Markov Prediction

A type of Markov Inference for predicting future state distributions without new evidence.

P(Xt+k∣e1:t)P(X_{t+k}\mid e_{1:t})

Prediction is Filtering without new evidence, so the proof for the next formula is the same.

P(Xt+k+1∣e1:t)=∑xt+kP(Xt+k+1∣xt+k)⋅P(xt+k∣e1:t)\mathrm{P}\left(\mathrm{X}_{t+k+1} \mid \mathrm{e}_{1: t}\right)=\sum_{\mathrm{x}_{t+k}} \mathrm{P}\left(\mathrm{X}_{t+k+1} \mid \mathrm{x}_{t+k}\right) \cdot P\left(\mathrm{x}_{t+k} \mid \mathrm{e}_{1: t}\right)