rDirichlet {IMIFA}

Simulate Mixing Proportions from a Dirichlet Distribution

Description

Generates samples from the Dirichlet distribution with parameter alpha efficiently by simulating Gamma(alpha, 1) random variables and normalising them.

Usage

rDirichlet(G,
           alpha,
           nn = 0L)

Arguments

G

The number of clusters for which weights need to be sampled.

alpha

The Dirichlet hyperparameter, either of length 1 or G. When the length of alpha is 1, this amounts to assuming an exchangeable prior, which doesn't favour one component over another. Be warned that this will be recycled if necessary. Larger values have the effect of making the returned samples more equal.

nn

A vector giving the number of observations in each of G clusters so that Dirichlet posteriors rather than priors can be sampled from. This defaults to 0, i.e. simulation from the prior. Must be non-negative. Be warned that this will be recycled if necessary.

Value

A Dirichlet vector of G weights which sum to 1.

Note

Though the function is available for standalone use, note that few checks take place, in order to speed up repeated calls to the function inside mcmc_IMIFA. In particular, alpha and nn may be invisibly recycled.

While small values of alpha have the effect of increasingly concentrating the mass onto fewer components, note that this function may return NaN for excessively small values of alpha, when nn=0; see the details of rgamma for small shape values.

References

Devroye, L. (1986) Non-Uniform Random Variate Generation, New York, NY, USA: Springer-Verlag, p. 594.

Examples

(prior      <- rDirichlet(G=5, alpha=1))
(posterior  <- rDirichlet(G=5, alpha=1, nn=c(20, 41, 32, 8, 12)))
(asymmetric <- rDirichlet(G=5, alpha=c(3,4,5,1,2), nn=c(20, 41, 32, 8, 12)))