ex) Discrete Markov-Chain
Data Dependency
Given $ \mathbf{X_t}, \mathbf{Y_t} $ is independent to every state
Measurement update
\(\begin{equation} \begin{aligned} p(x_k | Y_k) &= p(x_k | Y_{k-1}, y_k) \\ &∝ p(y_k | Y_{k-1}, x_k) p(x_k | Y_{k-1}) \\ &= p(y_k | x_k) p(x_k | Y_{k-1}) \end{aligned} \end{equation}\)
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