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Low-pass and Savitzky-Golay filter variance (left).
In [6], an adaptive Gaussian filtering algorithm, in which the filter variance is adapted to both noise characteristics and the local variance of the signal, is studied.
In other words, if we want to estimate the process (or observation) noise variance matrix with the Sage-Husa adaptive filter, variance matrix of the observation noise (or the process noise) should be already known.
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Figure 7 Kernel PDF estimator of filtered variance and adaptive cumulant.
How to achieve further variance reduction: for particle filtering, variance reduction can be achieved in several ways.
Here the modulation appeared excitation-inhibition-coupled, as identified by calculating a continuous power-index for the relevant 20 100 Hz band of neural activity ( = filtered variance in the time domain) in the left or right optic lobe (Figs. 9A; red and blue traces, respectively).
As a final filter the variance of an FFRP's target genes were required to be significantly correlated with the FFRP's expression (Benjamini-Hochberg multiple hypothesis correction ≤0.05).
Although this might seem irrelevant for the filtering problem, variance overestimation is critical when predicting future instances of the time-series, as the density becomes too wide to be informative.
Data were filtered by variance (variance quantile <0.60) to remove noise and to increase detection power [87].
PHR SNPs were subjected to additional filters (reproducibility, variance and nMinorHom).
For variable filtering by variance and imputation of missing values the bias was negligible.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com