/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaRatioOp_Laplace"]/message_doc[@name="BAverageConditional(Gamma, Gamma, Gamma, Gamma)"]/*'/>
public static Gamma BAverageConditional([SkipIfUniform] Gamma ratio, [Proper] Gamma A, [Proper] Gamma B, Gamma q)
{
if (ratio.IsPointMass)
{
// AAverageConditional computes (1st arg)/(2nd arg)
return(GammaRatioOp.BAverageConditional(ratio.Point, A));
}
if (B.IsPointMass)
{
throw new NotImplementedException();
}
if (q.IsUniform())
{
q = Q(ratio, A, B);
}
double x = q.GetMean();
double[] g = new double[] { x, 1, 0, 0 };
double bMean, bVariance;
GaussianOp_Laplace.LaplaceMoments(q, g, dlogfs(x, ratio, A), out bMean, out bVariance);
Gamma bMarginal = Gamma.FromMeanAndVariance(bMean, bVariance);
Gamma result = new Gamma();
result.SetToRatio(bMarginal, B, GammaProductOp_Laplace.ForceProper);
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaRatioOp_Laplace"]/message_doc[@name="LogAverageFactor(Gamma, Gamma, Gamma, Gamma)"]/*'/>
public static double LogAverageFactor(Gamma ratio, Gamma A, Gamma B, Gamma q)
{
if (B.IsPointMass)
{
return(GammaRatioOp.LogAverageFactor(ratio, A, B.Point));
}
if (A.IsPointMass)
{
// int Ga(a/b; y_s, y_r) Ga(b; s, r) db
// = int a^(y_s-1) b^(-y_s+1) exp(-a/b y_r) y_r^(y_s)/Gamma(y_s) Ga(b; s, r) db
// = a^(y_s-1) y_r^(y_s)/Gamma(y_s)/Gamma(s) r^s int b^(s-y_s) exp(-a/b y_r -rb) db
// this requires BesselK
throw new NotImplementedException();
}
if (ratio.IsPointMass)
{
return(GammaRatioOp.LogAverageFactor(ratio.Point, A, B));
}
// int Ga(a/b; y_s, y_r) Ga(a; s, r) da = b^s / (br + y_r)^(y_s + s-1) Gamma(y_s+s-1)
double x = q.GetMean();
double shape = A.Shape;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(ratio.Shape, shape);
double logf = shape * Math.Log(x) - shape2 * Math.Log(x * A.Rate + ratio.Rate) +
MMath.GammaLn(shape2) - A.GetLogNormalizer() - ratio.GetLogNormalizer();
double logz = logf + B.GetLogProb(x) - q.GetLogProb(x);
return(logz);
}
public static Gamma Q(Gamma ratio, [Proper] Gamma A, [Proper] Gamma B)
{
if (B.IsPointMass)
{
return(B);
}
if (ratio.IsPointMass)
{
return(GammaRatioOp.BAverageConditional(ratio.Point, A) * B);
}
double shape1 = A.Shape + B.Shape;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(A.Shape, ratio.Shape);
// find the maximum of the factor marginalized over Ratio and A, times B
// logf = s*log(b) - (s+ya-1)*log(b*r + yb)
// let b' = b*r and maximize over b'
double x = GammaFromShapeAndRateOp_Slow.FindMaximum(shape1, shape2, ratio.Rate, B.Rate / A.Rate);
if (x == 0)
{
return(B);
}
x /= A.Rate;
double[] dlogfss = dlogfs(x, ratio, A);
double dlogf = dlogfss[0];
double ddlogf = dlogfss[1];
return(GammaFromShapeAndRateOp_Laplace.GammaFromDerivatives(B, x, dlogf, ddlogf));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaRatioOp_Laplace"]/message_doc[@name="AAverageConditional(Gamma, Gamma, Gamma, Gamma)"]/*'/>
public static Gamma AAverageConditional(Gamma ratio, Gamma A, [SkipIfUniform] Gamma B, Gamma q)
{
if (ratio.IsPointMass)
{
return(GammaRatioOp.AAverageConditional(ratio.Point, B));
}
if (B.IsPointMass)
{
return(GammaRatioOp.AAverageConditional(ratio, B.Point));
}
if (A.IsPointMass)
{
throw new NotImplementedException();
}
double aMean, aVariance;
double x = q.GetMean();
double x2 = x * x;
double p = 1 / (ratio.Rate + A.Rate * x);
double p2 = p * p;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(ratio.Shape, A.Shape);
// aMean = shape2/(y_r/b + a_r)
// aVariance = E[shape2*(shape2+1)/(y_r/b + a_r)^2] - aMean^2 = var(shape2/(y_r/b + a_r)) + E[shape2/(y_r/b + a_r)^2]
// = shape2^2*var(1/(y_r/b + a_r)) + shape2*(var(1/(y_r/b + a_r)) + (aMean/shape2)^2)
double[] g = new double[] { x *p, ratio.Rate *p2, -2 *p2 *p *ratio.Rate *A.Rate, 6 *p2 *p2 *ratio.Rate *A.Rate *A.Rate };
double pMean, pVariance;
GaussianOp_Laplace.LaplaceMoments(q, g, dlogfs(x, ratio, A), out pMean, out pVariance);
aMean = shape2 * pMean;
aVariance = shape2 * shape2 * pVariance + shape2 * (pVariance + pMean * pMean);
Gamma aMarginal = Gamma.FromMeanAndVariance(aMean, aVariance);
Gamma result = new Gamma();
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="GammaRatioOp_Laplace"]/message_doc[@name="RatioAverageConditional(Gamma, Gamma, Gamma)"]/*'/>
public static Gamma RatioAverageConditional(Gamma ratio, [Proper] Gamma A, [SkipIfUniform] Gamma B)
{
if (B.IsPointMass)
{
return(GammaRatioOp.RatioAverageConditional(A, B.Point));
}
if (A.IsPointMass)
{
throw new NotImplementedException();
}
if (ratio.Rate < 1e-20)
{
ratio.Rate = 1e-20;
}
// int delta(r - a/b) Ga(a; s_a, r_a) da = b Ga(rb; s_a, r_a)
// int b Ga(rb; s_a, r_a) Ga(b; s_b, r_b) db = r^(s_a-1) / (r*r_a + r_b)^(s_a + s_b)
Gamma A2 = Gamma.FromShapeAndRate(A.Shape - 1, A.Rate);
Gamma B2 = Gamma.FromShapeAndRate(B.Shape + 2, B.Rate);
Gamma q = Q(B2, A2, ratio);
return(BAverageConditional(B2, A2, ratio, q));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaRatioVmpOp"]/message_doc[@name="AAverageLogarithm(double, double)"]/*'/>
public static Gamma AAverageLogarithm(double ratio, double B)
{
return(GammaRatioOp.AAverageConditional(ratio, B));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaRatioVmpOp"]/message_doc[@name="AAverageLogarithm(Gamma, double)"]/*'/>
public static Gamma AAverageLogarithm([SkipIfUniform] Gamma ratio, double B)
{
return(GammaRatioOp.AAverageConditional(ratio, B));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaRatioOp"]/message_doc[@name="LogAverageFactor(double, Gamma, double)"]/*'/>
public static double LogAverageFactor(double ratio, Gamma a, double b)
{
Gamma to_ratio = GammaRatioOp.RatioAverageConditional(a, b);
return(to_ratio.GetLogProb(ratio));
}