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Many of you will know about Markov chains. Named after Andrey Markov, [they] are mathematical systems that hop from one "state" (a situation or set of values) to another. For example, if you made a Markov chain model of a baby's behavior, you might include "playing," "eating", "sleeping," and "crying" as states, which together with other behaviors could form a 'state space': a list of all possible states. In addition, on top of the state space, a Markov chain tells you the probability of hopping, or "transitioning," from one state to any other state---e.g., the chance that a baby currently playing will fall asleep in the next five minutes without crying first.
Victor Powell and Lewis Lehe have produced a 'visual explanation' of how to produce Markov chains showing how they are used in a variety of disciplines; they are useful to computer scientists and engineers and many others. As they point out:
In the hands of meteorologists, ecologists, computer scientists, financial engineers and other people who need to model big phenomena, Markov chains can get to be quite large and powerful.
If you've not seen Markov chains in use before, or perhaps your knowledge is just a little rusty, then take a look at the link and see it they can be of any use to you.
(Score: 4, Interesting) by GeorgeScuttles on Monday March 02 2015, @03:36AM
At work, we make extensive use of Markov Chain Monte Carlo methods (successive draws of prior distributions from statistical models). It's a tool in the belt for determining likely states from unknown prior values (e.g., in weather forecasting one might ask, what will the effect be on the temperature, Y, at some location, if the prior temperature an hour before is X). They work great, with two absolutely major downsides (i) they tend to be pretty computationally intensive and (ii) if the prior distribution or model is wrong, they give you a completely incorrect answer. The second one can be mitigated by sensitivity studies, but that involves even more computation. Anyway, it's a great tool, discovered long ago, but only recently used because of modern computational infrastructure.
If you want some interesting reading material, look up bred vectors in Weather Forecasting versus Lyapunov vectors elsewhere.