conditional probability distribution

conditional probability distribution (plural conditional probability distributions)

1. (probability theory) The probability distribution of a random variable given the known outcome of another random variable.
   • 1999, Anders L. Madsen, Bruce D'Ambrosio, Lazy Propagation and Independence of Causal Influence, Anthony Hunter, Simon Parsons, Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Springer, page 293,

     A Bayesian network consists of a directed, acyclic graph and a set of conditional probability distributions. For each variable in the graph there is a conditional probability distribution of the variable given its parents.

   • 2010, Philipp Koehn, Statistical Machine Translation, Cambridge University Press, page 69,

     Note that for two independent random variables X and Y, the conditional probability distribution p(x|y) is the same as simply p(y).

   • 2015, Iman Behmanesh, Babak Moaveni, Geert Lombaert, Costas Papadimitriou, Chapter 6: Hierarchical Bayesian Model Updating for Probabilistic Damage Identification, H. Sezer Atamturktur, Babak Moaveni, Costas Papadimitriou, Tyler Schoenherr (editors), Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 33rd IMAC, Springer, page 58,

     Alternatively, Laplace asymptotic approximation can be used to approximate the conditional probability distributions of θ₁ in Eq. (6.12) as a Gaussian distribution to simplify the sampling process.

• conditional probability

• Bayes' theorem