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Parameter Estimation
Astro 193, Feb.25


Non-linear Models
· Define 2 and determine the best-fit parameters · No simple analytical solution · Involves iterative minimization of 2


Methods
· · · · Levenberg-Marquardt Gradient methods Simplex Monte Carlo


Comparison of the Methods
Levenberg-Marquardt
· Calculates derivatives of a statistics function over the parameter space of the function . · Convergence when the difference in the statistics in the iterative steps is smaller than the required tolerance. · Fast, but very dependent on initial conditions; known to fail in complex cases with poor initial parameter values. · Niter = 7


Comparison of the Methods
Simplex
Intercept vs. Slope

2 vs. slope

Slope/intercept traces

Moncar => Differential evolution algorithm

Niter = 266

Niter = 1274