Rev Language Reference

dnCategorical - The Categorical Distribution

The Categorical distribution generalizes the Bernoulli distribution, describing the probability of choosing from a number of outcomes, each with their own probability.

Aliases

  • dnCat

Usage

dnCategorical(Simplex p)

Arguments

p : Simplex (pass by const reference)
The probability for each category.

Domain Type

Natural

Details

The categorical distribution takes a parameter p, a simplex (i.e. vector, the elements of which sum to 1). It returns outcome i with probability p[i]. A typical scenario where a categorical variable is used is in the definition of a variable drawn from a mixture. A vector of mixture components is set up first, and then a stochastic variable drawn from a categorical distribution is used as an index in a deterministic assignment that points to a component in the mixture. See example below.

Example

# Define a stochastic variable x that is drawn from
# a categorical distribution with 4 categories, each
# category having the same probability, then examine
# the value of x.
x ~ dnCat( simplex(1,1,1,1) )
x

# Draw 10 values from the distribution and place them
# in a vector a, then examine a.
for ( i in 1:10 ) {
    a[i] <- x
    x.redraw()
}
a

# Use x in defining a deterministic variable y taking
# on values from a mixture of RealPos values representing
# rates from a discretized scaled gamma distribution
# with four categories.
shape ~ dnExp( 10.0 )
rates := fnDiscretizeGamma( shape, shape, 4 )
y := rates[x]

See Also

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