Class GaussianFromMeanAndVarianceOp

Provides outgoing messages for GaussianFromMeanAndVariance(Double, Double), given random arguments to the function.

Inheritance

Object

GaussianFromMeanAndVarianceOp

Inherited Members

Object.Equals(Object)

Object.Equals(Object, Object)

Object.GetHashCode()

Object.GetType()

Object.MemberwiseClone()

Object.ReferenceEquals(Object, Object)

Object.ToString()

Namespace: Microsoft.ML.Probabilistic.Factors

Assembly: Microsoft.ML.Probabilistic.dll

Syntax

[FactorMethod(typeof(Factor), "GaussianFromMeanAndVariance", new Type[]{})]
[Quality(QualityBand.Stable)]
public static class GaussianFromMeanAndVarianceOp

Fields

ForceProper

Declaration

public static bool ForceProper

Field Value

Type	Description
Boolean

nWeights

Declaration

public static int nWeights

Field Value

Type	Description
Int32

Methods

AverageLogFactor(Gaussian, Gaussian, Double)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Gaussian sample, Gaussian mean, double variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Double	variance	Constant value for variance.

Returns

Type	Description
Double	Average of the factor's log-value across the given argument distributions.

Remarks

The formula for the result is sum_(sample,mean) p(sample,mean) log(factor(sample,mean,variance)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	mean is not a proper distribution.

AverageLogFactor(Gaussian, Double, Double)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Gaussian sample, double mean, double variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Double	mean	Constant value for mean.
Double	variance	Constant value for variance.

Returns

Type	Description
Double	Average of the factor's log-value across the given argument distributions.

Remarks

The formula for the result is sum_(sample) p(sample) log(factor(sample,mean,variance)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.

AverageLogFactor(Double, Gaussian, Double)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(double sample, Gaussian mean, double variance)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Double	variance	Constant value for variance.

Returns

Type	Description
Double	Average of the factor's log-value across the given argument distributions.

Remarks

The formula for the result is sum_(mean) p(mean) log(factor(sample,mean,variance)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

Exceptions

Type	Condition
ImproperMessageException	mean is not a proper distribution.

AverageLogFactor(Double, Double, Double)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(double sample, double mean, double variance)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	mean	Constant value for mean.
Double	variance	Constant value for variance.

Returns

Type	Description
Double	Average of the factor's log-value across the given argument distributions.

Remarks

The formula for the result is log(factor(sample,mean,variance)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

BinomialTransform(Double[])

Declaration

public static void BinomialTransform(double[] x)

Parameters

Type	Name	Description
Double[]	x

InterpolateBesselKMoment(Double, Double[])

Approximate a moment of VG(x;a) by interpolating its values for integer shapes

Declaration

public static double InterpolateBesselKMoment(double a, double[] binomt)

Parameters

Type	Name	Description
Double	a	The starting integer shape
Double[]	binomt	The exact moment for integer shapes starting at a

Returns

Type	Description
Double	The interpolated moment

LaplacianTimesGaussianMoments(Double, Double, out Double, out Double, out Double)

Compute moments of 0.5*exp(-abs(x))*N(x;m,v)

Declaration

public static void LaplacianTimesGaussianMoments(double m, double v, out double logZ, out double mu, out double vu)

Parameters

Type	Name	Description
Double	m
Double	v
Double	logZ
Double	mu
Double	vu

LogAverageFactor(Gaussian, Gaussian, Gamma)

Evidence message for EP.

Declaration

public static double LogAverageFactor(Gaussian sample, Gaussian mean, Gamma variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample.
Gaussian	mean	Incoming message from mean.
Gamma	variance	Incoming message from variance.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(sum_(sample,mean,variance) p(sample,mean,variance) factor(sample,mean,variance)).

LogAverageFactor(Gaussian, Gaussian, Double)

Evidence message for EP.

Declaration

public static double LogAverageFactor(Gaussian sample, Gaussian mean, double variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Double	variance	Constant value for variance.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(sum_(sample,mean) p(sample,mean) factor(sample,mean,variance)).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	mean is not a proper distribution.

LogAverageFactor(Gaussian, Double, Double)

Evidence message for EP.

Declaration

public static double LogAverageFactor(Gaussian sample, double mean, double variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Double	mean	Constant value for mean.
Double	variance	Constant value for variance.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(sum_(sample) p(sample) factor(sample,mean,variance)).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.

LogAverageFactor(Double, Gaussian, Double)

Evidence message for EP.

Declaration

public static double LogAverageFactor(double sample, Gaussian mean, double variance)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Double	variance	Constant value for variance.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(sum_(mean) p(mean) factor(sample,mean,variance)).

Exceptions

Type	Condition
ImproperMessageException	mean is not a proper distribution.

LogAverageFactor(Double, Double, Double)

Evidence message for EP.

Declaration

public static double LogAverageFactor(double sample, double mean, double variance)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	mean	Constant value for mean.
Double	variance	Constant value for variance.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(factor(sample,mean,variance)).

LogEvidenceRatio(Gaussian, Gaussian, Gamma, Gaussian)

Evidence message for EP.

Declaration

[Quality(QualityBand.Experimental)]
public static double LogEvidenceRatio(Gaussian sample, Gaussian mean, Gamma variance, Gaussian to_sample)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample.
Gaussian	mean	Incoming message from mean.
Gamma	variance	Incoming message from variance.
Gaussian	to_sample	Previous outgoing message to sample.

Returns

Type	Description
Double	Logarithm of the factor's contribution the EP model evidence.

Remarks

The formula for the result is log(sum_(sample,mean,variance) p(sample,mean,variance) factor(sample,mean,variance) / sum_sample p(sample) messageTo(sample)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

LogEvidenceRatio(Gaussian, Gaussian, Double)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(Gaussian sample, Gaussian mean, double variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample.
Gaussian	mean	Incoming message from mean.
Double	variance	Constant value for variance.

Returns

Type	Description
Double	Logarithm of the factor's contribution the EP model evidence.

Remarks

The formula for the result is log(sum_(sample,mean) p(sample,mean) factor(sample,mean,variance) / sum_sample p(sample) messageTo(sample)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

LogEvidenceRatio(Gaussian, Double, Double)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(Gaussian sample, double mean, double variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample.
Double	mean	Constant value for mean.
Double	variance	Constant value for variance.

Returns

Type	Description
Double	Logarithm of the factor's contribution the EP model evidence.

Remarks

The formula for the result is log(sum_(sample) p(sample) factor(sample,mean,variance) / sum_sample p(sample) messageTo(sample)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

LogEvidenceRatio(Double, Gaussian, Double)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(double sample, Gaussian mean, double variance)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Double	variance	Constant value for variance.

Returns

Type	Description
Double	Logarithm of the factor's contribution the EP model evidence.

Remarks

The formula for the result is log(sum_(mean) p(mean) factor(sample,mean,variance)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

Exceptions

Type	Condition
ImproperMessageException	mean is not a proper distribution.

LogEvidenceRatio(Double, Double, Double)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(double sample, double mean, double variance)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	mean	Constant value for mean.
Double	variance	Constant value for variance.

Returns

Type	Description
Double	Logarithm of the factor's contribution the EP model evidence.

Remarks

The formula for the result is log(factor(sample,mean,variance)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

MeanAverageConditional(Gaussian, Gaussian, Gamma)

EP message to mean.

Declaration

[Quality(QualityBand.Experimental)]
public static Gaussian MeanAverageConditional(Gaussian sample, Gaussian mean, Gamma variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	mean	Incoming message from mean.
Gamma	variance	Incoming message from variance. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gaussian	The outgoing EP message to the mean argument.

Remarks

The outgoing message is a distribution matching the moments of mean as the random arguments are varied. The formula is proj[p(mean) sum_(sample,variance) p(sample,variance) factor(sample,mean,variance)]/p(mean).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	variance is not a proper distribution.

MeanAverageConditional(Gaussian, Double)

EP message to mean.

Declaration

public static Gaussian MeanAverageConditional(Gaussian sample, double variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Double	variance	Constant value for variance.

Returns

Type	Description
Gaussian	The outgoing EP message to the mean argument.

Remarks

The outgoing message is a distribution matching the moments of mean as the random arguments are varied. The formula is proj[p(mean) sum_(sample) p(sample) factor(sample,mean,variance)]/p(mean).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.

MeanAverageConditional(Double, Gaussian, Gamma)

EP message to mean.

Declaration

[Quality(QualityBand.Experimental)]
public static Gaussian MeanAverageConditional(double sample, Gaussian mean, Gamma variance)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Gaussian	mean	Incoming message from mean.
Gamma	variance	Incoming message from variance. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gaussian	The outgoing EP message to the mean argument.

Remarks

The outgoing message is a distribution matching the moments of mean as the random arguments are varied. The formula is proj[p(mean) sum_(variance) p(variance) factor(sample,mean,variance)]/p(mean).

Exceptions

Type	Condition
ImproperMessageException	variance is not a proper distribution.

MeanAverageConditional(Double, Double)

EP message to mean.

Declaration

public static Gaussian MeanAverageConditional(double sample, double variance)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	variance	Constant value for variance.

Returns

Type	Description
Gaussian	The outgoing EP message to the mean argument.

Remarks

The outgoing message is the factor viewed as a function of mean conditioned on the given values.

MeanAverageConditional(Double, Double, TruncatedGaussian)

EP message to mean.

Declaration

public static TruncatedGaussian MeanAverageConditional(double sample, double variance, TruncatedGaussian result)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	variance	Constant value for variance.
TruncatedGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
TruncatedGaussian	result

Remarks

The outgoing message is the factor viewed as a function of mean conditioned on the given values.

MeanAverageLogarithm(Gaussian, Double)

VMP message to mean.

Declaration

public static Gaussian MeanAverageLogarithm(Gaussian sample, double variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Double	variance	Constant value for variance.

Returns

Type	Description
Gaussian	The outgoing VMP message to the mean argument.

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except mean. The formula is exp(sum_(sample) p(sample) log(factor(sample,mean,variance))).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.

MeanAverageLogarithm(Double, Double)

VMP message to mean.

Declaration

public static Gaussian MeanAverageLogarithm(double sample, double variance)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	variance	Constant value for variance.

Returns

Type	Description
Gaussian	The outgoing VMP message to the mean argument.

Remarks

The outgoing message is the factor viewed as a function of mean conditioned on the given values.

NormalCdfMoment(Int32, Double, Double)

Declaration

public static double NormalCdfMoment(int n, double m, double v)

Parameters

Type	Name	Description
Int32	n
Double	m
Double	v

Returns

Type	Description
Double

NormalCdfMomentRatios(Int32, Double, Double)

Computes int_0^Inf x^n N(x;m,v) dx / N(m/sqrt(v);0,1)

Declaration

public static double[] NormalCdfMomentRatios(int nMax, double m, double v)

Parameters

Type	Name	Description
Int32	nMax
Double	m
Double	v

Returns

Type	Description
Double[]

NormalCdfMomentRecurrence(Int32, Double, Double)

Declaration

public static double NormalCdfMomentRecurrence(int n, double m, double v)

Parameters

Type	Name	Description
Int32	n
Double	m
Double	v

Returns

Type	Description
Double

NormalCdfMoments(Int32, Double, Double)

Compute int_0^Inf x^n N(x;m,v) dx for all integer n from 0 to nMax. Loses accuracy if m < -1.

Declaration

public static double[] NormalCdfMoments(int nMax, double m, double v)

Parameters

Type	Name	Description
Int32	nMax
Double	m
Double	v

Returns

Type	Description
Double[]

NormalVGMomentRatio(Int32, Int32, Double, Double)

Declaration

public static double NormalVGMomentRatio(int n, int a, double m, double v)

Parameters

Type	Name	Description
Int32	n
Int32	a
Double	m
Double	v

Returns

Type	Description
Double

NormalVGMomentRatios(Int32, Int32, Double, Double)

Compute int_0^Inf x^n N(x;m+v,v) VG(x;a) dx 2exp(m+v/2)/N(m/sqrt(v);0,1)

Declaration

public static double[][] NormalVGMomentRatios(int nMax, int aMax, double m, double v)

Parameters

Type	Name	Description
Int32	nMax
Int32	aMax
Double	m
Double	v

Returns

Type	Description
Double[][]	NormalVGMoment[a][n] where a ranges from 1 to aMax, n ranges from 0 to nMax+aMax-a

NormalVGMoments(Int32, Int32, Double, Double)

Compute int_0^Inf x^n N(x;m+v,v) VG(x;a) dx 2exp(m+v/2). Loses accuracy if m < -1.

Declaration

public static double[][] NormalVGMoments(int nMax, int aMax, double m, double v)

Parameters

Type	Name	Description
Int32	nMax
Int32	aMax
Double	m
Double	v

Returns

Type	Description
Double[][]	NormalVGMoment[a][n] where a ranges from 1 to aMax, n ranges from 0 to nMax+aMax-a

NormalVGMomentTable(Int32, Int32, Double, Double, Double[])

Declaration

public static double[][] NormalVGMomentTable(int nMax, int aMax, double m, double v, double[] moments1)

Parameters

Type	Name	Description
Int32	nMax
Int32	aMax
Double	m
Double	v
Double[]	moments1

Returns

Type	Description
Double[][]

SampleAverageConditional(Gaussian, Gaussian, Gamma)

EP message to sample.

Declaration

[Quality(QualityBand.Experimental)]
public static Gaussian SampleAverageConditional(Gaussian sample, Gaussian mean, Gamma variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	variance	Incoming message from variance. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gaussian	The outgoing EP message to the sample argument.

Remarks

The outgoing message is a distribution matching the moments of sample as the random arguments are varied. The formula is proj[p(sample) sum_(mean,variance) p(mean,variance) factor(sample,mean,variance)]/p(sample).

Exceptions

Type	Condition
ImproperMessageException	mean is not a proper distribution.
ImproperMessageException	variance is not a proper distribution.

SampleAverageConditional(Gaussian, Double)

EP message to sample.

Declaration

public static Gaussian SampleAverageConditional(Gaussian mean, double variance)

Parameters

Type	Name	Description
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Double	variance	Constant value for variance.

Returns

Type	Description
Gaussian	The outgoing EP message to the sample argument.

Remarks

The outgoing message is a distribution matching the moments of sample as the random arguments are varied. The formula is proj[p(sample) sum_(mean) p(mean) factor(sample,mean,variance)]/p(sample).

Exceptions

Type	Condition
ImproperMessageException	mean is not a proper distribution.

SampleAverageConditional(Gaussian, Double, Gamma)

EP message to sample.

Declaration

[Quality(QualityBand.Experimental)]
public static Gaussian SampleAverageConditional(Gaussian sample, double mean, Gamma variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample.
Double	mean	Constant value for mean.
Gamma	variance	Incoming message from variance. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gaussian	The outgoing EP message to the sample argument.

Remarks

The outgoing message is a distribution matching the moments of sample as the random arguments are varied. The formula is proj[p(sample) sum_(variance) p(variance) factor(sample,mean,variance)]/p(sample).

Exceptions

Type	Condition
ImproperMessageException	variance is not a proper distribution.

SampleAverageConditional(Double, Double)

EP message to sample.

Declaration

public static Gaussian SampleAverageConditional(double mean, double variance)

Parameters

Type	Name	Description
Double	mean	Constant value for mean.
Double	variance	Constant value for variance.

Returns

Type	Description
Gaussian	The outgoing EP message to the sample argument.

Remarks

The outgoing message is the factor viewed as a function of sample conditioned on the given values.

SampleAverageConditional(Double, Double, TruncatedGaussian)

EP message to sample.

Declaration

public static TruncatedGaussian SampleAverageConditional(double mean, double variance, TruncatedGaussian result)

Parameters

Type	Name	Description
Double	mean	Constant value for mean.
Double	variance	Constant value for variance.
TruncatedGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
TruncatedGaussian	result

Remarks

The outgoing message is the factor viewed as a function of sample conditioned on the given values.

SampleAverageLogarithm(Gaussian, Double)

VMP message to sample.

Declaration

public static Gaussian SampleAverageLogarithm(Gaussian mean, double variance)

Parameters

Type	Name	Description
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Double	variance	Constant value for variance.

Returns

Type	Description
Gaussian	The outgoing VMP message to the sample argument.

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except sample. The formula is exp(sum_(mean) p(mean) log(factor(sample,mean,variance))).

Exceptions

Type	Condition
ImproperMessageException	mean is not a proper distribution.

SampleAverageLogarithm(Double, Double)

VMP message to sample.

Declaration

public static Gaussian SampleAverageLogarithm(double mean, double variance)

Parameters

Type	Name	Description
Double	mean	Constant value for mean.
Double	variance	Constant value for variance.

Returns

Type	Description
Gaussian	The outgoing VMP message to the sample argument.

Remarks

The outgoing message is the factor viewed as a function of sample conditioned on the given values.

VarianceAverageConditional(Gaussian, Gaussian, Gamma)

EP message to variance.

Declaration

[Quality(QualityBand.Experimental)]
public static Gamma VarianceAverageConditional(Gaussian sample, Gaussian mean, Gamma variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	variance	Incoming message from variance. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gamma	The outgoing EP message to the variance argument.

Remarks

The outgoing message is a distribution matching the moments of variance as the random arguments are varied. The formula is proj[p(variance) sum_(sample,mean) p(sample,mean) factor(sample,mean,variance)]/p(variance).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	mean is not a proper distribution.
ImproperMessageException	variance is not a proper distribution.

VarianceAverageConditional(Gaussian, Double, Gamma)

EP message to variance.

Declaration

[Quality(QualityBand.Experimental)]
public static Gamma VarianceAverageConditional(Gaussian sample, double mean, Gamma variance)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Double	mean	Constant value for mean.
Gamma	variance	Incoming message from variance. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gamma	The outgoing EP message to the variance argument.

Remarks

The outgoing message is a distribution matching the moments of variance as the random arguments are varied. The formula is proj[p(variance) sum_(sample) p(sample) factor(sample,mean,variance)]/p(variance).

Exceptions

Type	Condition
ImproperMessageException	sample is not a proper distribution.
ImproperMessageException	variance is not a proper distribution.

VarianceAverageConditional(Double, Gaussian, Gamma)

EP message to variance.

Declaration

[Quality(QualityBand.Experimental)]
public static Gamma VarianceAverageConditional(double sample, Gaussian mean, Gamma variance)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	variance	Incoming message from variance. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gamma	The outgoing EP message to the variance argument.

Remarks

The outgoing message is a distribution matching the moments of variance as the random arguments are varied. The formula is proj[p(variance) sum_(mean) p(mean) factor(sample,mean,variance)]/p(variance).

Exceptions

Type	Condition
ImproperMessageException	mean is not a proper distribution.
ImproperMessageException	variance is not a proper distribution.

VarianceAverageConditional(Double, Double)

EP message to variance.

Declaration

public static GammaPower VarianceAverageConditional(double sample, double mean)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	mean	Constant value for mean.

Returns

Type	Description
GammaPower	The outgoing EP message to the variance argument.

Remarks

The outgoing message is the factor viewed as a function of variance conditioned on the given values.

VarianceAverageConditional(Double, Double, Gamma)

EP message to variance.

Declaration

[Quality(QualityBand.Experimental)]
public static Gamma VarianceAverageConditional(double sample, double mean, Gamma variance)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Double	mean	Constant value for mean.
Gamma	variance	Incoming message from variance. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Gamma	The outgoing EP message to the variance argument.

Remarks

The outgoing message is the factor viewed as a function of variance conditioned on the given values.

Exceptions

Type	Condition
ImproperMessageException	variance is not a proper distribution.

VarianceGammaTimesGaussianIntegral(Double, Double, Double)

Compute int_{-Inf}^{Inf} N(x;m,v) VG(x;a) dx * 2/N(m/sqrt(v);0,1)

Declaration

public static double VarianceGammaTimesGaussianIntegral(double a, double m, double v)

Parameters

Type	Name	Description
Double	a
Double	m
Double	v

Returns

Type	Description
Double

VarianceGammaTimesGaussianMoments2(Double, Double, Double, out Double, out Double)

Declaration

public static void VarianceGammaTimesGaussianMoments2(double a, double m, double v, out double mu, out double vu)

Parameters

Type	Name	Description
Double	a
Double	m
Double	v
Double	mu
Double	vu

VarianceGammaTimesGaussianMoments3(Double, Double, Double, out Double, out Double)

Declaration

public static void VarianceGammaTimesGaussianMoments3(double a, double m, double v, out double mu, out double vu)

Parameters

Type	Name	Description
Double	a
Double	m
Double	v
Double	mu
Double	vu

VarianceGammaTimesGaussianMoments4(Double, Double, Double, out Double, out Double)

Declaration

public static void VarianceGammaTimesGaussianMoments4(double a, double m, double v, out double mu, out double vu)

Parameters

Type	Name	Description
Double	a
Double	m
Double	v
Double	mu
Double	vu

VarianceGammaTimesGaussianMoments5(Double, Double, Double, out Double, out Double)

Declaration

public static void VarianceGammaTimesGaussianMoments5(double a, double m, double v, out double mu, out double vu)

Parameters

Type	Name	Description
Double	a
Double	m
Double	v
Double	mu
Double	vu