kindly explain to this to me (like im 5). what they are, the difference between Monte Carlo and MCMC simulations, how they’re used in Physics and Astronomy. I’ve been wondering since I heard about this from my seniors.
In: 5
Monte Carlo is type of stochastic algorithm. It basically goes like this: You choose a solution at random, check if it’s the right solution. If the solution is “good enough” or you’ve reached some other ending condition (maximum number of iterations for example), you stop. The important thing here is that you’re not looking for the perfect solution (that’s called a Las Vegas algorithm), so the program will always terminate in at most a known number of steps. Some examples of Monte Carlo algorithms are Random Walk, the Metropolis Algorithm, all types of genetic evolutionary algorithms…
Markov chain is just like a finite state machine, but instead of changing states based on inputs, it changes states with some probability. So you can have a state A, from which you can go to state B with probability 0.2 or to state C with probability 0.8. It’s difficult to explain in text. The important thing is that a markov chain doesn’t have a memory, the next state only depends on the current state. This is called “Markov property”.
Markov chains can be used to model various things, in physics and astronomy as well, and when you evaluate those models using some Monte Carlo algorithm, you have MCMC.
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