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In order to do a LRT between two mixture models with different numbers of components, I need to know the number of parameters. I would like to know the answer both for: a) Gaussian mixture model b) Betabinomial mixture model

I read that for mixtures of Gaussians the number of parameters is 3k-1 (k being the number of components). Where does this number come from?

Thanks!

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  • $\begingroup$ k means, k variances, and k weights that sum up to one, hence of effective dimension k-1 $\endgroup$ – Xi'an Mar 26 '18 at 11:19
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If there are no restrictions on the parameters of the components of a finite mixture model, then the only restriction is that the mixture weights should sum to one. Hence the total number of independent parameters in a $k$-mixture is:

$k*$(num of parameters of each component) $+ k-1$.

Since the Gaussian has 2 parameters the answer to a) is $3k-1$.

The BetaBinomial distribution is not a finite mixture model and has 2 parameters (if the number of trials $n$ is known)

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