How do I implement the standard deviation of the standard deviation in MATLAB?

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Glazio 2017-7-1

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评论： Image Analyst 2017-7-19

Are there in MATLAB already predefined functions to calculate the standard deviation of the standard deviation or the standard deviation of the average standard deviation?

(use Matlab R2012a)

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Image Analyst 2017-7-1

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You simply use std() again on the whole group (vector or matrix) of standard deviations that you have.

stdOfGroup = std(individualStDevs);

The standard deviation of the standard deviations will give you the correct result. It will give you the standard deviation of the standard deviations. What Star was showing was that this does not give you the standard deviation of the combined populations. But after your explanation I don't think you're after that.

You have a Monte Carlo simulation and it gives some output. Let's call it y. Now if you run the simulations lots of times, y will be different each time. If you plot y versus "number of runs" you might find y to be highly variable (high st dev) for low number of runs but y settles down to a "steady state" as the number of runs increases. So, say for less than a thousand runs, y might be 1000 +/- 200, but for a million runs y might be 1000 +/- 50, and for 10 million runs you might find y = 1000 +/- 10. So stdev decreases from 200 to 50 to 10 as the number of experiments/runs/trials increases from a thousand to ten million.

So what you might want to do is to plot y vs. number of runs and plot std(y) vs. # runs. You might have a funnel shaped scatterplot and you will probably observe how the width of the scatter decreases with number of runs. The y funnel will settle down to the steady state mean of y while the stdev funnel will settle down to 0 eventually (hopefully but not necessarily). So how do you decide on the number of runs to use? You could do a moving mean with moveman() or conv() and see where the mean of this scatter plot levels out. Or you could use movstd() or stdfilt() to get a measure of the "width" of the funnel by using it's standard deviation. So if your stddev funnel starts at 50 and narrows down towards zero, you might somewhat arbitrarily say a std dev of std of 5 (a funnel envelope width of 5) is good for you, then you just see how many runs that corresponds to.