The paper describes a new mechanism for inferring stochastic context free grammar rules from a corpus of training data. The approach is entirely statistical in nature and uses the theory of belief propagation in causal trees as described by Pearl [5]. In the proposed method the existing estimates of grammar rule probabilities are used to construct (partial) parse trees over segments of the utterance. A partial parse tree does not necessarily span an entire sentence, only some fragment of it. Belief propagation is then applied to these trees to obtain the posterior probability distribution of the non-terminal symbols at each grammar node. It is shown how the E-M algorithm can be used to re-estimate the production rule probabilities. The algorithm does not require any labels or segmentation of the input signal, and is thus completely un-supervised. A method for making the algorithm O(N2) rather than O(NZ) like the similar inside-outside algorithm is also proposed and evaluated. The method is compared against the bigram and trigram grammars and showed a significantly better performance.