Editing Probabilistic context-free grammar (section)

====Building a PCFG model====
A probabilistic context free grammar consists of terminal and nonterminal variables. Each feature to be modeled has a production rule that is assigned a probability estimated from a training set of RNA structures. Production rules are recursively applied until only terminal residues are left.

A starting non-terminal <math>\mathbf{\mathit{S}}</math> produces loops. The rest of the grammar proceeds with parameter <math>\mathbf{\mathit{L}}</math> that decide whether a loop is a start of a stem or a single stranded region {{mvar|s}} and parameter <math>\mathbf{\mathit{F}}</math> that produces paired bases.

The formalism of this simple PCFG looks like:
:                                                <math>\mathit{S \to LS|L}</math>
:                                                <math>\mathit{L \to s | dFd}</math>
:                                                <math>\mathit{F \to dFd | LS}</math>

The application of PCFGs in predicting structures is a multi-step process. In addition, the PCFG itself can be incorporated into probabilistic models that consider RNA evolutionary history or search homologous sequences in databases. In an evolutionary history context inclusion of prior distributions of RNA structures of a [[structural alignment]] in the production rules of the PCFG facilitates good prediction accuracy.<ref name="Knudsen 1999" />

A summary of general steps for utilizing PCFGs in various scenarios:
 
* Generate production rules for the sequences.
* Check ambiguity.
* Recursively generate parse trees of the possible structures using the grammar. 
* Rank and score the parse trees for the most plausible sequence.<ref name="Durbin 1998" />