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We pose the problem as estimating the parameters of a Gaussian mixture model (GMM) from samples of the underlying distribution, where the mixture weights are equal and set to 1/M.
Since we are concerned with the generation of plausible datasets, rather than just plausible samples of the underlying function values, it follows that we are actually interested in y(x) rather than f(x).
These input models are often constructed from a set of experimental samples of the underlying random field.
However, many of these large-scale, case-control studies did not use representative samples of the underlying populations from which the cases were derived.
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A solid sample of the underlying material may help clarify the magnitude of this contribution and help assign sources for the ions and elements detected.
First, our study children were identified through a convenience sample rather than a representative sample of the underlying population.
These analyses used methods developed for case-cohort samples that assume the controls in this study approximate a hypothetical sample of the underlying "cohort" that gave rise to the cases.
When this occurs, it suggests each group represents a good sample of the underlying distribution, and the two groups are combined to form a single null ensemble used to calculate final statistics.
This finding translates into an estimated overall population prevalence of 8.4%9595% CI 6.8%–10.1%) when findings are extrapolated from our stratified sample to the underlying population of the 9 sites by using direct standardization.
Now, drift and diffusion coefficients have bounded growth as stated in (7); moreover, sample paths of the diffusion process (i.e., the molecular binding process) are continuous since the sample paths of the underlying Brownian motion are continuous.
This means that the sampling rate of the output signal from the HE-AAC decoder will always be twice that of the sampling rate of the underlying AAC decoder.
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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