/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="IsGreaterThanOp"]/message_doc[@name="AAverageConditional(Bernoulli, Poisson, int)"]/*'/>
public static Poisson BAverageConditional([SkipIfUniform] Bernoulli isGreaterThan, int a, [Proper] Poisson b)
{
if (b.IsPointMass || !b.IsProper())
{
return(Poisson.Uniform());
}
double bMean = b.GetMean();
double sum = 0;
double bsum = 0;
if (b.Precision == 1)
{
if (a > 0)
{
sum = MMath.GammaUpper(a, b.Rate);
bsum = (sum - Math.Exp(b.GetLogProb(a - 1))) * b.Rate;
}
}
else
{
for (int i = 0; i < a; i++)
{
double p = Math.Exp(b.GetLogProb(i));
sum += p;
bsum += i * p;
}
if (sum > 1)
{
sum = 1; // this can happen due to round-off errors
}
if (bsum > bMean)
{
bsum = bMean;
}
}
double pT = isGreaterThan.GetProbTrue();
double pF = 1 - pT;
double Z = pT * sum + pF * (1 - sum);
double bZ = pT * bsum + pF * (bMean - bsum);
Poisson result = new Poisson(bZ / Z);
result.SetToRatio(result, b, false);
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="IsGreaterThanOp"]/message_doc[@name="AAverageConditional(Bernoulli, Poisson, int)"]/*'/>
public static Poisson AAverageConditional([SkipIfUniform] Bernoulli isGreaterThan, [Proper] Poisson a, int b)
{
if (a.IsPointMass || !a.IsProper())
{
return(Poisson.Uniform());
}
double aMean = a.GetMean();
double sum = 0;
double asum = 0;
if (a.Precision == 1)
{
if (b >= 0)
{
sum = MMath.GammaUpper(b + 1, a.Rate);
asum = (sum - Math.Exp(a.GetLogProb(b))) * a.Rate;
}
}
else
{
for (int i = 0; i <= b; i++)
{
double p = Math.Exp(a.GetLogProb(i));
sum += p;
asum += i * p;
}
if (sum > 1)
{
sum = 1; // this can happen due to round-off errors
}
if (asum > aMean)
{
asum = aMean;
}
}
double pT = isGreaterThan.GetProbTrue();
double pF = 1 - pT;
double Z = pF * sum + pT * (1 - sum);
double aZ = pF * asum + pT * (aMean - asum);
Poisson result = new Poisson(aZ / Z);
result.SetToRatio(result, a, false);
return(result);
}
/// <summary>
/// Evidence message for VMP
/// </summary>
/// <param name="sample">Incoming message from 'sample'.</param>
/// <param name="mean">Constant value for 'mean'.</param>
/// <returns>Average of the factor's log-value across the given argument distributions</returns>
/// <remarks><para>
/// The formula for the result is <c>sum_(sample) p(sample) log(factor(sample,mean))</c>.
/// Adding up these values across all factors and variables gives the log-evidence estimate for VMP.
/// </para></remarks>
public static double AverageLogFactor(Poisson sample, double mean)
{
return sample.GetMean() * mean - sample.GetMeanLogFactorial() - mean;
}
/// <summary>
/// Evidence message for VMP
/// </summary>
/// <param name="sample">Incoming message from 'sample'.</param>
/// <param name="mean">Incoming message from 'mean'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <returns>Average of the factor's log-value across the given argument distributions</returns>
/// <remarks><para>
/// The formula for the result is <c>sum_(sample,mean) p(sample,mean) log(factor(sample,mean))</c>.
/// Adding up these values across all factors and variables gives the log-evidence estimate for VMP.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="mean"/> is not a proper distribution</exception>
public static double AverageLogFactor(Poisson sample, [Proper] Gamma mean)
{
return sample.GetMean() * mean.GetMeanLog() - sample.GetMeanLogFactorial() - mean.GetMean();
}
/// <summary>VMP message to <c>mean</c>.</summary>
/// <param name="sample">Incoming message from <c>sample</c>. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <returns>The outgoing VMP message to the <c>mean</c> argument.</returns>
/// <remarks>
/// <para>The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except <c>mean</c>. The formula is <c>exp(sum_(sample) p(sample) log(factor(sample,mean)))</c>.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="sample" /> is not a proper distribution.</exception>
public static Gamma MeanAverageLogarithm([Proper] Poisson sample)
{
// p(mean) = exp(E[sample]*log(mean) - mean - E[log(sample!)])
return(new Gamma(sample.GetMean() + 1, 1));
}
/// <summary>Evidence message for VMP.</summary>
/// <param name="sample">Incoming message from <c>sample</c>.</param>
/// <param name="mean">Constant value for <c>mean</c>.</param>
/// <returns>Average of the factor's log-value across the given argument distributions.</returns>
/// <remarks>
/// <para>The formula for the result is <c>sum_(sample) p(sample) log(factor(sample,mean))</c>. Adding up these values across all factors and variables gives the log-evidence estimate for VMP.</para>
/// </remarks>
public static double AverageLogFactor(Poisson sample, double mean)
{
return(sample.GetMean() * mean - sample.GetMeanLogFactorial() - mean);
}
/// <summary>Evidence message for VMP.</summary>
/// <param name="sample">Incoming message from <c>sample</c>.</param>
/// <param name="mean">Incoming message from <c>mean</c>. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <returns>Average of the factor's log-value across the given argument distributions.</returns>
/// <remarks>
/// <para>The formula for the result is <c>sum_(sample,mean) p(sample,mean) log(factor(sample,mean))</c>. Adding up these values across all factors and variables gives the log-evidence estimate for VMP.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="mean" /> is not a proper distribution.</exception>
public static double AverageLogFactor(Poisson sample, [Proper] Gamma mean)
{
return(sample.GetMean() * mean.GetMeanLog() - sample.GetMeanLogFactorial() - mean.GetMean());
}
