/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="ExpOp_Laplace"]/message_doc[@name="DAverageConditional(Gamma, Gaussian, Gaussian)"]/*'/> public static Gaussian DAverageConditional([SkipIfUniform] Gamma exp, [Proper] Gaussian d, Gaussian to_d) { if (exp.IsPointMass) { return(ExpOp.DAverageConditional(exp.Point)); } Gaussian dPost = d * to_d; double dhat = dPost.GetMean(); double ehat = Math.Exp(dhat); double a = exp.Shape; double b = exp.Rate; double dlogf = (a - 1) - b * ehat; double ddlogf = -b * ehat; double r = -ddlogf; if (ForceProper && r < 0) { r = 0; } return(Gaussian.FromNatural(r * dhat + dlogf, r)); }
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="ExpOp_Laplace2"]/message_doc[@name="DAverageConditional(Gamma, Gaussian, double)"]/*'/> public static Gaussian DAverageConditional([SkipIfUniform] Gamma exp, [Proper] Gaussian d, double x) { if (exp.IsPointMass) { return(ExpOp.DAverageConditional(exp.Point)); } double expx = Math.Exp(x); double a = exp.Shape; double b = exp.Rate; double ddlogf = -b * expx; double dddlogf = ddlogf; double d4logf = ddlogf; double dlogf = (a - 1) + ddlogf; double v = 1 / (d.Precision - ddlogf); // this is Laplace's estimate of the posterior mean and variance double mpost = x + 0.5 * dddlogf * v * v; double vpost = v + 0.5 * d4logf * v * v * v + dddlogf * dddlogf * v * v * v * v; //double vpost = v + 0.25 * dddlogf * dddlogf * v * v * v * v; Gaussian result = Gaussian.FromMeanAndVariance(mpost, vpost); result.SetToRatio(result, d, ExpOp.ForceProper); return(result); }
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="LogOp_EP"]/message_doc[@name="LogAverageConditional(Gaussian, Gamma, Gaussian)"]/*'/> public static Gaussian LogAverageConditional([Proper] Gaussian log, [SkipIfUniform] Gamma d, Gaussian result) { var g = Gamma.FromShapeAndRate(d.Shape + 1, d.Rate); return(ExpOp.DAverageConditional(g, log, result)); }
public static Gaussian DAverageConditional([SkipIfUniform] Gamma exp, [Proper] Gaussian d) { // as a function of d, the factor is Ga(exp(d); shape, rate) = exp(d*(shape-1) -rate*exp(d)) if (exp.IsUniform()) { return(Gaussian.Uniform()); } if (exp.IsPointMass) { return(ExpOp.DAverageConditional(exp.Point)); } if (exp.Rate < 0) { throw new ImproperMessageException(exp); } if (exp.Rate == 0) { return(Gaussian.FromNatural(exp.Shape - 1, 0)); } if (d.IsUniform()) { if (exp.Shape <= 1) { throw new ArgumentException("The posterior has infinite variance due to input of Exp distributed as " + d + " and output of Exp distributed as " + exp + " (shape <= 1)"); } // posterior for d is a shifted log-Gamma distribution: // exp((a-1)*d - b*exp(d)) =propto exp(a*(d+log(b)) - exp(d+log(b))) // we find the Gaussian with same moments. // u = d+log(b) // E[u] = digamma(a-1) // E[d] = E[u]-log(b) = digamma(a-1)-log(b) // var(d) = var(u) = trigamma(a-1) double lnRate = Math.Log(exp.Rate); return(new Gaussian(MMath.Digamma(exp.Shape - 1) - lnRate, MMath.Trigamma(exp.Shape - 1))); } double aMinus1 = exp.Shape - 1; double b = exp.Rate; if (d.IsPointMass) { double x = d.Point; double expx = Math.Exp(x); double dlogf = aMinus1 - b * expx; double ddlogf = -b * expx; return(Gaussian.FromDerivatives(x, dlogf, ddlogf, true)); } double dmode, dmin, dmax; GetIntegrationBounds(exp, d, out dmode, out dmin, out dmax); double expmode = Math.Exp(dmode); int n = QuadratureNodeCount; double inc = (dmax - dmin) / (n - 1); MeanVarianceAccumulator mva = new MeanVarianceAccumulator(); for (int i = 0; i < n; i++) { double x = dmin + i * inc; double xMinusMode = x - dmode; double diff = aMinus1 * xMinusMode - b * (Math.Exp(x) - expmode) - 0.5 * ((x * x - dmode * dmode) * d.Precision - 2 * xMinusMode * d.MeanTimesPrecision); double p = Math.Exp(diff); mva.Add(x, p); if (double.IsNaN(mva.Variance)) { throw new Exception(); } } double dMean = mva.Mean; double dVariance = mva.Variance; Gaussian result = Gaussian.FromMeanAndVariance(dMean, dVariance); result.SetToRatio(result, d, true); return(result); }