mml

Class NormalUPM

java.lang.Object

la.la.Value

la.la.Function

la.la.Function.Native

mml.UPModel

mml.ByPdf

mml.Continuous

mml.NormalUPM

All Implemented Interfaces:

java.lang.Comparable<Value>

Direct Known Subclasses:

NormalMu

public class NormalUPM
extends Continuous

The class of UnParameterised Normal Models (Gaussian distributions). For most purposes MML.Normal and NormalUPM.M should be enough, with little need to call upon NormalUPM directly?

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
class	NormalUPM.Est The standard Estimator for a Normal Model with unknown μ and σ.
class	NormalUPM.M NormalUPM.M, a fully parameterised Normal Model (Gaussian probability distribution), Nμ,σ.

Nested classes/interfaces inherited from class mml.Continuous

Continuous.Bounded, Continuous.Transform, Continuous.Uniform

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

Modifier	Constructor and Description
protected	NormalUPM() A constructor for any subclass of NormalUPM that deals with its own problem-defining parameter(s), e.g., NormalMu.
	NormalUPM(Value t) Constructor for UnParameterised Normal Models; note t=triv! There is little need to call it -- use the previously prepared Normal.

Method Summary

Modifier and Type	Method and Description
NormalUPM.M	apply(Value ms) apply((μ, σ)), return a fully parameterised Normal M Model.
UPModel.Est	estimator(Value ps) Return an Estimator for the Normal distribution where parameter ps = (μmin, μmax, σmin, σmax) is for the Uniform prior on μ, and 1/σ on σ, within the bounds.
UPModel.Est	estimatorB(Value bounds) Return an Estimator for the Normal distribution where parameter bounds = (μmin, μmax) is for the Uniform prior on μ; σ ~ nearly 1/σ and is unbounded.
static Value.Cts	estSigma(Value ss, double k, double mu, double sigma1) estSigma is called upon by NormalUPM.estimatorB and also by NormalMu.estimatorB to estimate σ.
NormalUPM.M	sp2Model(double m1, double m2, Value mu_sig) Given (msg1, msg2, (μ, σ)) return a fully parameterised Normal M Model.
static Vector	ss(Vector ds, int lo, int hi) Given a data-set, ds, return its sufficient statistics, ss, that is [# of items, sum, sum of squares, nlAoM}].
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) Return the sufficient statistics of data-set ds; calls ss(la.maths.Vector, int, int)(ds).
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

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

NormalUPM

public NormalUPM(Value t)

Constructor for UnParameterised Normal Models; note t=triv! There is little need to call it -- use the previously prepared Normal.

NormalUPM

protected NormalUPM()

A constructor for any subclass of NormalUPM that deals with its own problem-defining parameter(s), e.g., NormalMu. Note '( )', no problem defining parameter seen here.

Method Detail

apply

public NormalUPM.M apply(Value ms)

apply((μ, σ)), return a fully parameterised Normal M Model.

Overrides:

apply in class UPModel

sp2Model

public NormalUPM.M sp2Model(double m1,
                            double m2,
                            Value mu_sig)

Given (msg1, msg2, (μ, σ)) return a fully parameterised Normal M Model.

Specified by:

sp2Model in class Continuous

stats

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

Return the sufficient statistics of data-set ds; calls ss(la.maths.Vector, int, int)(ds). 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

ss

public static Vector ss(Vector ds,
                        int lo,
                        int hi)

Given a data-set, ds, return its sufficient statistics, ss, that is [# of items, sum, sum of squares, nlAoM}]. Static ss(ds) is called by stats(ds), and elsewhere. (Beware of possible numerical stability problems if the data-set ds is huge.)

estimator

public UPModel.Est estimator(Value ps)

Return an Estimator for the Normal distribution where parameter ps = (μ_min, μ_max, σ_min, σ_max) is for the Uniform prior on μ, and 1/σ on σ, within the bounds. It tries to behave well in most situations.

Overrides:

estimator in class UPModel

estimatorB

public UPModel.Est estimatorB(Value bounds)

Return an Estimator for the Normal distribution where parameter bounds = (μ_min, μ_max) is for the Uniform prior on μ; σ ~ nearly 1/σ and is unbounded. This estimator requires minimal user input (parameter 'bounds'). It should not "blow up" even on zero data. It tries to behave well in most situations. On the other hand if you do need more control, implement another estimator. The Estimator calls estSigma(la.la.Value, double, double, double) to estimate σ. Also see estimator((,,,)).

estSigma

public static Value.Cts estSigma(Value ss,
                                 double k,
                                 double mu,
                                 double sigma1)

estSigma is called upon by NormalUPM.estimatorB and also by NormalMu.estimatorB to estimate σ. That is why estSigma is here and static. Note, k is the appropriate lattice constant for two or one parameters. The returned value may not be less than 2× the per-datum AoM. If the number of data is ≤1, sigma1 is returned.

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