For JointSNVMix1, the conditional distribution for each sample is modelled as a three component mixture of Binomial densities, where the densities correspond to the genotypes AA, AB, BB.
Then the complete data log-likelihood is: 10 Eq. 8 is a mixture of binomial regression equations fitted through the R package "mixtools".
In principle, it is preferable to model the counts as a mixture of negative binomial distributions to model over dispersion of the count data.
The other class of methods focuses on modeling over-dispersion in read counts, by means of models such as negative-binomial model, Poisson-Gamma model, beta-binomial model, and two-component mixture of beta-binomial model [ 19, 23– 26].
Mixtures of the negative binomial distribution have also been widely used in connection with applications in a plethora of fields.
Future research could extend the marginalized count regression models to mixtures of two negative binomial distributions or to those based on Eq. (11) as an alternative to MNB-Pois, to allow the mixing probabilities to depend on covariates, and to longitudinal data.
With the aim of expanding the pool of two-part marginalized models for counts, special consideration is given to data generating mechanisms based on mixtures of two Poissons and a negative binomial with a Poisson distribution.
Variational Bayes learning or mean field approximation is widely used in statistical models which are made of mixtures of exponential distributions, for example, normal mixtures, binomial mixtures, and hidden Markov models.
Mixtures of Poisson distributions (Mullahy, 1997) and negative binomial distributions (Deb and Holmes, 2000; Deb and Trivedi, 1997; Jimenez Martin et al., 2002) have been suggested for resource use data, and mixtures of Gamma distributions for cost data (Deb and Burgess, 2003).
Even Carl Linnaeus, who pioneered his system of binomial nomenclature in the mid-18th century, catalogued only one kind of animal – those that exist.
