## master project?

Posted in Books, Kids, Statistics, University life with tags , , , , , , , on July 25, 2022 by xi'an

A potential master project for my students next year inspired by an X validated question: given a Gaussian mixture density

$f(x)\propto\sum_{i=1}^m \omega_i \sigma^{-1}\,\exp\{-(x-\mu_i)^2/2\sigma^2\}$

with m known, the weights summing up to one, and the (prior) information that all means are within (-C,C), derive the parameters of this mixture from a sufficiently large number of evaluations of f. Pay attention to the numerical issues associated with the resolution.  In a second stage, envision this problem from an exponential spline fitting perspective and optimise the approach if feasible.