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I am looking at ways of finding the global best-fitting model to a set of data. The model is highly non-linear and has anywhere between 5 and 8 parameters.

I have used particle swarm optimisation with some success, as well as Metropolis-Hastings Markov Chain Monte Carlo.

At the end of any given run, there is still doubt as to whether the parameter space has been completely - or at least sufficiently - searched.

Are there any algorithms for model fitting which includes some measure of how thoroughly the parameter space has been searched?

For example, considering PSO, is some way of estimating how "sensitive" any given particle is to its present neighbourhood? Let us consider a PSO particle, passing a local cost minimum in the N-dimensional manifold at a certain velocity and a certain distance from the minimum. Can we quantify the probability that this particle would be attracted to and "investigate" the minimum?

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Have you considered Bayesian methods for estimating the likelihood of finding a better point elsewhere in the space? – Deathbreath Feb 14 '13 at 17:53
Have you found any solution for your problem? I am very interesting as well. Regards. – user8140 May 7 '14 at 14:32

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