March 9, 2004

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March 9, 2004

• Chapter 15Probabilistic Reasoning Over Time

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15.1 Time and Uncertainty

• Random variables might be dynamic over time, e.g.
  Healthy
• Snapshot or time slice
• Observable random variables Et et
• Unobservable random variables Xt xt
• Xab

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• Assumptions
• Stationary Process changes in state are governed
  by laws that are static
• Markov Assumptions (Markov Process or Markov
  Chain) current state depends on a finite history
  of previous states
• first order Markov Process, Figure 15.1
• second order Markov Process
• etc.

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Markov Assumptions

• P(Xt X0t-1 ) P(Xt Xt-1), transition model
• P(Et X0t, E0t-1) P(Et Xt), sensor model
• P(X0)
• Figure 15.2
• Complete joint distribution, P(X0, Xt, E1,
  Et), is easily calculable.

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15.2 Inference in Temporal Models

• Filtering, P(Xt e1t), forward algorithm
• Predicting, P(Xtk e1t), k gt 0, forward
  algorithm
• Smoothing, P(Xk e1t), 0 lt k lt t, forward
  backward algorithm
• Most Likely Explanation, argmax x1t, P(x1t
  e1t ), Viterbi algorithm