Updating mean and variance estimates an improved method dating ru messages ph

Posted by / 15-Apr-2016 15:55

The parallel algorithm below illustrates how to merge multiple sets of statistics calculated online.The algorithm can be extended to handle unequal sample weights, replacing the simple counter n with the sum of weights seen so far.Many possibilities exist but because of the incremental computation particular attention needs to be paid to numerical stability.If we were to ignore numerical accuracy we could use a simple derivation to show that the following updates for is very large.Meng provides a simple implementation requiring only 24 floating point operations per observation.Algorithms for calculating variance play a major role in computational statistics.West (1979) Assume that all floating point operations use standard IEEE 754 double-precision arithmetic.

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.

However, the algorithm can be improved by adopting the method of the assumed mean.

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.

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.

can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.

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we would like to calculate simple statistics like the weighted mean or weighted variance of the sample without having to store all samples, and by processing them one-by-one.