The major functions that you will use in Omega are:
- ~x : that is equal in distribution to
xbut conditionally independent given parents
- cond(x, y) : condition random variable
- cond(ω, ab) : condition random variable that contains statement by force
- rand(x, n; alg = Alg) :
nsamples from (possibly conditioned) random variable
- replace(x, θold => θnew) : causal intervention in random variable
- rid(x, θ) : random interventional distribution of
- rcd(x, θ) or x ∥ θ : random conditional distribution of
- Causal Inference:
- Conditioning: Restricts a RandVar to be consistent with a predicate. Conceptually, conditioning is the mechanism to add knowledge (observations, declarative facts, etcs) to a model.
- Intervention: A change to a model. Interventions support counterfactual "what if" questions.
- Lift: To lift a function means to construct a new function that transforms random variables.
- Model: A collection of Random Variables.
- Prior: Unconditioned distribution. In Bayesian inference terms, prior to having observed data
- Posterior: Technically identical to conditional distribution. The term posterior is used commonly in the context of Bayesian inference where the conditional distribution is having observed more data.
- Random Variable: a random variable is one kind of representation of a probability distribution.
- Realization (or outcome) space: Space (or type) of values that a random variable can take. Since Random Variable are functions, technically this is its domain. In Omega:
elemtype(x)is its realization space
- Realization of a random variable: a value in the realization space, typically understood to be drawn according to its distribution. In Omega, the result of
rand(x)is a realizataion of
- Probability Space: A tuple $(Ω, Σ, μ)$ where $Ω$ is a sample space, Σ is a sigma algebra (roughly, set of all subsets of Ω, and μ is a probability measure). In Omega:
bernoulli(w) boolbernoulli(w) betarv categorical constant exponential gammarv invgamma kumaraswamy logistic poisson normal uniform rademacher
Built-in Inference Algorithms
RejectionSample MI SSMH SSMHDrift HMC HMCFAST