Editing Probabilistic context-free grammar (section)

===== Estimate alignment probabilities =====
After calculating the column prior probabilities the alignment probability is estimated by summing over all possible secondary structures. Any column {{mvar|C}}  in a secondary structure <math>\sigma</math> for a sequence {{mvar|D}} of length {{mvar|l}} such that <math>D=(C_1,~C_2, ...C_l )</math> can be scored with respect to the alignment tree {{mvar|T}} and the mutational model {{mvar|M}}. The prior distribution given by the PCFG is <math>P(\sigma|M)</math>. The phylogenetic tree, {{mvar|T}} can be calculated from the model by maximum likelihood estimation. Note that gaps are treated as unknown bases and the summation can be done through [[dynamic programming]].<ref name="Baker 1979" /> 
:       <math>P(D|T,M)</math>
:               <math>=\sum P (D, \sigma |T,M)</math>
:               <math>=\sum P(D|\sigma, T, M) P(\sigma|T,M)</math>
:               <math>=\sum P(D|\sigma,T,M) P(\sigma|M)</math>