# AIMA: Probabilistic Reasoning Over Time

> Source: https://ollybritton.com/notes/textbooks/ai-a-modern-approach/uncertain-knowledge-and-reasoning/probabilistic-reasoning-over-time/ · Updated: 2021-04-04 · Tags: aima, notes

> In which we try to interpret the present, understand the past, and perhaps predict the future, even when very little is crystal clear.

### Summary
* The changing state of the world is handled by using a set of random variables to represent the state at each point in time.
* Representations can be designed to (roughly) satisfy the _Markov property_, so that the future is independent of the past given the present. Combined with the assumption that the process is _time-homogenous, this greatly simplifies the representation.
* A temporal probability model can be thought of as containing a _transition model_ describing the state evolution and a _sensor model_ describing the observation process.
* The principle inference tasks in temporal models are _filtering (state estimation), prediction, smoothing and computing the most likely explanation._ Each of these tasks can be achieved using simple, recursive algorithms whose run time is linear in the length of the sequence.
* Three families of temporal models were studies in more depth: _hidden Markov models, Kalman filters, and dynamic Bayesian networks_ (which include the other two as special cases).
* Unless special assumptions are made, as in Kalman filters, exact inference with many state variables is intractable. In practice, the _particle filtering_ algorithm and its descendants are an effective family of approximation algorithms.

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