multivariate poisson hidden markov models for analysis of spatial ...

CHAPTER 3
INFERENCE IN HIDDEN MARKOV MODELS
3.1 Introduction
Given the HMM model in Chapter 2, there are three basic computational problems that
are useful for solving real world problems. The three problems are as follows:
Problem 1: Given the observation sequence Y = { Y1, Y2,..., Y T
}, and the model
λ = ( A,
B,
π ) , how do we compute P[ Y=
y ; λ],
the probability or likelihood of
occurrence of the observation sequence Y = { Y1, Y2,..., Y T
} given the parameter set λ ?
We can consider problem 1 as an evaluation problem, namely given a model and a
sequence of observations, how do we compute the probability that the model produced
the observed sequence. We can also view this problem as how well the given model
matches a given observation sequence. For example, if we are trying to choose among
several computing models, the solution to problem 1 allows us to choose the model
which best matches the observations (Rabiner, 1989).
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