Sampling error when measuring the average diffusion coefficient

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Sampling errors is:

the error created when only a subset of a population is sampled - [@catipovic2013Improving the quantification of Brownian motion]

If we want to know the accuracy when determining the average diffusion coefficient, the error will be dominated by the standard deviation of the measured variances (see: calculating diffusion coefficient from jump statistics):

$$\sigma_\textrm{sampling} = \sqrt{\frac{2}{\textrm{N} -1}}$$

And, as expected, the more particles we measure the better sampling accuracy we'll get (although see: Sources of error in measuring diffusion coefficient through nanoparticle tracking analysis)

There's a caveat here, though. N is the number of measurements, so for 15 particles acquired along 100 frames these are 1500 data points. It is like building a distribution of all the jumps.

However, if we use the mean squared displacement (see: Calculating diffusion coefficient from mean squared displacement data) we have:


But in this case $N$ is the number of particles.


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Aquiles Carattino
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