Three Main Problems of an HMM and Their Algorithms

In this chapter, we will present the three main problems that a HMM can solve: finding probability of observations, finding hidden states, and calibrating the model parameters. We will present the HMM algorithms corresponding to these three problems and their applications to solving the examples of the “Ball Game” that were presented in Chapter 1. In practice, these algorithms have the problem of underflow when the observation data is large because the probability of the observations will be extremely small. Therefore, in this chapter, we will discuss the scaling method to fix this issue. We also present R codes for each of the algorithms which can be applied to real data sets in the next chapters. R codes of these algorithms and their applications are also presented in the chapter.