The probabilities computed for \ mathbf { Z } are posterior probabilities and are what is computed in the E step.
22.
In this example, the posterior probability mass is evenly split between the values 0.08 and 0.43.
23.
The posterior probabilities of GMM components computed using previous parameter values P ^ { \ text { old } } is:
24.
Therefore, the Haldane prior results in a posterior probability with expected value in the next trial equal to the maximum likelihood.
25.
Once the posterior probabilities of models have been estimated, one can make full use of the techniques of Bayesian model comparison.
26.
In the next step, we calculate a posterior probability distribution for both inclusion and coefficients by applying a standard statistical procedure.
27.
In particular, Bayes'theorem says that the posterior probability ( density ) is proportional to the likelihood times the prior probability.
28.
One advantage of such linear MMSE estimator is that it is not necessary to explicitly calculate the posterior probability density function of x.
29.
With H the observation matrix and R the observation error covariance matrix, which contains the posterior probability distribution, with Kriging mean:
30.
A Bayesian approach allows calculation of posterior probabilities of estimated phylogeny and alignment, which is a measure of the confidence in these estimates.
