mml

Class Dirichlet.M

java.lang.Object

la.la.Value

mml.Model

mml.UPModel.M

mml.ByPdf.M

mml.R_D.M

mml.Dirichlet.M

All Implemented Interfaces:

java.lang.Comparable<Value>, HasPdf

Enclosing class:

Dirichlet

public class Dirichlet.M
extends R_D.M

The fully parameterised Dirichlet Model (probability distribution); the UnParameterised Model is here. The business of M is in nlPdf(d).

Nested Class Summary

Nested classes/interfaces inherited from class mml.R_D.M

R_D.M.Transform

Nested classes/interfaces inherited from class mml.Model

Model.Defaults

Nested classes/interfaces inherited from class la.la.Value

Value.Atomic, Value.Bool, Value.Char, Value.Chars, Value.Cts, Value.Defer, Value.Discrete, Value.Enum, Value.Inc_Or, Value.Int, Value.Lambda, Value.List, Value.Maybe, Value.Option, Value.Real, Value.Scannable, Value.Structured, Value.Triv, Value.Tuple

Field Summary

Fields

Modifier and Type	Field and Description
Vector	alpha M's statistical parameter; αi > 0, 0 ≤ i < D.
double	logB The (log(B)) normalising constant.

Fields inherited from class mml.Model

msg1, msg2, sp

Fields inherited from class la.la.Value

C, comparator, CR, E, eight, ffalse, five, fiveR, four, fourR, half, negCR, negOne, negOneR, negTenR, nilVal, nine, None, one, oneR, PI, PIby2, point01, point1, point5, point9, quarter, seven, six, ten, tenR, three, threeR, triv, ttrue, two, twoR, zero, zeroR

Constructor Summary

Constructors

Constructor and Description
M(double msg1, double msg2, Value alpha) Note, the length of the statistical parameter α is D = K + 1.

Method Summary

Modifier and Type	Method and Description
double	nlLH(Value ss) Assumes that statistics are the data-set itself.
double	nlPdf(Value d) pdf(d) = (∏i diαi-1) / B(α) where datum 'd' is a Vector in [0,1]D such that ||d||1 = 1.
Vector	random() Generate a Dirichlet-distributed random variate, a Vector of D elements.

Methods inherited from class mml.R_D.M

D, random_x, random, transform

Methods inherited from class mml.ByPdf.M

nlPr, nlPr, pdf

Methods inherited from class mml.UPModel.M

asGiven, asGiven, stats, stats, toString

Methods inherited from class mml.Model

asEstimator, asUPModel, m1m2sp, msg, msg1, msg1bits, msg2, msg2bits, msgBits, nl2LH, nl2Pr, pr, random, randomSeries, statParams, stats, stats, sumNlPr, transform, type, zeroTriv

Methods inherited from class la.la.Value

AoM, apply, bOp, compareTo, cons, cts, elt, errMsg, error, force, isTuple, just, main, n, nElts, nlAoM, pair, print, quad, real, RTE, triple, tuple, UOE, uOp, x

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

alpha

public final Vector alpha

M's statistical parameter; α_i > 0, 0 ≤ i < D.

logB

public final double logB

The (log(B)) normalising constant.

Constructor Detail

M

public M(double msg1,
         double msg2,
         Value alpha)

Note, the length of the statistical parameter α is D = K + 1.

Method Detail

nlPdf

public double nlPdf(Value d)

pdf(d) = (∏_i d_i^α_i-1) / B(α) where datum 'd' is a Vector in [0,1]^D such that ||d||₁ = 1. Hence 'd' has K = D - 1 degrees of freedom, which has implications for d's nlAoM (as for Direction). Note, if α_i > 1 then a datum 'd' s.t. d_i = 0 has pdf(d)=0 and nlPr(d)=∞. Also see nlPr(d).

Specified by:

nlPdf in interface HasPdf

Specified by:

nlPdf in class ByPdf.M

nlLH

public double nlLH(Value ss)

Assumes that statistics are the data-set itself.

Specified by:

nlLH in class Model

random

public Vector random()

Generate a Dirichlet-distributed random variate, a Vector of D elements. It makes use of Continuous.M.random(). (See [wikip][10/2014].)

Overrides:

random in class R_D.M