Intercepts
By Elijah Bernstein-Cooper, May 30, 2015, 0 comments.

Determine relevance of including an intercept in the model. This means we would solve for the DGR, width and an intercept for each cloud. Previous attempts to include an intercept led to large intercepts, on order of negative several magnitudes in . See this post for more details.

Plot vs. with the fitted DGR with and without an intercept for each cloud.

Currently I am experiencing problems deriving a reasonable intercept. Below is a hess diagram of vs. for California of the masked pixels. The black line shows the derived relationship between and using the MLE method i.e. the best-fit DGR + width. The red line is a least-squares fit to the given , i.e., not fitting for . It seems quite obvious that an intercept is needed to correctly describe the data.

Below is a likelihood space for California without fitting for an intercept.

The likelihood spaces for California while fitting for an intercept are distorted and do not have a clear MLE.