Identifying CpG Islands: Sliding Window and Hidden Markov Model Approaches - Mathematical Concepts and Methods in Modern Biology - page 277

Table 9.5 The set of parameters of a HMM describing a DNA sequence. The model incorporates information about din-
ucleotide frequencies. Here the block matrices P + and P − are the “+” and “ − ” transition matrices from Table 9.1 The

process remains in the the “+” and “ − ” region with probabilities p and q , respectively. When switching between the “+”

and “ − ” regions, this model assumes that all states in the new region are equally likely. For each of the emission symbols

k ∈ M , the model assumes that only the states k + and k − from can Q emit k . The initial distribution is uniform.

Transitions Emissions Initial

A + C + T + G + A − C − T − G − A C T G

A + (1 − p )/4 (1 − p )/4 (1 − p )/4 (1 − p )/4 1 0 0 0 0.125

C + (1 − p )/4 (1 − p )/4 (1 − p )/4 (1 − p )/4 0 1 0 0 0.125

(P + ) ∗ p T + (1− p )/4 (1− p )/4 (1− p )/4 (1− p )/4 0 0 1 0 0.125

G + (1 − p )/4 (1 − p )/4 (1 − p )/4 (1 − p )/4 0 0 0 1 0.125

A − (1 − q )/4 (1 − q )/4 (1 − q )/4 (1 − q )/4 1 0 0 0 0.125

C − (1 − q )/4 (1 − q )/4 (1 − q )/4 (1 − q )/4 0 1 0 0 0.125

P − ) ∗ T − (1 − q )/4 (1 − q )/4 (1 − q )/4 (1 − q )/4 ( q 0 0 1 0 0.125

G − (1− q )/4 (1− q )/4 (1− q )/4 (1− q )/4 0 0 0 1 0.125