public void ExpOpGammaPower_PointExp()
{
double power = -1;
double vd = 1e-4;
vd = 1e-3;
Gaussian d = new Gaussian(0, vd);
Gaussian uniform = Gaussian.Uniform();
GammaPower expPoint = GammaPower.PointMass(2, power);
GammaPower to_exp_point = ExpOp.ExpAverageConditional(expPoint, d, uniform);
Gaussian to_d_point = ExpOp.DAverageConditional(expPoint, d, uniform);
double to_exp_oldError = double.PositiveInfinity;
double to_d_oldError = double.PositiveInfinity;
for (int i = 0; i < 100; i++)
{
double ve = System.Math.Pow(10, -i);
GammaPower exp = GammaPower.FromMeanAndVariance(2, ve, power);
GammaPower to_exp = ExpOp.ExpAverageConditional(exp, d, uniform);
Gaussian to_d = ExpOp.DAverageConditional(exp, d, uniform);
double to_exp_error = to_exp.MaxDiff(to_exp_point);
double to_d_error = System.Math.Abs(to_d.GetMean() - to_d_point.GetMean());
Trace.WriteLine($"ve={ve}: to_exp={to_exp} error={to_exp_error} to_d={to_d} error={to_d_error}");
Assert.True(to_exp_error <= to_exp_oldError);
to_exp_oldError = to_exp_error;
Assert.True(to_d_error <= to_d_oldError);
to_d_oldError = to_d_error;
}
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PlusGammaOp"]/message_doc[@name="SumAverageConditional(GammaPower, GammaPower)"]/*'/>
public static GammaPower SumAverageConditional([SkipIfUniform] GammaPower a, [SkipIfUniform] GammaPower b, GammaPower result)
{
a.GetMeanAndVariance(out double aMean, out double aVariance);
b.GetMeanAndVariance(out double bMean, out double bVariance);
double mean = aMean + bMean;
double variance = aVariance + bVariance;
return(GammaPower.FromMeanAndVariance(mean, variance, result.Power));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaPowerProductOp_Laplace"]/message_doc[@name="BAverageConditional(GammaPower, GammaPower, GammaPower, Gamma, GammaPower)"]/*'/>
public static GammaPower BAverageConditional([SkipIfUniform] GammaPower product, [Proper] GammaPower A, [Proper] GammaPower B, Gamma q, GammaPower result)
{
if (B.Shape < A.Shape)
{
return(AAverageConditional(product, B, A, q, result));
}
if (A.IsPointMass)
{
return(GammaProductOp.BAverageConditional(product, A.Point, result));
}
if (B.IsPointMass)
{
return(GammaPower.Uniform(result.Power)); // TODO
}
if (product.IsUniform())
{
return(product);
}
if (q.IsUniform())
{
q = Q(product, A, B);
}
double qPoint = q.GetMean();
GammaPower bMarginal;
// threshold ensures 6/qPoint^4 does not overflow
double threshold = Math.Sqrt(Math.Sqrt(6 / double.MaxValue));
if (result.Power < 0 && qPoint > threshold)
{
double iqMean, iqVariance;
GetIQMoments(product, A, q, qPoint, out iqMean, out iqVariance);
GammaPower iqMarginal = GammaPower.FromMeanAndVariance(iqMean, iqVariance, -1);
bMarginal = GammaPower.FromShapeAndRate(iqMarginal.Shape, iqMarginal.Rate, result.Power);
}
else
{
// B.Shape >= A.Shape therefore Q is the approximate distribution of B^(1/B.Power).
// We compute the approximate moments of q = b^(1/b.Power) to get a Gamma distribution and then raise to B.Power.
double qMean, qVariance;
GetQMoments(product, A, q, qPoint, out qMean, out qVariance);
bMarginal = GammaPower.FromGamma(Gamma.FromMeanAndVariance(qMean, qVariance), result.Power);
}
result.SetToRatio(bMarginal, B, GammaProductOp_Laplace.ForceProper);
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PlusGammaOp"]/message_doc[@name="AAverageConditional(GammaPower, GammaPower)"]/*'/>
public static GammaPower AAverageConditional([SkipIfUniform] GammaPower sum, [SkipIfUniform] GammaPower a, [SkipIfUniform] GammaPower b, GammaPower result)
{
if (sum.IsUniform())
{
return(sum);
}
sum.GetMeanAndVariance(out double sumMean, out double sumVariance);
b.GetMeanAndVariance(out double bMean, out double bVariance);
double rMean = Math.Max(0, sumMean - bMean);
double rVariance = sumVariance + bVariance;
double aVariance = a.GetVariance();
if (rVariance > aVariance)
{
if (sum.Power == 1)
{
GetGammaMomentDerivs(a, out double mean, out double dmean, out double ddmean, out double variance, out double dvariance, out double ddvariance);
mean += b.GetMean();
variance += b.GetVariance();
GetGammaDerivs(mean, dmean, ddmean, variance, dvariance, ddvariance, out double ds, out double dds, out double dr, out double ddr);
GetDerivLogZ(sum, GammaPower.FromMeanAndVariance(mean, variance, sum.Power), ds, dds, dr, ddr, out double dlogZ, out double ddlogZ);
return(GammaPowerFromDerivLogZ(a, dlogZ, ddlogZ));
}
else if (sum.Power == -1)
{
GetInverseGammaMomentDerivs(a, out double mean, out double dmean, out double ddmean, out double variance, out double dvariance, out double ddvariance);
mean += b.GetMean();
variance += b.GetVariance();
if (variance > double.MaxValue)
{
return(GammaPower.Uniform(a.Power)); //throw new NotSupportedException();
}
GetInverseGammaDerivs(mean, dmean, ddmean, variance, dvariance, ddvariance, out double ds, out double dds, out double dr, out double ddr);
if (sum.IsPointMass && sum.Point == 0)
{
return(GammaPower.PointMass(0, a.Power));
}
GetDerivLogZ(sum, GammaPower.FromMeanAndVariance(mean, variance, sum.Power), ds, dds, dr, ddr, out double dlogZ, out double ddlogZ);
return(GammaPowerFromDerivLogZ(a, dlogZ, ddlogZ));
}
}
return(GammaPower.FromMeanAndVariance(rMean, rVariance, result.Power));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PlusGammaVmpOp"]/message_doc[@name="SumAverageLogarithm(GammaPower, GammaPower, GammaPower)"]/*'/>
public static GammaPower SumAverageLogarithm([SkipIfUniform] GammaPower a, [SkipIfUniform] GammaPower b, GammaPower result)
{
if (a.IsUniform() || b.IsUniform())
{
result.SetToUniform();
return(result);
}
if (result.Power == -1)
{
bool aHasInfiniteMean = (a.Power == -1 && a.Shape <= 1);
bool bHasInfiniteMean = (b.Power == -1 && b.Shape <= 1);
if (aHasInfiniteMean)
{
if (bHasInfiniteMean)
{
return(InvGammaFromShapeAndMeanInverse(Math.Min(a.Shape, b.Shape), MeanInverseOfSum(a, b)));
}
else
{
return(InvGammaFromShapeAndMeanInverse(a.Shape, MeanInverseOfSum(a, b)));
}
}
else if (bHasInfiniteMean)
{
return(InvGammaFromShapeAndMeanInverse(b.Shape, MeanInverseOfSum(a, b)));
}
}
a.GetMeanAndVariance(out double aMean, out double aVariance);
b.GetMeanAndVariance(out double bMean, out double bVariance);
double mean = aMean + bMean;
double variance = aVariance + bVariance;
if (result.Power == -1 && variance > double.MaxValue && false)
{
// mean is finite
return(InvGammaFromMeanAndMeanInverse(mean, MeanInverseOfSum(a, b)));
}
return(GammaPower.FromMeanAndVariance(mean, variance, result.Power));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaPowerProductOp_Laplace"]/message_doc[@name="ProductAverageConditional(GammaPower, GammaPower, GammaPower, Gamma, GammaPower)"]/*'/>
public static GammaPower ProductAverageConditional(GammaPower product, [Proper] GammaPower A, [SkipIfUniform] GammaPower B, Gamma q, GammaPower result)
{
if (B.Shape < A.Shape)
{
return(ProductAverageConditional(product, B, A, q, result));
}
if (B.IsPointMass)
{
return(GammaProductOp.ProductAverageConditional(A, B.Point));
}
if (B.IsUniform())
{
return(GammaPower.Uniform(result.Power));
}
if (A.IsPointMass)
{
return(GammaProductOp.ProductAverageConditional(A.Point, B));
}
if (product.IsPointMass)
{
return(GammaPower.Uniform(result.Power)); // TODO
}
if (A.Power != product.Power)
{
throw new NotSupportedException($"A.Power ({A.Power}) != product.Power ({product.Power})");
}
if (B.Power != product.Power)
{
throw new NotSupportedException($"B.Power ({B.Power}) != product.Power ({product.Power})");
}
if (A.Rate == 0)
{
if (B.Rate == 0)
{
return(GammaPower.FromShapeAndRate(Math.Min(A.Shape, B.Shape), 0, result.Power));
}
else
{
return(A);
}
}
if (B.Rate == 0)
{
return(B);
}
double qPoint = q.GetMean();
double r = product.Rate;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(product.Shape, A.Shape) + (1 - A.Power);
GammaPower productMarginal;
// threshold ensures 6/qPoint^4 does not overflow
double threshold = Math.Sqrt(Math.Sqrt(6 / double.MaxValue));
if (shape2 > 2 && result.Power < 0 && qPoint > threshold)
{
// Compute the moments of product^(-1/product.Power)
// Here q = b^(1/b.Power)
// E[a^(-1/a.Power) b^(-1/b.Power)] = E[(q r + a_r)/(shape2-1)/q]
// var(a^(-1/a.Power) b^(-1/b.Power)) = E[(q r + a_r)^2/(shape2-1)/(shape2-2)/q^2] - E[a^(-1/a.Power) b^(-1/b.Power)]^2
// = (var((q r + a_r)/q) + E[(q r + a_r)/q]^2)/(shape2-1)/(shape2-2) - E[(q r + a_r)/q]^2/(shape2-1)^2
// = var((q r + a_r)/q)/(shape2-1)/(shape2-2) + E[(q r + a_r)/(shape2-1)/q]^2/(shape2-2)
double iqMean, iqVariance;
GetIQMoments(product, A, q, qPoint, out iqMean, out iqVariance);
double ipMean = (r + A.Rate * iqMean) / (shape2 - 1);
double ipVariance = (iqVariance * A.Rate * A.Rate / (shape2 - 1) + ipMean * ipMean) / (shape2 - 2);
// TODO: use ipVarianceOverMeanSquared
GammaPower ipMarginal = GammaPower.FromMeanAndVariance(ipMean, ipVariance, -1);
if (ipMarginal.IsUniform())
{
return(GammaPower.Uniform(result.Power));
}
else
{
productMarginal = GammaPower.FromShapeAndRate(ipMarginal.Shape, ipMarginal.Rate, result.Power);
}
bool check = false;
if (check)
{
// Importance sampling
MeanVarianceAccumulator mvaInvQ = new MeanVarianceAccumulator();
MeanVarianceAccumulator mvaInvProduct = new MeanVarianceAccumulator();
Gamma qPrior = Gamma.FromShapeAndRate(B.Shape, B.Rate);
double shift = (product.Shape - product.Power) * Math.Log(qPoint) - shape2 * Math.Log(A.Rate + qPoint * r) + qPrior.GetLogProb(qPoint) - q.GetLogProb(qPoint);
for (int i = 0; i < 1000000; i++)
{
double qSample = q.Sample();
// logf = (y_s-y_p)*log(b) - (s+y_s-pa)*log(r + b*y_r)
double logf = (product.Shape - product.Power) * Math.Log(qSample) - shape2 * Math.Log(A.Rate + qSample * r) + qPrior.GetLogProb(qSample) - q.GetLogProb(qSample);
double weight = Math.Exp(logf - shift);
mvaInvQ.Add(1 / qSample, weight);
double invProduct = (r + A.Rate / qSample) / (shape2 - 1);
mvaInvProduct.Add(invProduct, weight);
}
Trace.WriteLine($"invQ = {mvaInvQ}, {iqMean}, {iqVariance}");
Trace.WriteLine($"invProduct = {mvaInvProduct}");
Trace.WriteLine($"invA = {mvaInvProduct.Variance * (shape2 - 1) / (shape2 - 2) + mvaInvProduct.Mean * mvaInvProduct.Mean / (shape2 - 2)}, {ipMean}, {ipVariance}");
Trace.WriteLine($"productMarginal = {productMarginal}");
}
}
else
{
// Compute the moments of y = product^(1/product.Power)
// yMean = E[shape2*b/(b y_r + a_r)]
// yVariance = E[shape2*(shape2+1)*b^2/(b y_r + a_r)^2] - yMean^2
// = var(shape2*b/(b y_r + a_r)) + E[shape2*b^2/(b y_r + a_r)^2]
// = shape2^2*var(b/(b y_r + a_r)) + shape2*(var(b/(b y_r + a_r)) + (yMean/shape2)^2)
// Let g = b/(b y_r + a_r)
double denom = qPoint * r + A.Rate;
double denom2 = denom * denom;
double rOverDenom = r / denom;
double[] gDerivatives = (denom == 0)
? new double[] { 0, 0, 0, 0 }
: new double[] { qPoint / denom, A.Rate / denom2, -2 * A.Rate / denom2 * rOverDenom, 6 * A.Rate / denom2 * rOverDenom * rOverDenom };
double gMean, gVariance;
GaussianOp_Laplace.LaplaceMoments(q, gDerivatives, dlogfs(qPoint, product, A), out gMean, out gVariance);
double yMean = shape2 * gMean;
double yVariance = shape2 * shape2 * gVariance + shape2 * (gVariance + gMean * gMean);
productMarginal = GammaPower.FromGamma(Gamma.FromMeanAndVariance(yMean, yVariance), result.Power);
}
result.SetToRatio(productMarginal, product, GammaProductOp_Laplace.ForceProper);
if (double.IsNaN(result.Shape) || double.IsNaN(result.Rate))
{
throw new InferRuntimeException("result is nan");
}
return(result);
}
public static GammaPower GammaPowerFromDifferentPower(GammaPower message, double newPower)
{
if (message.Power == newPower)
{
return(message); // same as below, but faster
}
if (message.IsUniform())
{
return(GammaPower.Uniform(newPower));
}
// Making two hops ensures that the desired mean powers are finite.
if (message.Power > 0 && newPower < 0 && newPower != -1)
{
return(GammaPowerFromDifferentPower(GammaPowerFromDifferentPower(message, -1), newPower));
}
if (message.Power < 0 && newPower > 0 && newPower != 1)
{
return(GammaPowerFromDifferentPower(GammaPowerFromDifferentPower(message, 1), newPower));
}
// Project the message onto the desired power
if (newPower == 1 || newPower == -1 || newPower == 2)
{
message.GetMeanAndVariance(out double mean, out double variance);
if (!double.IsPositiveInfinity(mean))
{
return(GammaPower.FromMeanAndVariance(mean, variance, newPower));
}
// Fall through
}
bool useMean = false;
if (useMean)
{
// Constraints:
// mean = Gamma(Shape + newPower)/Gamma(Shape)/Rate^newPower =approx (Shape/Rate)^newPower
// mean2 = Gamma(Shape + 2*newPower)/Gamma(Shape)/Rate^(2*newPower) =approx ((Shape + newPower)/Rate)^newPower * (Shape/Rate)^newPower
// mean2/mean^2 = Gamma(Shape + 2*newPower)*Gamma(Shape)/Gamma(Shape + newPower)^2 =approx ((Shape + newPower)/Shape)^newPower
// Shape =approx newPower/((mean2/mean^2)^(1/newPower) - 1)
// Rate = Shape/mean^(1/newPower)
message.GetMeanAndVariance(out double mean, out double variance);
double meanp = System.Math.Pow(mean, 1 / newPower);
double mean2p = System.Math.Pow(variance + mean * mean, 1 / newPower);
double shape = newPower / (mean2p / meanp / meanp - 1);
if (double.IsInfinity(shape))
{
return(GammaPower.PointMass(mean, newPower));
}
double rate = shape / meanp;
return(GammaPower.FromShapeAndRate(shape, rate, newPower));
}
else
{
// Compute the mean and variance of x^1/newPower
double mean = message.GetMeanPower(1 / newPower);
double mean2 = message.GetMeanPower(2 / newPower);
double variance = System.Math.Max(0, mean2 - mean * mean);
if (double.IsPositiveInfinity(mean * mean))
{
variance = mean;
}
return(GammaPower.FromGamma(Gamma.FromMeanAndVariance(mean, variance), newPower));
}
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaPowerProductOp_Laplace"]/message_doc[@name="AAverageConditional(GammaPower, GammaPower, GammaPower, Gamma, GammaPower)"]/*'/>
public static GammaPower AAverageConditional([SkipIfUniform] GammaPower product, GammaPower A, [SkipIfUniform] GammaPower B, Gamma q, GammaPower result)
{
if (B.Shape < A.Shape)
{
return(BAverageConditional(product, B, A, q, result));
}
if (B.IsPointMass)
{
return(GammaProductOp.AAverageConditional(product, B.Point, result));
}
if (A.IsPointMass)
{
return(GammaPower.Uniform(A.Power)); // TODO
}
if (product.IsUniform())
{
return(product);
}
double qPoint = q.GetMean();
GammaPower aMarginal;
if (product.IsPointMass)
{
// Z = int Ga(y/q; s, r)/q Ga(q; q_s, q_r) dq
// E[a] = E[product/q]
// E[a^2] = E[product^2/q^2]
// aVariance = E[a^2] - aMean^2
double productPoint = product.Point;
if (productPoint == 0)
{
aMarginal = GammaPower.PointMass(0, result.Power);
}
else
{
double iq = 1 / qPoint;
double iq2 = iq * iq;
double[] iqDerivatives = new double[] { iq, -iq2, 2 * iq2 * iq, -6 * iq2 * iq2 };
double iqMean, iqVariance;
GaussianOp_Laplace.LaplaceMoments(q, iqDerivatives, dlogfs(qPoint, product, A), out iqMean, out iqVariance);
double aMean = productPoint * iqMean;
double aVariance = productPoint * productPoint * iqVariance;
aMarginal = GammaPower.FromGamma(Gamma.FromMeanAndVariance(aMean, aVariance), result.Power);
}
}
else
{
if (double.IsPositiveInfinity(product.Rate))
{
return(GammaPower.PointMass(0, result.Power));
}
if (A.Power != product.Power)
{
throw new NotSupportedException($"A.Power ({A.Power}) != product.Power ({product.Power})");
}
if (B.Power != product.Power)
{
throw new NotSupportedException($"B.Power ({B.Power}) != product.Power ({product.Power})");
}
double r = product.Rate;
double r2 = r * r;
double g = 1 / (qPoint * r + A.Rate);
double g2 = g * g;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(product.Shape, A.Shape) + (1 - A.Power);
// From above:
// a^(y_s-pa + a_s-1) exp(-(y_r b + a_r)*a)
if (shape2 > 2)
{
// Compute the moments of a^(-1/a.Power)
// Here q = b^(1/b.Power)
// E[a^(-1/a.Power)] = E[(q r + a_r)/(shape2-1)]
// var(a^(-1/a.Power)) = E[(q r + a_r)^2/(shape2-1)/(shape2-2)] - E[a^(-1/a.Power)]^2
// = (var(q r + a_r) + E[(q r + a_r)]^2)/(shape2-1)/(shape2-2) - E[(q r + a_r)]^2/(shape2-1)^2
// = var(q r + a_r)/(shape2-1)/(shape2-2) + E[(q r + a_r)/(shape2-1)]^2/(shape2-2)
double[] qDerivatives = new double[] { qPoint, 1, 0, 0 };
double qMean, qVariance;
GaussianOp_Laplace.LaplaceMoments(q, qDerivatives, dlogfs(qPoint, product, A), out qMean, out qVariance);
double iaMean = (qMean * r + A.Rate) / (shape2 - 1);
double iaVariance = (qVariance * r2 / (shape2 - 1) + iaMean * iaMean) / (shape2 - 2);
GammaPower iaMarginal = GammaPower.FromMeanAndVariance(iaMean, iaVariance, -1);
if (iaMarginal.IsUniform())
{
if (result.Power > 0)
{
return(GammaPower.PointMass(0, result.Power));
}
else
{
return(GammaPower.Uniform(result.Power));
}
}
else
{
aMarginal = GammaPower.FromShapeAndRate(iaMarginal.Shape, iaMarginal.Rate, result.Power);
}
bool check = false;
if (check)
{
// Importance sampling
MeanVarianceAccumulator mvaB = new MeanVarianceAccumulator();
MeanVarianceAccumulator mvaInvA = new MeanVarianceAccumulator();
Gamma bPrior = Gamma.FromShapeAndRate(B.Shape, B.Rate);
q = bPrior;
double shift = (product.Shape - product.Power) * Math.Log(qPoint) - shape2 * Math.Log(A.Rate + qPoint * r) + bPrior.GetLogProb(qPoint) - q.GetLogProb(qPoint);
for (int i = 0; i < 1000000; i++)
{
double bSample = q.Sample();
// logf = (y_s-y_p)*log(b) - (s+y_s-pa)*log(r + b*y_r)
double logf = (product.Shape - product.Power) * Math.Log(bSample) - shape2 * Math.Log(A.Rate + bSample * r) + bPrior.GetLogProb(bSample) - q.GetLogProb(bSample);
double weight = Math.Exp(logf - shift);
mvaB.Add(bSample, weight);
double invA = (bSample * r + A.Rate) / (shape2 - 1);
mvaInvA.Add(invA, weight);
}
Trace.WriteLine($"b = {mvaB}, {qMean}, {qVariance}");
Trace.WriteLine($"invA = {mvaInvA} {mvaInvA.Variance * (shape2 - 1) / (shape2 - 2) + mvaInvA.Mean * mvaInvA.Mean / (shape2 - 2)}, {iaMean}, {iaVariance}");
Trace.WriteLine($"aMarginal = {aMarginal}");
}
}
else
{
// Compute the moments of a^(1/a.Power)
// aMean = shape2/(b y_r + a_r)
// aVariance = E[shape2*(shape2+1)/(b y_r + a_r)^2] - aMean^2 = var(shape2/(b y_r + a_r)) + E[shape2/(b y_r + a_r)^2]
// = shape2^2*var(1/(b y_r + a_r)) + shape2*(var(1/(b y_r + a_r)) + (aMean/shape2)^2)
double[] gDerivatives = new double[] { g, -r * g2, 2 * g2 * g * r2, -6 * g2 * g2 * r2 * r };
double gMean, gVariance;
GaussianOp_Laplace.LaplaceMoments(q, gDerivatives, dlogfs(qPoint, product, A), out gMean, out gVariance);
double aMean = shape2 * gMean;
double aVariance = shape2 * shape2 * gVariance + shape2 * (gVariance + gMean * gMean);
aMarginal = GammaPower.FromGamma(Gamma.FromMeanAndVariance(aMean, aVariance), result.Power);
}
}
result.SetToRatio(aMarginal, A, GammaProductOp_Laplace.ForceProper);
if (double.IsNaN(result.Shape) || double.IsNaN(result.Rate))
{
throw new InferRuntimeException("result is nan");
}
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PlusGammaOp"]/message_doc[@name="AAverageConditional(GammaPower, GammaPower)"]/*'/>
public static GammaPower AAverageConditional2([SkipIfUniform] GammaPower sum, [SkipIfUniform] GammaPower a, [SkipIfUniform] GammaPower b, GammaPower result)
{
if (sum.IsUniform() || b.IsUniform())
{
result.SetToUniform();
return(result);
}
if (sum.IsPointMass && sum.Point == 0)
{
if (b.IsPointMass || a.Shape / a.Power <= b.Shape / b.Power)
{
result.Point = 0;
return(result);
}
else
{
result.SetToUniform();
return(result);
}
}
if (sum.IsProper() && b.IsProper())
{
sum.GetMeanAndVariance(out double sumMean, out double sumVariance);
b.GetMeanAndVariance(out double bMean, out double bVariance);
double rMean = sumMean - bMean;
double rVariance = sumVariance + bVariance;
double aVariance = a.GetVariance();
if (aVariance >= rVariance)
{
if (rMean < 0)
{
// If b cannot be less than x, then sum cannot be less than x.
double tailProbability = 0.1;
double bLowerBound = b.GetQuantile(tailProbability);
// If sum cannot be more than x, then b cannot be more than x.
double sumUpperBound = sum.GetQuantile(1 - tailProbability);
if (sumUpperBound > bLowerBound)
{
// Compute the mean of the truncated distributions.
// sum is truncated to [bLowerBound, infinity]
sumMean = TruncatedGammaPowerGetMean(sum, bLowerBound, double.PositiveInfinity);
// b is truncated to [0, sumUpperBound]
bMean = TruncatedGammaPowerGetMean(b, 0, sumUpperBound);
rMean = sumMean - bMean;
}
else
{
//result.Point = 0;
//return result;
}
}
if (rMean > 0)
{
result = GammaPower.FromMeanAndVariance(rMean, rVariance, result.Power);
if (ForceProper && result.Power == 1 && result.Shape < 1)
{
result.Shape = 1;
// Set rate such that shape/rate = rMean
result.Rate = result.Shape / rMean;
}
return(result);
}
}
}
// logZ = sum.GetLogAverageOf(toSum)
// where toSum = SumAverageConditional(a, b)
// Compute the derivatives wrt a.Rate to get the message to A.
if (sum.Power == 1)
{
GetGammaMomentDerivs(a, out double mean, out double dmean, out double ddmean, out double variance, out double dvariance, out double ddvariance);
mean += b.GetMean();
variance += b.GetVariance();
GetGammaDerivs(mean, dmean, ddmean, variance, dvariance, ddvariance, out double ds, out double dds, out double dr, out double ddr);
GetDerivLogZ(sum, GammaPower.FromMeanAndVariance(mean, variance, sum.Power), ds, dds, dr, ddr, out double dlogZ, out double ddlogZ);
return(GammaPowerFromDerivLogZ(a, dlogZ, ddlogZ));
}
else if (sum.Power == -1)
{
bool aHasInfiniteMean = (a.Power == -1 && a.Shape <= 1);
bool bHasInfiniteMean = (b.Power == -1 && b.Shape <= 1);
if (aHasInfiniteMean)
{
if (bHasInfiniteMean)
{
if (a.Shape <= b.Shape)
{
return(sum);
}
else
{
result.SetToUniform();
return(result);
}
}
else
{
return(sum);
}
}
else if (bHasInfiniteMean)
{
result.SetToUniform();
return(result);
}
GetInverseGammaMomentDerivs(a, out double mean, out double dmean, out double ddmean, out double variance, out double dvariance, out double ddvariance);
mean += b.GetMean();
variance += b.GetVariance();
if (variance > double.MaxValue)
{
return(GammaPower.Uniform(a.Power)); //throw new NotSupportedException();
}
GetInverseGammaDerivs(mean, dmean, ddmean, variance, dvariance, ddvariance, out double ds, out double dds, out double dr, out double ddr);
if (sum.IsPointMass && sum.Point == 0)
{
return(GammaPower.PointMass(0, a.Power));
}
GetDerivLogZ(sum, GammaPower.FromMeanAndVariance(mean, variance, sum.Power), ds, dds, dr, ddr, out double dlogZ, out double ddlogZ);
return(GammaPowerFromDerivLogZ(a, dlogZ, ddlogZ));
}
else
{
throw new NotImplementedException($"sum.Power == {sum.Power}");
}
}
