The likelihood term, P (x|g), is the probability of the training sentence pairs under the grammar, while the prior term, P (g), describes our initial expectations about what consitutes a plausible grammar.
we incorporate priors encoding our preference for a briefer and more succinct grammar, namely that: (a) the grammar should be small, with few rules rewriting each non-terminal; and (b) terminal rules which specify phrasal translation correspondence should be small, with few symbols on their right hand side.