MichaelClerx
commented
4 years ago and find where the, now one dimensional, likelihood exceeds a certain chi squared quantile.
That's not really what I was going for. It's simpler: We have a gaussian noise model, and its variance is one of the parameters we estimate. So in the plot we simply show what the estimated +/- 1 sigma interval looks like
The Maximum Likelihood Notebook estimates confidence intervals using a profile likelihood estimation.
It’s a 3 dimensional parameter space and the MLEs are found by maximizing the likelihood. The confidence intervals of one of the parameters in the example are then found by fixing the other parameters and find where the, now one dimensional, likelihood exceeds a certain chi squared quantile.
Is moving along only the one parameter dimension allowed, here? As far as I understood do we have to move in the direction of the smallest gradient and not constrain ourselves to the one parameter. In other words, the CI are likely larger than estimated in the example, because the original problem was a 3 dimensional one.
I could update this notebook, once I’ve integrated a profile likelihood estimation, but I wanted to ask first whether the above described estimation was intentional.