w * and w must be conditionally independent given I since w * is not observed by the comprehender, giving us (through Bayes' Rule): For present purposes we constrain the comprehender's model of noise so that T and I are conditionally independent given w, an assumption that can be relaxed in future work.
3 This allows us the further simplification to a comprehender's average inferences about sentence identity and structure involve a tradeoff between (i) the prior probability of a grammatical derivation given a speaker's linguistic knowledge and (ii) the fidelity of the derivation's yield to the true sentence, as measured by a combination of true noise processes and the comprehender's beliefs about those processes.