/// <summary>EP message to <c>isPositive</c>.</summary>
/// <param name="x">Incoming message from <c>x</c>. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <returns>The outgoing EP message to the <c>isPositive</c> argument.</returns>
/// <remarks>
/// <para>The outgoing message is a distribution matching the moments of <c>isPositive</c> as the random arguments are varied. The formula is <c>proj[p(isPositive) sum_(x) p(x) factor(isPositive,x)]/p(isPositive)</c>.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="x" /> is not a proper distribution.</exception>
public static Bernoulli IsPositiveAverageConditional([SkipIfUniform, Proper] Gaussian x)
{
Bernoulli result = new Bernoulli();
if (x.IsPointMass)
{
result.Point = Factor.IsPositive(x.Point);
}
else if (x.IsUniform())
{
result.LogOdds = 0.0;
}
else if (!x.IsProper())
{
throw new ImproperMessageException(x);
}
else
{
// m/sqrt(v) = (m/v)/sqrt(1/v)
double z = x.MeanTimesPrecision / Math.Sqrt(x.Precision);
// p(true) = NormalCdf(z)
// log(p(true)/p(false)) = NormalCdfLogit(z)
result.LogOdds = MMath.NormalCdfLogit(z);
}
return(result);
}
/// <summary>
/// Evidence message for EP
/// </summary>
/// <param name="isPositive">Incoming message from 'isPositive'.</param>
/// <param name="x">Incoming message from 'x'.</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_(isPositive,x) p(isPositive,x) factor(isPositive,x))</c>.
/// </para></remarks>
public static double LogAverageFactor(Bernoulli isPositive, Gaussian x)
{
Bernoulli to_isPositive = IsPositiveAverageConditional(x);
return(isPositive.GetLogAverageOf(to_isPositive));
#if false
// Z = p(b=T) p(x > 0) + p(b=F) p(x <= 0)
// = p(b=F) + (p(b=T) - p(b=F)) p(x > 0)
if (x.IsPointMass)
{
return(Factor.IsPositive(x.Point) ? isPositive.GetLogProbTrue() : isPositive.GetLogProbFalse());
}
else if (x.IsUniform())
{
return(Bernoulli.LogProbEqual(isPositive.LogOdds, 0.0));
}
else
{
// m/sqrt(v) = (m/v)/sqrt(1/v)
double z = x.MeanTimesPrecision / Math.Sqrt(x.Precision);
if (isPositive.IsPointMass)
{
return(isPositive.Point ? MMath.NormalCdfLn(z) : MMath.NormalCdfLn(-z));
}
else
{
return(MMath.LogSumExp(isPositive.GetLogProbTrue() + MMath.NormalCdfLn(z), isPositive.GetLogProbFalse() + MMath.NormalCdfLn(-z)));
}
}
#endif
}
/// <summary>Evidence message for EP.</summary>
/// <param name="isPositive">Constant value for <c>isPositive</c>.</param>
/// <param name="x">Constant value for <c>x</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(factor(isPositive,x))</c>.</para>
/// </remarks>
public static double LogAverageFactor(bool isPositive, double x)
{
return((isPositive == Factor.IsPositive(x)) ? 0.0 : Double.NegativeInfinity);
}
