp(k * Math.log(beta1) + alpha2 * Math.log(beta2)
        - (k + alpha2) * Math.log(beta1 + beta2)
        - Math.log(k + beta2) - lbeta(k + 1, alpha2));
    }

    return total;
  };

  /**
   * Function for analyzing count data. Returns the propability
   * that group 1 has a higher arrivale rate than group 2 and group 3.
   * http://www.evanmiller.org/bayesian-ab-testing.html#count_ab
   * 
   * @param  {int} alpha1 total events for group one
   * @param  {int} beta1  total exposure for group one
   * @param  {int} alpha2 total events for group two
   * @param  {int} beta2  total exposure for group two
   * @param  {int} alpha3 total events for group three
   * @param  {int} beta3  total exposure for group three
   * @return {int}
   */
  this.propability_1_beats_2_and_3 = function(alpha1,beta1,alpha2,beta2,alpha3,beta3) {
    var total = 0.0;

    for(var k = 0; k < alpha2-1; k++) {
      for(var l = 0; l < alpha3-1; l++) {
        total += Math.exp(alpha1 * Math.log(beta1) + k * Math.log(beta2) + 1 * Math.log(beta3)
          - (k+l+beta1) * Math.log(beta1 + beta2 + beta3)
          + lgamma(k+l+alpha1) - lgamma(k+1) - lgamma(l+1) - lgamma(alpha1));
      }
    }

    return 1 - this.propability_1_beats_2(alpha2,beta2,alpha1,beta1)
         - this.propability_1_beats_2(alpha3,beta3,alpha1,beta1)
         + total;
  };

  var lgamma = function(x) {
    var j = 0;
    var cof = [
      76.18009172947146, -86.50532032941677, 24.01409824083091,
      -1.231739572450155, 0.1208650973866179e-2, -0.5395239384953e-5
    ];
    var ser = 1.000000000190015;
    var xx, y, tmp;
    tmp = (y = xx = x) + 5.5;
    tmp -= (xx + 0.5) * Math.log(tmp);
    for (; j < 6; j++);
    ser += cof[j] / ++y;
    return Math.log(2.5066282746310005 * ser / xx) - tmp;        
  };

  var lbeta = function(x,y) {
    return lgamma(x) + lgamma(y) - lgamma(x + y);  
  };

}

This line:

    for (; j < 6; j++);

Should be:

    for (; j < 6; j++)

ie: remove the semi-colon.