/// <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);
}
