I want to compare observations with a set of simulated data, but I'm struggling to find the best way of doing so:

  • My observations consist on a set of datapoints (~100) in a 3 dimensional space
  • I simulated these observation using a model that depends on several parameters, as well as on the initial conditions

Since there are many variables involved, I can't easily compare observations and simulations, so my idea was to use the observations to define a probability distribution function, and then check the likelihood of each simulated point to be generated by this PDF. I don't know much about statistics, but for what I've read a Kolmogorov-Smirnof test would be the best option if my data was 1D. However, since it's not, I'm not sure what would be the best approach to do this comparison. I'd appreciate any ideas



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