/// <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 <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 '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>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());
}
