diff --git a/dynamax/hidden_markov_model/models/abstractions.py b/dynamax/hidden_markov_model/models/abstractions.py index defc70762..ca799c14e 100644 --- a/dynamax/hidden_markov_model/models/abstractions.py +++ b/dynamax/hidden_markov_model/models/abstractions.py @@ -526,15 +526,15 @@ class HMM(SSM): The model is defined as follows - $$z_1 \mid u_1 \sim \mathrm{Cat}(\pi_0(u_1, \\theta_{\mathsf{init}}))$$ - $$z_t \mid z_{t-1}, u_t, \\theta \sim \mathrm{Cat}(\pi(z_{t-1}, u_t, \\theta_{\mathsf{trans}}))$$ - $$y_t | z_t, u_t, \\theta \sim p(y_t \mid z_t, u_t, \\theta_{\mathsf{emis}})$$ + $$z_1 \mid u_1 \sim \mathrm{Cat}(\pi_0(u_1, \theta_{\mathsf{init}}))$$ + $$z_t \mid z_{t-1}, u_t, \theta \sim \mathrm{Cat}(\pi(z_{t-1}, u_t, \theta_{\mathsf{trans}}))$$ + $$y_t | z_t, u_t, \theta \sim p(y_t \mid z_t, u_t, \theta_{\mathsf{emis}})$$ where $z_t \in \{1,\ldots,K\}$ is a *discrete* latent state. There are parameters for the initial distribution, the transition distribution, and the emission distribution: - $$\\theta = (\\theta_{\mathsf{init}}, \\theta_{\mathsf{trans}}, \\theta_{\mathsf{emis}})$$ + $$\theta = (\theta_{\mathsf{init}}, \theta_{\mathsf{trans}}, \theta_{\mathsf{emis}})$$ For "standard" models, we will assume the initial distribution is fixed and the transitions follow a simple transition matrix, @@ -542,7 +542,7 @@ class HMM(SSM): $$z_1 \mid u_1 \sim \mathrm{Cat}(\pi_0)$$ $$z_t \mid z_{t-1}=k \sim \mathrm{Cat}(\pi_{z_k})$$ - where $\\theta_{\mathsf{init}} = \pi_0$ and $\\theta_{\mathsf{trans}} = \{\pi_k\}_{k=1}^K$. + where $\theta_{\mathsf{init}} = \pi_0$ and $\theta_{\mathsf{trans}} = \{\pi_k\}_{k=1}^K$. The parameters are stored in a :class:`HMMParameterSet` object.