The 1/e2 beam waist was determined to be 246 nm in the green channel and 375 nm in the red channel by fitting a 2D Gaussian to a profile through the diffraction limited transcription site.
Typically, the location of an individual particle is defined by the fitting a 2D Gaussian function with a set standard deviation that encompasses the pixel pattern.
The intensity extrema are found at sub-pixel accuracy by fitting a 2D function, usually a polynomial or a Gaussian, to the neighbourhood of each peak and setting the derivatives to zero [44].
This allows the centers of the isolated probes that appear as a diffraction limited spot (∼250 nm in size) to be localized with ∼10 20 nm precision by fitting to a 2D Gaussian or related point spread function model; a statistical buildup of the locations of multiple "on" events leads to an image below the diffraction limit.
Two-component Gaussian mixture approximation - The density is approximated by fitting a two component Gaussian mixture a 1 N ( μ 1, σ 1 2 ) + a 2 N ( μ 2, σ 2 2 ), where μ 1, μ 2, σ 1 2, σ 2 2, a 1, and a2 are estimated from the observations.
Tuning width was estimated by fitting a Gaussian with 3 parameters (amplitude, width, and basis level) for each experiment and filter condition, and using a paired 2-tailed t-test comparing filter conditions within experiments.
Geomorphology 60, 337 358], with burial doses (Db) calculated by fitting a single Gaussian curve to the peak of a multi-Gaussian summed probability distribution (PDFGaussian).
An estimation of energy resolution was obtained by fitting a Gaussian on the photopeak (662 keV) of the energy spectrum.
The pdf is a probability density function of the GC content being different from the average, which is estimated by fitting a mixture of Gaussian distributions (Additional file 1: Figure S2).
A reconstruction of the underlying probability density is achieved by fitting a Gaussian mixture model (GMM) (Equation 4) to the particles, p u x t | z 0 : t ; π, μ, Σ = ∑ k = 1 K π k · N x t ; μ k, Σ k (4).
