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## Main Question or Discussion Point

I have several data points with error bars, and these error bars are different sizes for each of the data points. I'd like to fit a model function to them which has non-linear parameters, and be able to get error bars on the model parameters, ie. if my model is something like [itex]f(x) = A + B(t-t_c)^\alpha[/itex], I want to be able to get error bars on A, B, [itex]t_c[/itex] and [itex]\alpha[/itex].

I was thinking of using a Monte Carlo algorithm, but this seems like it might be unnecessarily slow. Unless someone has pointers on how to make good guesses of the model parameters for the Monte Carlo to reduce the amount of rejected moves. I've done this sort of thing with discrete variables before, but not continuous ones, so I'm a little confused on how to make good MC moves for a continuous variable when you don't know a priori what level of precision you need in the variable.

I was thinking of using a Monte Carlo algorithm, but this seems like it might be unnecessarily slow. Unless someone has pointers on how to make good guesses of the model parameters for the Monte Carlo to reduce the amount of rejected moves. I've done this sort of thing with discrete variables before, but not continuous ones, so I'm a little confused on how to make good MC moves for a continuous variable when you don't know a priori what level of precision you need in the variable.