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Dirichlet prior for a nonparametric distribution

Source: R/constructors.R
Dirichlet.Rd

A Dirichlet prior over the weights of a nonparametric probability mass function, used to specify an estimated NonParametric() distribution whose PMF is estimated during model fitting. Give either alpha directly, or a reference prior PMF together with a concentration.

Usage

Dirichlet(alpha, prior, concentration, ...)

Arguments

alpha

A positive numeric vector of concentration parameters.

prior

Either a numeric PMF vector (zero-indexed, i.e. the first entry represents probability mass at zero) or a dist_spec object. If a dist_spec object is provided it will be discretised and the PMF extracted. If numeric, it will be normalised to sum to one internally.

concentration

A positive scalar controlling how tightly the Dirichlet prior concentrates around the supplied PMF. The Dirichlet alpha vector is computed as alpha_i = concentration * p_i where p_i is the prior PMF. Guidance on values:

  • concentration = 1: weak prior, each alpha equals the PMF value (near-uniform for roughly equal PMF entries)

  • concentration = 5-20: moderate flexibility around the reference shape

  • concentration = 50+: strong anchoring to the reference PMF

...

Not used.

Value

A <dist_spec>.

See also

NonParametric() to use the prior, and Distributions for an overview.

Examples

Dirichlet(c(1, 1, 1, 1))
#> - dirichlet distribution:
#>   alpha:
#>     1 1 1 1
Dirichlet(prior = c(0.1, 0.3, 0.4, 0.2), concentration = 10)
#> - dirichlet distribution:
#>   alpha:
#>     1 3 4 2