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
Everyone gave you great answers already, but I’d like to add an example for astronomy.
Last year I did an internship and the goal was to determine if a star had a stellar companion, in other words another body orbiting around it.
To do this we had to analyse the movement of a spiral arm in the debris disk around the star (this arm is a zone of higher density of debris). The issue was that the arm is not a clear cut, and we needed to modelize the rest of the debris disk, minus the arm, to then substract that model from the data. The resulting image would have a clearer spiral arm we could analyze.
And to model the disk we had a bunch of parameters: the angle from the plane of view, the angle from the “north” of the system, the critical radius (the radius at which you have the highest density), etc…
So I was tasked with exploring the parameter space to find the best model to fit the data. To do that, the MCMC method starts at one point of the parameter space, and then moves to a close neighbor, and see how it fits. If the fit is better, it continues to move in that general direction. Otherwise it choses another direction.
If you want to try it for yourself (for example with a simple polynomial function), you can play with the EMCEE python package, which is designed for MCMC exploration.
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