mml

Class vMF.M

java.lang.Object

la.la.Value

mml.Model

mml.UPModel.M

mml.ByPdf.M

mml.R_D.M

mml.Direction.M

mml.vMF.M

All Implemented Interfaces:

java.lang.Comparable<Value>, HasPdf

Enclosing class:

vMF

public class vMF.M
extends Direction.M

The fully parameterised von Mises - Fisher Model of Directions in R^D. Its statistical parameters are mean μ and concentration κ. The UnParameterised Model is vMF.

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
double	kappa The concentration parameter, κ.
double	logCD The concentration parameter, κ.
Vector	mu The mean Direction, μ.
double[]	mu_x The mean Direction mu as double[].

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 sp) The vMF's statistical parameters sp = (μ, κ).

Method Summary

Modifier and Type	Method and Description
double	kappa() κ ≥ 0, the concentration parameter.
Vector	mu() μ, the mean, a Direction in RD.
double	nlLH(Value ss) Given statistics, ss = stats(ds) of a data-set, ds, return the negative log likelihood of ds.
double	nlPdf(Value v) The negative log pdf(v) for datum Direction v, return - κ μ.v - log CD(κ).
void	random(double[] x) Generate a random Direction, a random unit Vector in RD.

Methods inherited from class mml.Direction.M

nlPr

Methods inherited from class mml.R_D.M

D, random_x, random, transform

Methods inherited from class mml.ByPdf.M

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

mu

public final Vector mu

The mean Direction, μ.

mu_x

public final double[] mu_x

The mean Direction mu as double[].

kappa

public final double kappa

The concentration parameter, κ.

logCD

public final double logCD

The concentration parameter, κ.

Constructor Detail

M

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

The vMF's statistical parameters sp = (μ, κ). Note, to be safe, the constructor normalises the Vector μ.

Method Detail

mu

public Vector mu()

μ, the mean, a Direction in R^D.

kappa

public double kappa()

κ ≥ 0, the concentration parameter. κ = 0 gives the Uniform Model. For large κ, κ ~ 1/σ², the variance.

nlPdf

public double nlPdf(Value v)

The negative log pdf(v) for datum Direction v, return - κ μ.v - log CD(κ). Note that v need not be already normalised -- that is taken care of. Also see nlPr(v).

Specified by:

nlPdf in interface HasPdf

Specified by:

nlPdf in class Direction.M

nlLH

public double nlLH(Value ss)

Given statistics, ss = stats(ds) of a data-set, ds, return the negative log likelihood of ds.

Specified by:

nlLH in class Model

random

public void random(double[] x)

Generate a random Direction, a random unit Vector in R^D. Called by R_D.M.random_x(). See T.A.Wood, Simulation of the von Mises Fisher distribution, Communications in Statistics - Simulation and Computation, 23(1), pp.157-164, 1994.

Overrides:

random in class R_D.M