/// <summary>
/// Evaluates E[log(1+exp(x))] under a Gaussian distribution with specified mean and variance.
/// </summary>
/// <param name="mean"></param>
/// <param name="variance"></param>
/// <returns></returns>
public static double Log1PlusExpGaussian(double mean, double variance)
{
double[] nodes = new double[11];
double[] weights = new double[11];
Quadrature.GaussianNodesAndWeights(mean, variance, nodes, weights);
double z = 0;
for (int i = 0; i < nodes.Length; i++)
{
double x = nodes[i];
double f = MMath.Log1PlusExp(x);
z += weights[i] * f;
}
return(z);
}
