Updating mean and variance estimates an improved method leonardo dicaprio dating 2016
We can use a property of the variance to avoid the catastrophic cancellation in this formula, namely the variance is invariant with respect to changes in a location parameter are small then there are no problems with the sum of its squares, on the contrary, if they are large it necessarily means that the variance is large as well.
For a particularly robust two-pass algorithm for computing the variance, one can first compute and subtract an estimate of the mean, and then use this algorithm on the residuals.
This is particularly bad if the standard deviation is small relative to the mean.
However, the algorithm can be improved by adopting the method of the assumed mean.
It is often useful to be able to compute the variance in a single pass, inspecting each value only once; for example, when the data are being collected without enough storage to keep all the values, or when costs of memory access dominate those of computation.
For such an online algorithm, a recurrence relation is required between quantities from which the required statistics can be calculated in a numerically stable fashion.