/// <summary>Evidence message for EP.</summary>
/// <param name="sample">Incoming message from <c>sample</c>.</param>
/// <param name="mean">Incoming message from <c>mean</c>.</param>
/// <returns>Logarithm of the factor's average value across the given argument distributions.</returns>
/// <remarks>
/// <para>The formula for the result is <c>log(sum_(sample,mean) p(sample,mean) factor(sample,mean))</c>.</para>
/// </remarks>
public static double LogAverageFactor(Poisson sample, Gamma mean)
{
if (sample.IsUniform())
{
return(0);
}
if (sample.IsPointMass)
{
return(LogAverageFactor(sample.Point, mean, MeanAverageConditional(sample.Point)));
}
if (sample.Precision != 0)
{
throw new NotImplementedException("sample.Precision != 0 is not implemented");
}
return(-mean.Shape * Math.Log(1 + (1 - sample.Rate) / mean.Rate) - sample.GetLogNormalizer());
}
