[Serializable]
[DataContract]
[Quality(QualityBand.Experimental)]
public struct ConjugateDirichlet : IDistribution<double>, IDistribution, ICloneable, HasPoint<double>, CanGetLogProb<double>, SettableTo<ConjugateDirichlet>, SettableToProduct<ConjugateDirichlet>, SettableToProduct<ConjugateDirichlet, ConjugateDirichlet>, Diffable, SettableToUniform, SettableToRatio<ConjugateDirichlet>, SettableToRatio<ConjugateDirichlet, ConjugateDirichlet>, SettableToPower<ConjugateDirichlet>, SettableToWeightedSum<ConjugateDirichlet>, Sampleable<double>, CanGetMean<double>, CanGetVariance<double>, CanGetMeanAndVarianceOut<double, double>, CanSetMeanAndVariance<double, double>, CanGetLogAverageOf<ConjugateDirichlet>, CanGetLogAverageOfPower<ConjugateDirichlet>, CanGetAverageLog<ConjugateDirichlet>, CanGetLogNormalizer

Constructors

ConjugateDirichlet(ConjugateDirichlet)

Copy constructor.

Declaration

public ConjugateDirichlet(ConjugateDirichlet that)

Parameters

Type	Name	Description
ConjugateDirichlet	that

ConjugateDirichlet(Double, Double, Double, Double)

Creates a Conjugate Dirichlet distribution with given shape and scale parameters (scale = 1/rate)

Declaration

public ConjugateDirichlet(double shape, double scale, double D, double K)

Parameters

Type	Name	Description
Double	shape
Double	scale	scale = 1/rate
Double	D
Double	K

Remarks

The distribution is x^{Shape-1} exp(-Ratex) / B(x,D)^K where B(x,D)=Gamma(x)^D/Gamma(Dx).

Fields

approximationMethod

Approximation method to use for non-analytic expectations.

Declaration

public static ConjugateDirichlet.ApproximationMethod approximationMethod

Field Value

Type	Description
ConjugateDirichlet.ApproximationMethod

D

Parameter D for the distribution

Declaration

[DataMember]
public double D

Field Value

Type	Description
Double

K

Parameter K for the distribution

Declaration

[DataMember]
public double K

Field Value

Type	Description
Double

Rate

Rate parameter for the distribution

Declaration

[DataMember]
public double Rate

Field Value

Type	Description
Double

Shape

Shape parameter for the distribution

Declaration

[DataMember]
public double Shape

Field Value

Type	Description
Double

Properties

IsPointMass

Asks whether the instance is a point mass

Declaration

[IgnoreDataMember]
public readonly bool IsPointMass { get; }

Property Value

Type	Description
Boolean

Point

Sets/gets the instance as a point mass

Declaration

[IgnoreDataMember]
public double Point { get; set; }

Property Value

Type	Description
Double

Methods

Clone()

Clones this Conjugate Dirichlet.

Declaration

public object Clone()

Returns

Type	Description
Object	An object which is a clone of the current instance. This must be cast if you want to assign the result to a Conjugate Dirichlet type

Equals(Object)

Override of the Equals method

Declaration

public override bool Equals(object thatd)

Parameters

Type	Name	Description
Object	thatd	The instance to compare to

Returns

Type	Description
Boolean	True if the two distributions are the same in value, false otherwise

Overrides

ValueType.Equals(Object)

FromMeanAndMeanLog(Double, Double)

Constructs a Conjugate Dirichlet distribution with the given mean and mean logarithm.

Declaration

public static ConjugateDirichlet FromMeanAndMeanLog(double mean, double meanLog)

Parameters

Type	Name	Description
Double	mean	Desired expected value.
Double	meanLog	Desired expected logarithm.

Returns

Type	Description
ConjugateDirichlet	A new Gamma distribution.

Remarks

This function is equivalent to maximum-likelihood estimation of a Gamma distribution from data given by sufficient statistics. This function is significantly slower than the other constructors since it involves nonlinear optimization. The algorithm is a generalized Newton iteration, described in "Estimating a Gamma distribution" by T. Minka, 2002.

FromMeanAndVariance(Double, Double)

Creates a new Gamma distribution from mean and variance

Declaration

public static ConjugateDirichlet FromMeanAndVariance(double mean, double variance)

Parameters

Type	Name	Description
Double	mean	Mean
Double	variance	Variance

Returns

Type	Description
ConjugateDirichlet	A new Gamma instance

FromNatural(Double, Double, Double, Double)

Constructs a Conjugate Dirichlet distribution from its natural parameters.

Declaration

public static ConjugateDirichlet FromNatural(double shapeMinus1, double rate, double D, double K)

Parameters

Type	Name	Description
Double	shapeMinus1	shape - 1
Double	rate	rate = 1/scale
Double	D
Double	K

Returns

Type	Description
ConjugateDirichlet	A new Conjugate Dirichlet distribution

FromShapeAndRate(Double, Double)

Constructs a Gamma distribution with the given shape and rate parameters.

Declaration

[Construction(new string[]{"Shape", "Rate"})]
public static ConjugateDirichlet FromShapeAndRate(double shape, double rate)

Parameters

Type	Name	Description
Double	shape	shape
Double	rate	rate = 1/scale

Returns

Type	Description
ConjugateDirichlet	A new Gamma distribution.

FromShapeAndScale(Double, Double)

Constructs a Gamma distribution with the given shape and scale parameters.

Declaration

public static ConjugateDirichlet FromShapeAndScale(double shape, double scale)

Parameters

Type	Name	Description
Double	shape	shape
Double	scale	scale

Returns

Type	Description
ConjugateDirichlet	A new Gamma distribution.

GammaApproximation()

This is an asymptotic approximation to this distribution, derived from the Rocktaeschel approximation: ln Gamma(x) \approx (x-.5)ln(x) - x +.5ln(2*pi)

Declaration

public Gamma GammaApproximation()

Returns

Type	Description
Gamma	A gamma approximation to this distribution

GetAverageLog(ConjugateDirichlet)

The expected logarithm of that distribution under this distribution.

Declaration

public double GetAverageLog(ConjugateDirichlet that)

Parameters

Type	Name	Description
ConjugateDirichlet	that	The distribution to take the logarithm of.

Returns

Type	Description
Double	`sum_x this.Evaluate(x)*Math.Log(that.Evaluate(x))`

Remarks

This is also known as the cross entropy.

GetHashCode()

Override of GetHashCode method

Declaration

public override int GetHashCode()

Returns

Type	Description
Int32	The hash code for this instance

Overrides

ValueType.GetHashCode()

GetLogAverageOf(ConjugateDirichlet)

The log of the integral of the product of this Conjugate Dirichlet and that Conjugate Dirichlet

Declaration

public double GetLogAverageOf(ConjugateDirichlet that)

Parameters

Type	Name	Description
ConjugateDirichlet	that	That Conjugate Dirichlet

Returns

Type	Description
Double	The log inner product

GetLogAverageOfPower(ConjugateDirichlet, Double)

Declaration

public double GetLogAverageOfPower(ConjugateDirichlet that, double power)

Parameters

Type	Name	Description
ConjugateDirichlet	that
Double	power

Returns

Type	Description
Double

GetLogNormalizer()

Gets log normalizer

Declaration

public double GetLogNormalizer()

Returns

Type	Description
Double

GetLogProb(Double)

Logarithm of this Conjugate Dirichlet density function.

Declaration

public double GetLogProb(double x)

Parameters

Type	Name	Description
Double	x	Where to evaluate the density

Returns

Type	Description
Double	log(Conjugate Dirichlet(x))

GetLogProb(Double, Double, Double, Double, Double)

Logarithm of the Conjugate Dirichlet density function.

Declaration

public static double GetLogProb(double x, double shape, double rate, double D, double K)

Parameters

Type	Name	Description
Double	x	Where to evaluate the density
Double	shape	Shape parameter
Double	rate	Rate parameter
Double	D	D parameter
Double	K	K parameter

Returns

Type	Description
Double	log(Conjugate Dirichlet(x;shape,rate,D,K))

Remarks

The distribution is x^{Shape-1} exp(-Ratex) / B(x,D)^K where B(x,D)=Gamma(x)^D/Gamma(Dx)

GetMean()

Gets the expected value E(x) - calculated as shape/rate

Declaration

public double GetMean()

Returns

Type	Description
Double	E(x)

GetMeanAndVariance(out Double, out Double)

Gets the mean and variance. Note for K!=0 this requires quadrature.

Declaration

public void GetMeanAndVariance(out double mean, out double variance)

Parameters

Type	Name	Description
Double	mean	Where to put the mean
Double	variance	Where to put the variance

GetMeanInverse()

Computes E[1/x]

Declaration

public double GetMeanInverse()

Returns

Type	Description
Double

GetMeanLog()

Computes E[log(x)] using quadrature if necessary

Declaration

public double GetMeanLog()

Returns

Type	Description
Double	E[log(x)]

GetMeanLogGamma(Double)

Compute E[log G(factor * x)] using quadrature

Declaration

public double GetMeanLogGamma(double factor)

Parameters

Type	Name	Description
Double	factor	Multiplier for x

Returns

Type	Description
Double	E[log G(factor * x)]

GetMeanPower(Double)

Computes E[x^power]

Declaration

public double GetMeanPower(double power)

Parameters

Type	Name	Description
Double	power

Returns

Type	Description
Double

GetMode()

Declaration

public double GetMode()

Returns

Type	Description
Double

GetScale()

Gets the scale (1/rate)

Declaration

public double GetScale()

Returns

Type	Description
Double

GetShapeAndScale(out Double, out Double)

Gets the shape and scale (1/rate)

Declaration

public void GetShapeAndScale(out double shape, out double scale)

Parameters

Type	Name	Description
Double	shape	Where to put the shape
Double	scale	Where to put the scale

GetUnnormalisedLogProb(Double)

Declaration

public double GetUnnormalisedLogProb(double x)

Parameters

Type	Name	Description
Double	x

Returns

Type	Description
Double

GetVariance()

Gets the variance - calculated as shape/rate^2

Declaration

public double GetVariance()

Returns

Type	Description
Double	Variance

IsProper()

Asks whether this Conjugate Dirichlet instance is proper or not. A Conjugate Dirichlet distribution is proper if it's approximating gamma is proper

Declaration

public bool IsProper()

Returns

Type	Description
Boolean	True if proper, false otherwise

IsProper(Double, Double)

Asks whether a Conjugate Dirichlet distribution is proper or not. A Conjugate Dirichlet distribution is proper only if Shape > 0 and Rate > 0.

Declaration

public static bool IsProper(double shape, double rate)

Parameters

Type	Name	Description
Double	shape	shape parameter for the Conjugate Dirichlet
Double	rate	rate parameter for the Conjugate Dirichlet

Returns

Type	Description
Boolean	True if proper, false otherwise

IsUniform()

Asks whether this instance is uniform

Declaration

public bool IsUniform()

Returns

Type	Description
Boolean	True if uniform, false otherwise

MaxDiff(Object)

The maximum difference between the parameters of this Conjugate Dirichlet and that Conjugate Dirichlet

Declaration

public double MaxDiff(object thatd)

Parameters

Type	Name	Description
Object	thatd	That Conjugate Dirichlet

Returns

Type	Description
Double	The maximum difference

Remarks

a.MaxDiff(b) == b.MaxDiff(a)

Newton1DMaximise(Double, Converter<Double, Double>, Converter<Double, Double>, Converter<Double, Double>)

Declaration

public static double Newton1DMaximise(double initx, Converter<double, double> f, Converter<double, double> dfxfunc, Converter<double, double> dhxfunc)

Parameters

Type	Name	Description
Double	initx
Converter<Double, Double>	f
Converter<Double, Double>	dfxfunc
Converter<Double, Double>	dhxfunc

Returns

Type	Description
Double

PointMass(Double)

Creates a point mass Conjugate Dirichlet distribution

Declaration

public static ConjugateDirichlet PointMass(double mean)

Parameters

Type	Name	Description
Double	mean	The location of the point mass

Returns

Type	Description
ConjugateDirichlet	A new point mass Conjugate Dirichlet distribution

Sample()

Samples from this Conjugate Dirichlet distribution

Declaration

public double Sample()

Returns

Type	Description
Double	The sample value

Sample(Double)

Samples from this Conjugate Dirichlet distribution

Declaration

public double Sample(double result)

Parameters

Type	Name	Description
Double	result	Ignored

Returns

Type	Description
Double	The sample value

Sample(Double, Double)

Samples from a Conjugate Dirichlet distribution with given shape and scale

Declaration

public static double Sample(double shape, double scale)

Parameters

Type	Name	Description
Double	shape	shape parameter
Double	scale	scale parameter

Returns

Type	Description
Double	The sample value

SampleFromMeanAndVariance(Double, Double)

Samples from a Conjugate Dirichlet distribution with given mean and variance

Declaration

[ParameterNames(new string[]{"sample", "mean", "variance"})]
public static double SampleFromMeanAndVariance(double mean, double variance)

Parameters

Type	Name	Description
Double	mean	mean parameter
Double	variance	variance parameter

Returns

Type	Description
Double	The sample value

SetMeanAndVariance(Double, Double)

Sets the mean and variance

Declaration

public void SetMeanAndVariance(double mean, double variance)

Parameters

Type	Name	Description
Double	mean	Mean
Double	variance	Variance

SetNatural(Double, Double, Double, Double)

Sets the natural parameters of the distribution.

Declaration

public void SetNatural(double shapeMinus1, double rate, double D, double K)

Parameters

Type	Name	Description
Double	shapeMinus1	The shape parameter - 1.
Double	rate	rate = 1/scale
Double	D
Double	K

SetShapeAndRate(Double, Double)

Sets the shape and rate (rate = 1/scale) parameters of the distribution.

Declaration

public void SetShapeAndRate(double shape, double rate)

Parameters

Type	Name	Description
Double	shape
Double	rate	rate = 1/scale

SetShapeAndScale(Double, Double)

Sets the shape and scale for this instance

Declaration

public void SetShapeAndScale(double shape, double scale)

Parameters

Type	Name	Description
Double	shape	Shape
Double	scale	Scale

SetTo(ConjugateDirichlet)

Sets this Conjugate Dirichlet instance to have the parameter values of that Conjugate Dirichlet instance

Declaration

public void SetTo(ConjugateDirichlet that)

Parameters

Type	Name	Description
ConjugateDirichlet	that	That Conjugate Dirichlet

SetToPower(ConjugateDirichlet, Double)

Sets the parameters to represent the power of a source Conjugate Dirichlet to some exponent.

Declaration

public void SetToPower(ConjugateDirichlet dist, double exponent)

Parameters

Type	Name	Description
ConjugateDirichlet	dist	The source Conjugate Dirichlet
Double	exponent	The exponent

SetToProduct(ConjugateDirichlet, ConjugateDirichlet)

Sets the parameters to represent the product of two Gammas.

Declaration

public void SetToProduct(ConjugateDirichlet a, ConjugateDirichlet b)

Parameters

Type	Name	Description
ConjugateDirichlet	a	The first Conjugate Dirichlet
ConjugateDirichlet	b	The second Conjugate Dirichlet

Remarks

The result may not be proper. No error is thrown in this case.

SetToRatio(ConjugateDirichlet, ConjugateDirichlet, Boolean)

Sets the parameters to represent the ratio of two Conjugate Dirichlets.

Declaration

public void SetToRatio(ConjugateDirichlet numerator, ConjugateDirichlet denominator, bool forceProper)

Parameters

Type	Name	Description
ConjugateDirichlet	numerator	The numerator Conjugate Dirichlet
ConjugateDirichlet	denominator	The denominator Conjugate Dirichlet
Boolean	forceProper

Remarks

The result may not be proper. No error is thrown in this case.

SetToSum(Double, ConjugateDirichlet, Double, ConjugateDirichlet)

Set the mean and variance to match a mixture of two Gammas.

Declaration

public void SetToSum(double weight1, ConjugateDirichlet dist1, double weight2, ConjugateDirichlet dist2)

Parameters

Type	Name	Description
Double	weight1	The first weight
ConjugateDirichlet	dist1	The first Conjugate Dirichlet
Double	weight2	The second weight
ConjugateDirichlet	dist2	The second Conjugate Dirichlet

SetToUniform()

Sets this Conjugate Dirichlet instance to be a uniform distribution

Declaration

public void SetToUniform()

SmartProposal(out Double, out Double)

Find a Laplace approximation to the density of this distribution under a change of variable x=log(y)

Declaration

public void SmartProposal(out double mean, out double variance)

Parameters

Type	Name	Description
Double	mean	Mean of approximation
Double	variance	Variance of approximation

ToString()

ToString override

Declaration

public override string ToString()

Returns

Type	Description
String	String representation of the instance

Overrides

ValueType.ToString()

Uniform()

Create a uniform Conjugate Dirichlet distribution.

Declaration

[Construction(UseWhen = "IsUniform")]
public static ConjugateDirichlet Uniform()

Returns

Type	Description
ConjugateDirichlet	A new uniform Conjugate Dirichlet distribution

Operators

Division(ConjugateDirichlet, ConjugateDirichlet)

Creates a new Conjugate Dirichlet which the ratio of two other Conjugate Dirichlets

Declaration

public static ConjugateDirichlet operator /(ConjugateDirichlet numerator, ConjugateDirichlet denominator)

Parameters

Type	Name	Description
ConjugateDirichlet	numerator	numerator Conjugate Dirichlet
ConjugateDirichlet	denominator	denominator Conjugate Dirichlet

Returns

Type	Description
ConjugateDirichlet	Result

Equality(ConjugateDirichlet, ConjugateDirichlet)

Equals operator

Declaration

public static bool operator ==(ConjugateDirichlet a, ConjugateDirichlet b)

Parameters

Type	Name	Description
ConjugateDirichlet	a
ConjugateDirichlet	b

Returns

Type	Description
Boolean

ExclusiveOr(ConjugateDirichlet, Double)

Raises a distribution to a power.

Declaration

public static ConjugateDirichlet operator ^(ConjugateDirichlet dist, double exponent)

Parameters

Type	Name	Description
ConjugateDirichlet	dist	The distribution.
Double	exponent	The power to raise to.

Returns

Type	Description
ConjugateDirichlet	`dist` raised to power `exponent`.

Inequality(ConjugateDirichlet, ConjugateDirichlet)

Not equals operator

Declaration

public static bool operator !=(ConjugateDirichlet a, ConjugateDirichlet b)

Parameters

Type	Name	Description
ConjugateDirichlet	a
ConjugateDirichlet	b

Returns

Type	Description
Boolean

Multiply(ConjugateDirichlet, ConjugateDirichlet)

Creates a new Conjugate Dirichlet which the product of two other Conjugate Dirichlets

Declaration

public static ConjugateDirichlet operator *(ConjugateDirichlet a, ConjugateDirichlet b)

Parameters

Type	Name	Description
ConjugateDirichlet	a	First Conjugate Dirichlet
ConjugateDirichlet	b	Second Conjugate Dirichlet

Returns

Type	Description
ConjugateDirichlet	Result

Implements

IDistribution<T>

IDistribution

System.ICloneable

HasPoint<T>

CanGetLogProb<T>

SettableTo<T>

SettableToProduct<T>

SettableToProduct<T, U>

Diffable

SettableToUniform

SettableToRatio<T>

SettableToRatio<T, U>

SettableToPower<T>

SettableToWeightedSum<T>

Sampleable<T>

CanGetMean<MeanType>

CanGetVariance<VarType>

CanGetMeanAndVarianceOut<MeanType, VarType>

CanSetMeanAndVariance<MeanType, VarType>

CanGetLogAverageOf<T>

CanGetLogAverageOfPower<T>

CanGetAverageLog<T>

CanGetLogNormalizer