README.md

statkit

A statistics toolkit for javascript.

Usage

Install using npm:

npm install statkit

Fit a linear regression model using MCMC:

var sk = require("statkit.js");

// log-likelihood for the model y ~ N(m*x + b, 1/t)
function lnlike(theta, x, y) {
  var m = theta[0], b = theta[1], t = theta[2];
  var s = 0.0;
  for (var i = 0; i < x.length; i++) {
    var r = y[i] - (m * x[i] + b);
    s += r*r*t - Math.log(t);
  }
  return -0.5*s;
}

// uniform log-prior for m, b, t
function lnprior(theta) {
  var m = theta[0], b = theta[1], t = theta[2];
  if (0.0 < m && m < 1.0 && 0.0 < b && b < 10.0 && 0.0 < t && t < 100.0) {
    return 0.0;
  }
  return -Infinity;
}

// posterior log-probability function
function lnpost(theta, x, y) {
  var lp = lnprior(theta);
  if (!isFinite(lp)) {
    return -Infinity;
  }
  return lp + lnlike(theta, x, y);
}

var x = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5];
var y = [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68];

var res = sk.metropolis(function(theta) { return lnpost(theta, x, y); },
  [0.5, 3.0, 1.0], 1000000, 0.1, 50000, 100);

console.log('acceptance rate:', res.accepted)
console.log('posteriors (16/50/84 percentiles):')
console.log('m', sk.quantile(res.chain[0], 0.16),
  sk.median(res.chain[0]), sk.quantile(res.chain[0], 0.84))
console.log('b', sk.quantile(res.chain[1], 0.16),
  sk.median(res.chain[1]), sk.quantile(res.chain[1], 0.84))
console.log('t', sk.quantile(res.chain[2], 0.16),
  sk.median(res.chain[2]), sk.quantile(res.chain[2], 0.84))

Calculate a confidence interval for a correlation using the bootstrap method:

var sk = require("statkit");

var lsat = [576, 635, 558, 578, 666, 580, 555,
            661, 651, 605, 653, 575, 545, 572, 594];
var gpa = [3.39, 3.30, 2.81, 3.03, 3.44, 3.07, 3.00,
           3.43, 3.36, 3.13, 3.12, 2.74, 2.76, 2.88, 2.96];

var corr = sk.corr(gpa, lsat);
var ci = sk.bootci(100000, sk.corr, gpa, lsat);

console.log("corr = ", corr, "ci = ", ci);

Perform a linear regression on the first data set in Anscombe's quartet:

var sk = require("statkit");

var x = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5];
var y = [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68];

var A = new Array(x.length*2);
for (var i = 0; i < x.length; ++i) {
  A[2*i] = 1;
  A[2*i + 1] = x[i];
}
var b = sk.lstsq(x.length, 2, A, y);

console.log("intercept = ", b[0], "slope = ", b[1]);

Functions

• min(a) - Minimum
• max(a) - Maximum
• range(a) - Range
• quantile(a) - Quantile
• median(a) - Median
• iqr(a) - Interquartile range
• mean(a) - Mean
• gmean(a) - Geometric mean
• hmean(a) - Harmonic mean
• var(a) - Variance
• std(a) - Standard deviation
• skew(a) - Skewness
• kurt(a) - Kurtosis
• corr(x, y) - Correlation between x and y
• entropy(p) - Entropy
• kldiv(p, q) - Kullback–Leibler divergence
• shuffle(a) - Shuffle using the Fisher–Yates shuffle
• sample(a) - Sample with replacement
• boot(nboot, bootfun, data...) - Bootstrap the bootfun statistic
• bootci(nboot, bootfun, data...) - Calculate bootstrap confidence intervals using the normal model
• randn() - Draw random sample from the standard normal distribution using the Marsaglia polar method
• normcdf(x) - Normal cumulative distribution function
• norminv(p) - Normal inverse cumulative distribution function
• lufactor(A, n) - Compute pivoted LU decomposition
• lusolve(LU, p, b) - Solve Ax=b given the LU factorization of A
• qrfactor(m, n, A) - Compute QR factorization of A
• qrsolve(m, n, QR, tau, b) - Solve the least squares problem min ||Ax = b|| using QR factorization QR of A
• lstsq(m, n, A, b) - Solve the least squares problem min ||Ax = b||
• metropolis(lnpost, p, iterations, scale, burn, thin) - Sample from lnpost starting at p using the Metropolis-Hastings algorithm

Credits

(c) 2014 Erik Rigtorp erik@rigtorp.se. MIT License