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MLE method using random restart

Usage

mle_random_restart(rtheta0, options)

Arguments

rtheta0

initial guess of MLE distribution, defaults to MVN with wide variance

Details

An interesting idea is to use random restarts to find the MLE. This is similar to the idea of simulated annealing, but instead of using a temperature parameter, we just try a bunch of random starting and then try to find the MLE from each of those starting points using `mle_solver`. The best MLE is returned.

A reasonable `rtheta0` is a multivariate normal distribution with a wide variance. This is because we want to explore the entire parameter space.

If we already have a candidate MLE `x`, we can use that as the sampling distribution of the MLE (MVN with mean `point(x)` and variance-covariance `vcov(x)`). This will generate random starting points that are close to the candidate MLE, which may help us find a better MLE.