mml

Class ExponentialUPM

java.lang.Object

la.la.Value

la.la.Function

la.la.Function.Native

mml.UPModel

mml.ByPdf

mml.Continuous

mml.ExponentialUPM

All Implemented Interfaces:

java.lang.Comparable<Value>

public class ExponentialUPM
extends Continuous

The class of UnParameterised (negative-) Exponential Model(s). For most purposes MML.Exponential and ExponentialUPM.M should be enough. Also see Laplace.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
class	ExponentialUPM.M The fully parameterised (negative-) Exponential Model, has statistical parameter A, its mean.

Nested classes/interfaces inherited from class mml.Continuous

Continuous.Bounded, Continuous.Transform, Continuous.Uniform

Nested classes/interfaces inherited from class mml.UPModel

UPModel.Est

Nested classes/interfaces inherited from class la.la.Function.Native

Function.Native.WithInverse

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

Function.Cts2Cts, Function.Cts2Cts2Cts, Function.CtsD2CtsD, Function.HasInverse, Function.Native, Function.Native2, Function.Native3

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 inherited from class mml.UPModel

dp

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
ExponentialUPM(Value t)

Method Summary

Modifier and Type	Method and Description
UPModel.Est	estimator(Value ps) The prior is 1/A over [lwb, upb] and, with this prior, the MML estimate is the sample mean.
double	logF(double N, double A) F = N / A2.
ExponentialUPM.M	sp2Model(double m1, double m2, Value A) Given two-part message lengths msg1 & msg2, and statistical parameter sp, return a fully parameterised M-Model.
Vector	stats(boolean add, Value ss0, Value ss1) Combine sufficient statisticses 'ss0' and 'ss1' additively (add=true), or remove ss1 from ss0 (add=false).
Vector	stats(Vector ds, int lo, int hi) The sufficient statistics ss = stats(ds) of elements [lo, hi) of data-set ds; are [N, ∑ds(i), ∑nlAoM].
java.lang.String	toString() Return a String representation of 'this' UnParameterised Model, including its problem-defining parameters.

Methods inherited from class mml.Continuous

transform

Methods inherited from class mml.UPModel

apply, defnParams, main, stats, stats, transform

Methods inherited from class la.la.Function

bOp, fromBop, fromUop, type, uOp

Methods inherited from class la.la.Value

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

Methods inherited from class java.lang.Object

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

Constructor Detail

ExponentialUPM

public ExponentialUPM(Value t)

Method Detail

stats

public Vector stats(Vector ds,
                    int lo,
                    int hi)

The sufficient statistics ss = stats(ds) of elements [lo, hi) of data-set ds; are [N, ∑ds(i), ∑nlAoM]. Also see ExponentialUPM.M.nlLH(la.la.Value). More on stats here.

Specified by:

stats in class UPModel

stats

public Vector stats(boolean add,
                    Value ss0,
                    Value ss1)

Description copied from class: UPModel

Combine sufficient statisticses 'ss0' and 'ss1' additively (add=true), or remove ss1 from ss0 (add=false). Also see stats(ds,lo,hi).

Specified by:

stats in class UPModel

sp2Model

public ExponentialUPM.M sp2Model(double m1,
                                 double m2,
                                 Value A)

Description copied from class: UPModel

Given two-part message lengths msg1 & msg2, and statistical parameter sp, return a fully parameterised M-Model. If 'this' UPModel produces a Model m, then sp2Model(m.msg1(), m.msg2(), m.statParams()) must be equivalent to m. Also see apply(sp).

Specified by:

sp2Model in class Continuous

logF

public double logF(double N,
                   double A)

F = N / A². Negative log likelihood, - log L = N log A + (SUM x_i)/A. d/d A {- log L} = N/A - (SUM x_i)/A^2. So max_LH estimate, A = (SUM x_i)/N, equals the mean. d^2/d A^2 {- log L} = - N/A^2 + 2(SUM x_i)/A^3. In expectation, F = E(d^2/d A^2 (- log L)) = - N/A^2 + 2 N A / A^3 = N/A^2. Also see estimator(ps).

estimator

public UPModel.Est estimator(Value ps)

The prior is 1/A over [lwb, upb] and, with this prior, the MML estimate is the sample mean. The Estimator's parameters ps = ⟨lwb, upb⟩, the range of A, WARNING, NOT YET TESTED(???). Also see logF(N, A).

Overrides:

estimator in class UPModel

toString

public java.lang.String toString()

Description copied from class: UPModel

Return a String representation of 'this' UnParameterised Model, including its problem-defining parameters.

Overrides:

toString in class UPModel