Editing Probabilistic context-free grammar (section)

==Relation with hidden Markov models==
PCFGs models extend [[context-free grammar]]s the same way as [[hidden Markov model]]s extend [[regular grammar]]s.

The [[Inside–outside algorithm|Inside-Outside algorithm]] is an analogue of the [[Forward-backward algorithm|Forward-Backward algorithm]]. It computes the total probability of all derivations that are consistent with a given sequence, based on some PCFG.  This is equivalent to the probability of the PCFG generating the sequence, and is intuitively a measure of how consistent the sequence is with the given grammar. The Inside-Outside algorithm is used in model [[Parameterization theorem|parametrization]] to estimate prior frequencies observed from training sequences in the case of RNAs.

[[Dynamic programming]] variants of the [[CYK algorithm]] find the [[Viterbi algorithm|Viterbi parse]] of a RNA sequence for a PCFG model.  This parse is the most likely derivation of the sequence by the given PCFG.