Algorithms & Data Structures

// Bayesian A/B Test Calculator
class BayesianABTest {
  constructor(alphaA = 1, betaA = 1, alphaB = 1, betaB = 1) {
    this.priorA = { alpha: alphaA, beta: betaA }
    this.priorB = { alpha: alphaB, beta: betaB }
  }
  
  updatePosterior(conversions, trials, prior) {
    return {
      alpha: prior.alpha + conversions,
      beta: prior.beta + (trials - conversions)
    }
  }
  
  calculateProbability(posteriorA, posteriorB, samples = 10000) {
    let wins = 0
    
    for (let i = 0; i < samples; i++) {
      const sampleA = this.betaSample(posteriorA.alpha, posteriorA.beta)
      const sampleB = this.betaSample(posteriorB.alpha, posteriorB.beta)
      if (sampleA > sampleB) wins++
    }
    
    return wins / samples
  }
  
  betaSample(alpha, beta) {
    // Simplified beta distribution sampling
    const x = this.gammaSample(alpha)
    const y = this.gammaSample(beta)
    return x / (x + y)
  }
  
  gammaSample(shape) {
    // Marsaglia and Tsang method (simplified)
    let d = shape - 1/3
    let c = 1 / Math.sqrt(9 * d)
    
    while (true) {
      let x = this.normalRandom()
      let v = Math.pow(1 + c * x, 3)
      if (v > 0 && Math.log(Math.random()) < 0.5 * x * x + d - d * v + d * Math.log(v)) {
        return d * v
      }
    }
  }
  
  normalRandom() {
    // Box-Muller transform
    const u1 = Math.random()
    const u2 = Math.random()
    return Math.sqrt(-2 * Math.log(u1)) * Math.cos(2 * Math.PI * u2)
  }
}

// Example usage
const test = new BayesianABTest()

// Simulate A/B test results
// Variant A: 120 conversions out of 1000 trials
const posteriorA = test.updatePosterior(120, 1000, test.priorA)

// Variant B: 100 conversions out of 1000 trials  
const posteriorB = test.updatePosterior(100, 1000, test.priorB)

// Calculate probability that A is better than B
const probability = test.calculateProbability(posteriorA, posteriorB)

console.log(`Posterior A: α=${posteriorA.alpha}, β=${posteriorA.beta}`)
console.log(`Posterior B: α=${posteriorB.alpha}, β=${posteriorB.beta}`)
console.log(`Probability that A is better than B: ${(probability * 100).toFixed(2)}%`)