B | R Documentation |
Numerical techniques for calculating the normalizing constant for the hyperdirichlet distribution
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)
H |
Object of class hyper2 |
powers |
Vector of length |
disallowed |
Function specifying a subset of the simplex
over which to integrate; default |
e , p |
A vector; see details |
ip |
A vector of probabilities corresponding to |
include.Jacobian |
Boolean, with default |
give |
Boolean, with default |
normalize |
Boolean, indicates whether return value of
|
... |
Further arguments passed to |
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_{i=1}^n {p_i}^{{\rm powers}[i]}
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
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
The adapt package is no longer available on CRAN; from 1.4-3, the
package uses adaptIntegrate
of the cubature package.
Robin K. S. Hankin
loglik
# Two different measures of central tendency:
# mean_hyper2(chess,tol=0.1) # takes ~10s to run
maxp(chess) # faster
# 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]
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