/// <summary>
/// Get the integral of this distribution times another distribution raised to a power.
/// </summary>
/// <param name="that"></param>
/// <param name="power"></param>
/// <returns></returns>
public double GetLogAverageOfPower(Beta that, double power)
{
if (IsPointMass)
{
return(power * that.GetLogProb(Point));
}
else if (that.IsPointMass)
{
if (power < 0)
{
throw new DivideByZeroException("The exponent is negative and the distribution is a point mass");
}
return(this.GetLogProb(that.Point));
}
else
{
var product = this * (that ^ power);
return(product.GetLogNormalizer() - this.GetLogNormalizer() - power * that.GetLogNormalizer());
}
}
/// <summary>
/// The log of the integral of the product of this Beta and that Beta
/// </summary>
/// <param name="that">That beta</param>
/// <returns>The log inner product</returns>
public double GetLogAverageOf(Beta that)
{
if (IsPointMass)
{
return(that.GetLogProb(Point));
}
else if (that.IsPointMass)
{
return(GetLogProb(that.Point));
}
else
{
// int_p Beta(p;a1,a0) Beta(p;b1,b0) d_p = int_p Beta(p;a1+b1-1,a0+b0-1)*z
// where z = Beta(a1+b1-1,a0+b0-1) / (Beta(a1,a0) Beta(b1,b0))
double newTrueCount = TrueCount + that.TrueCount - 1;
double newFalseCount = FalseCount + that.FalseCount - 1;
//if (newTrueCount <= 0 || newFalseCount <= 0) throw new ArgumentException("The product is improper");
return(BetaLn(newTrueCount, newFalseCount)
- BetaLn(TrueCount, FalseCount) - BetaLn(that.TrueCount, that.FalseCount));
}
}