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by kernel_sanders
4358 days ago
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I'm interested in the above article and the above two comments, however, I don't understand the Lottery example. Can you clarify how it does have the Markov property? I'm not seeing how the distribution of possible winning numbers relates at all to the current state. I'm trying to phrase this in the language of the above two comments. Help me out if I've got it all wrong. =) |
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The lottery ignores the previous state and is defined purely by the noise, so it is a (trivial) markov process.
More complex systems depend on the entire history (e.g. to model a poker player you have to consider all of their actions up to the current). Newtonian systems are markov, if you know the state of the system you can run it forward in time deterministically. Even if your knowledge of the state of the Newtonian system is not fully known, you can still run the distribution of states forward in time precisely.
current_state = previous_state + process_noise
typically expressed in matrix math but the idea is as simple as that.