Number of bins of a histogram rule

estBinSize() gives the number of bins of one of the histogram rules "Sturges", "Sqrt", "Rice", "Doane", "Freedman.Diaconis" and "Scott.Normal" for a pseudotime vector, multiplied by drop_fac.

Usage

estBinSize(time_vector, nPoints, drop_fac, bin_method)

Arguments

time_vector: The pseudotime values to bin.
nPoints: The number of values of time_vector.
drop_fac: The factor that multiplies the number of bins of the rule; values below 1 give fewer, wider bins.
bin_method: The rule (see Details).

Value

The number of bins of the rule times drop_fac, not rounded; sc.squeeze() rounds it up.

Details

With n the number of points (nPoints), the rules give:

"Sturges": log2(n) + 1 bins (Sturges 1926). Srivastava et al. (2024), Supplementary Section S1.1, writes the number of bins as \(B = [(\log_2(N)+1) \times k]\), with k the drop factor of their Section 2.1, and every other rule the same way, with the brackets around the whole product: the rule times drop_fac is rounded up.
"Sqrt": sqrt(n) bins, a common rule of thumb.
"Rice": 2 n^(1/3) bins (Lane and Scott), close to the oversmoothed number of bins (2n)^(1/3) of Terrell and Scott (1985).
"Doane": 1 + log2(n) + log2(1 + |g| / s) bins, with g the sample skewness of the points and s = sqrt(6 (n - 2) / ((n + 1) (n + 3))) (Doane 1976).
"Freedman.Diaconis": bins of width 2 IQR / n^(1/3), with IQR the interquartile range of the points (Freedman and Diaconis 1981).
"Scott.Normal": bins of width 3.49 sd / n^(1/3), with sd the standard deviation of the points (Scott 1979).

The widths of Freedman-Diaconis and Scott are turned into a number of bins by dividing the range of the points by them. A width of 0 (all points equal, or for Freedman-Diaconis equal first and third quartiles) or an undefined width (Scott with a single point) gives one bin, with a message.

References

Sturges HA (1926). The choice of a class interval. Journal of the American Statistical Association 21(153), 65-66. doi:10.1080/01621459.1926.10502161

Doane DP (1976). Aesthetic frequency classifications. The American Statistician 30(4), 181-183. doi:10.1080/00031305.1976.10479172

Scott DW (1979). On optimal and data-based histograms. Biometrika 66(3), 605-610. doi:10.1093/biomet/66.3.605

Freedman D, Diaconis P (1981). On the histogram as a density estimator: L2 theory. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 57(4), 453-476. doi:10.1007/BF01025868

Terrell GR, Scott DW (1985). Oversmoothed nonparametric density estimates. Journal of the American Statistical Association 80(389), 209-214. doi:10.1080/01621459.1985.10477163

Lane DM, Scott D. Histograms. In Online Statistics Education: A Multimedia Course of Study, Rice University. https://onlinestatbook.com/2/graphing_distributions/histograms.html

Srivastava P, Benegas Coll M, Götz S, Nueda MJ, Conesa A (2024). scMaSigPro: differential expression analysis along single-cell trajectories. Bioinformatics 40(7), btae443. doi:10.1093/bioinformatics/btae443

Author

Priyansh Srivastava spriyansh29@gmail.com