Just as de Moivre and Laplace sought for and found the normal approximation to the binomial, Pearson sought for and found a multivariate normal approximation to the multinomial distribution.
32.
Dirichlet distributions are very often used as prior distributions in Bayesian statistics, and in fact the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution.
33.
In factor analysis and latent trait analysis the latent variables are treated as continuous normally distributed variables, and in latent profile analysis and latent class analysis as from a multinomial distribution.
34.
Blei and Lafferty argue that applying Gibbs sampling to do inference in this model is more difficult than in static models, due to the nonconjugacy of the Gaussian and multinomial distributions.
35.
Where there are more than two categories, and an exact test is required, the multinomial test, based on the multinomial distribution, must be used instead of the binomial test.
36.
Yes, I ran into the same problem, which is why I went to the multinomial distribution & ndash; rather than remove one of the highest rollls, remove them all.
37.
Note also that in the case of the Bernoulli, binomial, categorical and multinomial distributions, the support of the distributions is not the same type of data as the parameter being predicted.
38.
Note that the same formula is derived in the article on the Dirichlet-multinomial distribution, as part of a more general discussion of integrating Dirichlet distribution priors out of a Bayesian network.
39.
The beta-binomial is a one-dimensional version of the Dirichlet-multinomial distribution, as the binomial and beta distributions are univariate versions of the multinomial and Dirichlet distributions, respectively.
40.
For categorical and multinomial distributions, the parameter to be predicted is a " K "-vector of probabilities, with the further restriction that all probabilities must add up to 1.
