Mean and count priors parameterizations for Beta and Dirichlet

[bob-carpenter]

• add following parameterization of Beta

Beta_mean(theta | mu, phi) = Beta(theta | mu * phi, (1 - mu) * phi)

We could add it without any customized gradients first.

• ditto for Dirichlet

Dirichlet_mean(theta | mu, phi) = Dirichlet(theta | mu * phi)

• add a simple symmetric Dirichlet

Dirichlet_sym(theta | alpha) = Dirichlet(theta | rep(alpha, size(theta))

• and a similar symmetric Beta

Beta_sym(theta | alpha) = Beta(theta | alpha, alpha)

The latter two will save memory by allowing simpler vari implementations.

• go off and do this in Stan math with tests
• expose functions in language

[bgoodri]

I think this should be in stan-dev/math.