We are continuing to test the derived intercept as outlined in the previous post
I performed a test of calculating the likelihoods. The cube has 5 channels. Integrating the three channels in the center will recreate a scaled image of the image, minus an intercept. The outer channels will create an image deviating away from a scaled image. The scalar is the dust-to-gas ratio.
The DGR should be 0.5, the intercept 0.9, and the width 3. Indeed this is what we find by using the likelihood calculation code for the three parameters. Below are the resulting images.
Some comments from Snez about yesterday’s post:
In trying to compare with Lee+12 results I think your test with setting intercept to 0 is the closest to what Lee+12 did (if of course the code is working properly and is handling intercept in the likelihood equation correctly even when set to 0). So, can we trust that km/sec is a reliable result that should be compared with Lee+12? How does this compare to your old code you used before trying to include the intercept?
I am a bit concerned about this small HI width as in Lee+12 we in section 3 compared N(HI) and with several previous studies and concluded that we agree with previous results - most of these previous studies had almost 2 times larger that what your code is getting.
Looking at your tests with and without the intercept - is a negative intercept meaningful? From the basic fitting equation in the paper and also based on the Av data we are using, I think we expect a positive intercept. Maybe you could do a simple test to check this: you can make a fake Av image; take the HI data cube and multiply by a single/fixed DGR and then play by adding a constant of say 100 or 0 - that way when you use this fake Av image you know what the constant value has to be and see what you get.
I am also surprised to see that your DGR and become slightly smaller when you set intercept to 0. If there is essentially no background (intercept=0) then at each pixel Av has a higher value than otherwise, meaning that DGRxN(HI) term should be higher. Hmm…. I think more testing is needed, and I would also like to discuss your iterative method (need the updated methods section for this).