The probabilistic model

Let us denote the observed data with $\boldsymbol{X}= (\mathbf{x}(1), \ldots, \mathbf{x}(T))$, the hidden state values with $\boldsymbol{S}= ( \mathbf{s}(1), \ldots, \mathbf{s}(T) )$ and all the other model parameters with $\boldsymbol {\theta }$. These other parameters consist of the weights and biases of the MLP networks and hyperparameters defining the prior distributions of other parameters.