Hierarchical Gilbert Hidden Markov Model Plugin

The Hierarchical Gilbert Hidden Markov Model (GHMM) plugin defines a discrete-time, 0-1 observation, hierarchical HMM[#!fernando2006!#], in which a Markov chain (in this case, a gilbert model) is associated with each hidden state, and is responsible for the symbol emissions. Figure illustrates the structure of such a two-level hierarchical model.

Figure: Example of a hierarchical HMM with 3 hidden states, in which a Gilbert Markov chain is associated with each hidden state.

After each transition $(S_i, S_j)$ in the the hidden chain (the upper-level in this two-level hierarchy), the lower-level model associated with $S_j$ emits symbols by transiting for a determined number of steps, called a batch, before the upper-level chain makes another transition^11.6. A symbol is emitted every time the lower-level Markov chain makes one transition, thus reaching one of its states. In case this lower-level chain is a gilbert model, as is the case in this plugin, symbol $0$ is emitted every time the lower-level state $I_0$ is reached, and symbol $1$ is emitted every time the lower-level state $I_1$ is reached, where $I_k$, with $k =\{0,1\}$, defines a lower-level state. Each lower-level state emits one, and only one, symbol, and different lower-level states, inside a same hidden state, cannot both emit the same symbol. This plugin is a contribution of [#!fernando2006!#].