Algorithms for calculating variance

Algorithms for calculating variance play a major role in computational statistics. A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values. Naïve algorithm A formula for calculating the variance of an entire population of size N is: :\sigma^2 = \overline{(x^2)} - \bar x^2 = \frac {\sum_{i=1}^N x_i^2 - (\sum_{i=1}^N x_i)^2/N}{N}. Using Bessel's correction to calculate an unbiased estimate of the population variance from a finite sample of n observations, the formula is: :s^2 = \left(\frac {\sum_{i=1}^n x_i^2} n - \left( \frac {\sum_{i=1}^n x_i} n \right)^2\right) \cdot \frac {n}{n-1}. Therefore, a naïve algorithm to calculate the estimated variance is given by the following:

Let n ← 0, Sum ← 0, SumSq ← 0
For each datum x: ** n ← n + 1 ** Sum ← Sum + x

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (1)

Related publications

Related people

Related units

Related concepts

Related courses (3)

Related courses

Related lectures (4)

Related lectures

FIN-472: Computational finance

Participants of this course will master computational techniques frequently used in mathematical finance applications. Emphasis will be put on the implementation and practical aspects.

MICRO-455: Applied machine learning

Real-world engineering applications must cope with a large dataset of dynamic variables, which cannot be well approximated by classical or deterministic models. This course gives an overview of methods from Machine Learning for the analysis of non-linear, highly noisy and multi dimensional data

ME-474: Numerical flow simulation

This course provides practical experience in the numerical simulation of fluid flows. Numerical methods are presented in the framework of the finite volume method. A simple solver is developed with Matlab, and a commercial software is used for more complex problems.

Algorithms for calculating variance

Crystal structure evaluation: calculating relative stabilities and other criteria: general discussion

Crystal structure evaluation: calculating relative stabilities and other criteria: general discussion