R: Normalizing constant for the hyperdirichlet distribution

B {hyper2}

R Documentation

Normalizing constant for the hyperdirichlet distribution

Description

Numerical techniques for calculating the normalizing constant for the hyperdirichlet distribution

Usage

B(H, disallowed=NULL, give=FALSE, ...)
probability(H, disallowed=NULL, ...)
mgf(H, powers, ...) 
dhyper2(ip,H,...)
dhyper2_e(e,H,include.Jacobian=TRUE)
mean_hyper2(H, normalize=TRUE, ...)
Jacobian(e)
e_to_p(e)
p_to_e(p)

Arguments

`H`	Object of class hyper2
`powers`	Vector of length `dim(x)` whose elements are the powers of the expectation; see details section
`disallowed`	Function specifying a subset of the simplex over which to integrate; default `NULL` means to integrate over the whole simplex. The integration proceeds over `p` with `disallowed(p)` evaluating to `FALSE`
`e,p`	A vector; see details
`ip`	A vector of probabilities corresponding to `indep(p)` where `p` is vector with unit sum
`include.Jacobian`	Boolean, with default `TRUE` meaning to include the Jacobian transformation in the evaluation, and `FALSE` meaning to ignore it; use `FALSE` for likelihood work and `TRUE` for probability densities
`give`	Boolean, with default `FALSE` meaning to return the value of the integral and `TRUE` meaning to return the full output of `adaptIntegrate()`
`normalize`	Boolean, indicates whether return value of `mean_hyper2()` is normalized to have unit sum
`...`	Further arguments passed to `adaptIntegrate()`

Details

Function B() returns the normalizing constant of a hyperdirichlet likelihood function. Internally, p is converted to e (by e_to_p()) and the integral proceeds over a hypercube. This function can be very slow, especially if disallowed is used.
Function dhyper2(ip,H) is a probability density function on the independent components of a unit-sum vector, that is, ip=indep(p). This function calls B() each time so might be a performance bottleneck.
Function probability() gives the probability of an observation from a hyperdirichlet distribution satisfying !disallowed(p).
Function mgf() is the moment generating function, taking an argument that specifies the powers of p needed: the expectation of prod p^powers is returned.
Function mean_hyper2() returns the mean value of the hyperdirichlet distribution. This is computationally slow (consider maxp() for a measure of central tendency). The function takes a normalize argument, not passed to adaptIntegrate(): this is Boolean with FALSE meaning to return the value found by integration directly, and default TRUE meaning to normalize so the sum is exactly 1

Value

Function B() returns a scalar: the normalization constant
Function dhyper2() is a probability density function over indep(p)
Function mean() returns a k-tuple with unit sum
Function mgf() returns a scalar equal to the expectation of p^power
Functions is.proper() and validated() return a Boolean
Function probability() returns a scalar, a (Bayesian) probability

Note

The adapt package is no longer available on CRAN; from 1.4-3, the package uses adaptIntegrate of the cubature package.

Author(s)

Robin K. S. Hankin

Examples


data(chess)
mean_hyper2(chess,tol=0.1)
maxp(chess)

# Using the 'disallowed' argument typically results in slow run times;
# use high tol for speed:

probability(chess,disallowed=function(p){p[1]>p[2]},tol=0.5)
probability(chess,disallowed=function(p){p[1]<p[2]},tol=0.5)

# Above should sum to 1 [they are exclusive and exhaustive events]

[Package hyper2 version 2.0-1 Index]