Infer.NET user guide : The Infer.NET Modelling API

Increment log density

Sometimes it is convenient to specify parts of the model directly in terms of their log density instead of writing a sampler. This can be done using Variable.ConstrainEqualRandom.
When you write Variable.ConstrainEqualRandom(x, dist), you are incrementing the log density by dist.GetLogProb(x).
If you just want to increment the log density by x, use

/// Increments the log density by x
Variable.ConstrainEqualRandom(x, Gaussian.FromNatural(1,0));

or

/// Increments the log density by x
Variable.ConstrainEqualRandom(x, Gamma.FromNatural(0,-1));

as appropriate. For example:

/// Increments the log-density by -0.5*x*x - MMath.LnSqrt2PI
Variable.ConstrainEqualRandom(x, new Gaussian(0, 1))

increments the log-density by (new Gaussian(0,1)).GetLogProb(x) which is equal to -0.5*x*x - MMath.LnSqrt2PI. This is equivalent to:

Variable<double> y = Variable.GaussianFromMeanAndVariance(x, 1);
y.ObservedValue = 0;

Unlike sampling, ConstrainEqualRandom works with improper distributions. Improper distributions are unnormalized, which means Gaussian.FromNatural(1,0).GetLogProb(x) == Gamma.FromNatural(0,-1).GetLogProb(x) == x.