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26.1 Stan functions

real hmm_marginal(matrix log_omega, matrix Gamma, vector rho)
Returns the log probability density of $y$, with $x_n$ integrated out at each iteration. The arguments represent (1) the log density of each output, (2) the transition matrix, and (3) the initial state vector.

• log_omega: $\log \omega_{kn} = \log p(y_n \mid x_n = k, \phi)$, log density of each output,

• Gamma: $\Gamma_{ij} = p(x_n = j | x_{n - 1} = i, \phi)$, the transition matrix,

• rho: $\rho_k = p(x_0 = k \mid \phi)$, the initial state probability.

int[] hmm_latent_rng(matrix log_omega, matrix Gamma, vector rho)
Returns a length $N$ array of integers over $\{1, ..., K\}$, sampled from the joint posterior distribution of the hidden states, $p(x \mid \phi, y)$. May be only used in transformed data and generated quantities.

matrix hmm_hidden_state_prob(matrix log_omega, matrix Gamma, vector rho)
Returns the matrix of marginal posterior probabilities of each hidden state value. This will be a $K \times N$ matrix. The $i^\mathrm{th}$ column is a simplex of probabilities for the $n^\mathrm{th}$ variable. Moreover, let $A$ be the output. Then $A_{ij} = p(x_j = i \mid \phi, y)$. This function may only be used in transformed data and generated quantities.