ABSTRACT
A commonly used method of fitting HMMs is the EM algorithm, which we shall describe in Section 4.2, the crux of this chapter. The tools we need to do so are the forward and the backward probabilities, which are also used for decoding and state prediction in Chapter 5. In establishing some useful propositions concerning the forward and backward probabilities we invoke several properties of HMMs which are fairly obvious given the structure of an HMM; we defer the proofs of such properties to Appendix B.
