{"articles":{"monte-carlo-sample-size-to-error@computational-statistical-methods":{"content":"<p>The Monte Carlo error is \\({\\sqrt{{{\\operatorname{Var} {\\frac{1}{N} {\\sum}_{i} h({X}_{i})}}}} = \\sqrt{\\frac{{\\sigma}^{2}}{n}}}\\). <br> A linear improvement in the Monte Carlo estimator requires a quadratic increase in the number of samples: To get a twice as good estimator (halve the variance), the number of samples must be quadrupled. To get an \\(n\\) times better estimator, the number of samples must be \\({n}^{2}\\).</p>","names":[[["Sample size to error",""]]]}},"style":"Note"}