Modern Data Mining Algorithms in C++ and CUDA C by Timothy Masters

Author:Timothy Masters
Language: eng
Format: epub
ISBN: 9781484259887
Publisher: Apress

(4.2)

We have already defined the initial observation’s probability of being in state i to be p0(i). This can be generalized to the probability of being in state i when we are at time t, given the observations through that time. Bayes’ theorem gives us Equation (4.3). From here on, to save notational excesses, we will refer to just pt(i), omitting the joint behavior with prior observations but understanding its presence.

(4.3)

Recall the basic conditional probability rule P(A) = P(A|B) • P(B), which also applies to likelihoods here. This lets us compute α0(i), the likelihood associated with the first observation, conditional on the process being in state i, as shown in Equation (4.4). In this equation, fi(x0) is the probability density of x0 conditional on being in state i, and p0(i) is the probability of being in state i.

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