What's your opinion on Markov chain?

What are they used for?
I've wondered that.

>>1472686
Do a quick search.
http://www.makeuseof.com/tag/markov-chains-5-nifty-real-world-uses/

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They are very important, I made a bot with them once in python!

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I had the urge to read about Markov chain Monte Carlo methods this morning because of their use in Bayesian inference which I've always thought was the closest thing to a mathematical model of common sense we have.

Basically if you have some observations and you're trying to figure out how these observations affect your beliefs about the way the world works you can use Bayes' rule. Like if you had a coin and you were trying to figure out if it were fair or not, you could start out with a guess that it was fair and then flip it a bunch of times, using Bayes' rule to update your beliefs about how it was weighted after observing each flip.

However, figuring out these update rules analytically can result in a lot of messy algebra and intractable integrals so instead you construct a Markov chain with transition rules that cause it to have the same tendencies as your model of the world given the observations you've made. You can then iterate this chain a bunch of times to generate plausible samples of what your new beliefs ought to be. So if you were doing it for your coin you could then take the mean of these samples and have a good guess for the bias of the coin after a flip.

It's more complicated than that and there are pretty big limitations (or else we'd have AIs and stuff) but I still thought it was pretty neat.

Nerd.

>>1472691
Oh neato. I didn't know there were practical uses.

>>1474264
It's very useful in simulation.