I am reading a paper, and it is said "state observationprobability densities were single mixture Gaussian observation densities". My question is: Isn't a single mixture gaussian the same that a regular 1-D gaussian?

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    $\begingroup$ I single mixture sounds to me like a mixture of two different Gaussian distributions which may not look like a single Gaussian distribution at all. It is likely to be bimodal. The existence of a mean and covariance matrix can happen with a mixture distribution without it being a single Gaussian distribution. $\endgroup$ – Michael R. Chernick Aug 14 '17 at 16:47

Single mixture gaussian does not seem to be an accepted term, but it is probably equivalent to a regular gaussian distribution, either univariate or multivariate (more context is needed to tell which).

Without knowing which paper you are talking about, I would guess that the authors modeled state observation distribution as a single gaussian, but wanted to hint that the model could be generalized to a gaussian mixture with $n > 1$ components, even though they did not do so.

edit: paper is here

After reading the context in the paper, I am more confident that the authors intended single mixture gaussian to just mean a normal gaussian distribution, as they talk about a single mean and covariance matrix.

  • $\begingroup$ Thanks! But isn't the author talking here about a multivariate gaussian with every dimension being the dimension of the feature vector (in this case, 6 AR coefficients and RMS, so dimension 7)? $\endgroup$ – Moltimor Aug 14 '17 at 20:31

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