mml

Class Linear1.Est

java.lang.Object

la.la.Value

la.la.Function

la.la.Function.Native

mml.Estimator

mml.UPModel.Est

mml.UPFunctionModel.Est

mml.Linear1.Est

All Implemented Interfaces:

java.lang.Comparable<Value>

Enclosing class:

Linear1

public class Linear1.Est
extends UPFunctionModel.Est

An Estimator of a, b and σ in y = a x +b + N(0,σ), where estimator parameter ps = ⟨b_min, b_max, σ_min, σ_max⟩ . It is possible to change the prior(a,b,σ) by overriding it in a subclass of Est.

Nested Class Summary

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

Modifier and Type	Field and Description
double	bMax Bounds on 'b'; prior, pr(b) is uniform.
double	bMin Bounds on 'b'; prior, pr(b) is uniform.
protected double	k3 latticeConstant(3).
protected double	R_b bMax-bMin and log(sigmaMax)-Math.log(sigmaMin) resp.
protected double	R_s bMax-bMin and log(sigmaMax)-Math.log(sigmaMin) resp.
double	sigmaMax Bounds on σ; prior, pr(σ) ~ 1/σ .
double	sigmaMin Bounds on σ; prior, pr(σ) ~ 1/σ .

Fields inherited from class mml.Estimator

params

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
Est(Value ps) Parameter ps = ⟨bMin, bMax, sigmaMin, sigmaMax⟩.

Method Summary

Modifier and Type	Method and Description
double	logF(double N, double sigma, double x2bar, double xbar) The log of the Fisher information from N, σ, mean(xi2), and mean(xi).
double	nlPrior(double a, double b, double sigma) The negative log prior on ⟨a, b, σ⟩.
Linear1.M	ss2Model(Value ss) Given sufficient statistics ss = stats(ds) of a data-set ds, estimate a fully parameterised Model.

Methods inherited from class mml.UPFunctionModel.Est

ds2FunctionModel, ds2Model, ss2FunctionModel

Methods inherited from class mml.UPModel.Est

defnParams, sp2Model, stats, stats, toString

Methods inherited from class mml.Estimator

apply, asUPModel, ds2Model, ds2ModelSp, ss2ModelSp, stats, stats

Methods inherited from class la.la.Function

bOp, fromBop, fromUop, main, 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

Field Detail

bMin

public final double bMin

Bounds on 'b'; prior, pr(b) is uniform.

bMax

public final double bMax

Bounds on 'b'; prior, pr(b) is uniform.

sigmaMin

public final double sigmaMin

Bounds on σ; prior, pr(σ) ~ 1/σ .

sigmaMax

public final double sigmaMax

Bounds on σ; prior, pr(σ) ~ 1/σ .

R_b

protected double R_b

bMax-bMin and log(sigmaMax)-Math.log(sigmaMin) resp.

R_s

protected double R_s

bMax-bMin and log(sigmaMax)-Math.log(sigmaMin) resp.

k3

protected double k3

latticeConstant(3).

Constructor Detail

Est

public Est(Value ps)

Parameter ps = ⟨bMin, bMax, sigmaMin, sigmaMax⟩.

Method Detail

nlPrior

public double nlPrior(double a,
                      double b,
                      double sigma)

The negative log prior on ⟨a, b, σ⟩. This is, uniform on the slope-angle arctan(a) in (-π/2,π/2), uniform on b over its range, and 1/σ on σ over its range. A subclass can override the (-log) prior if necessary.

logF

public double logF(double N,
                   double sigma,
                   double x2bar,
                   double xbar)

The log of the Fisher information from N, σ, mean(x_i²), and mean(x_i). (Remember that the x_i are "common knowledge.")

ss2Model

public Linear1.M ss2Model(Value ss)

Given sufficient statistics ss = stats(ds) of a data-set ds, estimate a fully parameterised Model.

Specified by:

ss2Model in class UPFunctionModel.Est