Tuning an analysis

Number of stripes

Warning

Rigorous rules for choosing the proper number of stripes are still being developed.

Run a few initial tests with different values. e.g. 10, 50, 100. If there is significant disagreement in the scalings measured, vary about those trial numbers. The correct number of stripes to use is that number such that when varied up or down a little, the scaling does not change.

Fit interval

In the result figure plotting \(S(l)\) vs \(\ln(l)\), if the results are good there should be a region that appears linear. You want the fit interval to cover this region. \(S(l)\) is logged in calculation, \(\ln(l)\) is logged by the scale of the plot. The fitting function accounts for this.

Histogram binning method

At each window length in the analysis, a histogram is constructed to represent the probability density function of the diffusion trajectory slices corresponding to that window length. To give valid results, the histogram must accurately represent the probability density function.

There is no histogram method that's always best. You can read more about the available methods in NumPy's numpy.histogram_bin_edges documentation. The default method for pymdea is the doane method; it performs reasonably well in most cases and is better suited to non-normal distributions than some of the others.

Maximum window length

The window_length_stop option in DeaEngine specifies what the longest window length used in the analysis should be, as a proportion of the data series' length. The default setting for this options is 0.25; that is 1/4th the overall data series length. Window lengths longer than this often begin to have difficulty resolving the underlying probability density. In some cases longer window lengths can be reasonable.

As window length approaches the overall length of the data series there are fewer and fewer diffusion trajectories, and consequently the histogram for the window length's diffusion trajectories begins to poorly represent the probability density. This is apparent when plotting \(S(l)\) vs \(\ln(l)\), e.g., with DeaPlot.s_vs_l. When the window lengths become too long to give good statistics, the corresponding entropies rapidly decreases and fall off.

Number of window lengths

The max_fit option in DeaEngine specifies the maximum number of window lengths used in the analysis. The default value is 250, which is enough to give good statistics from the linear fit but few enough not to bloat runtime. Increasing this is rarely necessary. Decreasing this can speed up analysis, and is especially useful for very long input data series, e.g., when the series has \(10^7\) or more points.