Max Is Not Sum - Viterbi Decoding of a CpG-Island HMM Step by Step

Viterbi returns the best single path, not the total observation probability.

highlighted = computed this step

Viterbi takes a maximum over paths

The value 81/2048 is the joint probability of one hidden path, not the probability of the observation.

\max_{\text{path}} P(\text{path},\text{obs})=\frac{81}{2048}

Summing all 8 state paths gives 15/128, which is larger than the best single path probability.

P(\text{obs})=\sum_{\text{paths}}=\frac{15}{128}