# Probability

Probabilistic statements use one of three operators, or the keyword factor:

x <~ p;
x ~> p;
x ~ p;
factor w;


Let x be a value of basic type (e.g. Real) or optional type (e.g. Real?), or object of Random type (e.g. Random<Real>), and p be an object of Distribution type. Then:

• x <~ p simulates a variate x from the distribution p,
• x ~> p observes a variate x from the distribution p,
• x ~ p assumes that x is distributed according to p.

If x has a value, x ~ p typically acts like x ~> p, while if it does not have a value, x ~ p eventually acts something like x <~ p, possibly after analytical optimizations.

These statements emit events to an event handler, which is simply an object of type Handler. By default, there is no event handler registered, so the events are ignored. To register an event handler h, use a with block:

with h {
// do something probabilistic
}

The factor statement sends an arbitrary log-weight w to the event handler.

Event handlers are typically used as an interface between inference methods and models, creating the opportunity for inference methods to intervene in model execution.