Probabilistic Reasoning over Time
Track a world that changes while you watch it through a noisy sensor: the two assumptions that make it tractable, the forward and backward recursions that answer every query about the past and present, and the separate algorithm needed for the most likely history.
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Markov Processes and Sensor Models
25 min · 100 XPState against evidence, the Markov assumption that bounds the past, the sensor Markov assumption that bounds the present, and the joint distribution the two of them factorise.
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Filtering, Prediction, and Smoothing
30 min · 120 XPThe forward recursion that maintains a belief about now, what happens to it when the evidence stops, and the backward pass that lets later evidence improve an earlier estimate.
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The Most Likely Sequence
30 min · 120 XPWhy the most likely history is not the sequence of individually most likely states, and the Viterbi recursion that finds it by replacing a sum with a maximum.
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Continuous State and the Kalman Filter
30 min · 120 XPThe same predict-and-update cycle when the state is a real number: why Gaussians are the special case that stays closed under it, and what the gain is actually weighing.
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