Can we use expected value to calculate measured value?

Newbie
1

I’m not sure if this is a proper question here (if not please point me to somewhere thanks a lot)

I’m trying to fit some drift chamber (not perfect cylinder) data value, where I have measurement t_m (drift time measurement), and expectation (\rho_e, \phi_e, \theta_e, Z_e) (4 parameters for a straight line). And I also have a relation that:

t = f(\rho, \phi, \theta, Z)

Now I have 2 options for \chi^2 defination, the first is

\chi^2 = \sum \left(\frac{t_e - t_m}{\sigma_t}\right)^2

which is fine, but the problem is the second one (I believe is being used everywhere)

\chi^2 = \sum \left(\frac{r_e - r_m}{\sigma_r}\right)^2

where the r is drift distance. You can see that in order to get the measurement of drift distance I need more than 1 parameter to calculate it, but the only measurement I have is time, so I need to use t_m and something like \rho_e to calculate it, like r_m = f(\rho_e, \phi_e, \theta_e, t_m) where the measurement and expectation is mixed. So is the second defination of \chi2 wrong if r-t is not 1-to-1 relation?

2

Hi,

I confirm that this is an interesting topic, but perhaps not very related to ROOT.

Cheers,
D

3

Thank you, can you please suggest if there is a good place to ask such question?