Frequently asked questions¶
Why should I use jaxspec over xspec or associated ?¶
We have taken great care to make jaxspec as easy to use as possible. It can be installed with pip install jaxspec
and that's it. It is also easy to use and provides well documented use cases. The default methods are fast yet robust
for inferring model parameters in most usecases. It is also easy to integrate with other software as it exposes the
likelihood function, so if you want to use your own methods and just need a forward model with instrument folding, we
provide a compilable and GPU friendly one that can also be used as your usual numpy function.
How can I compare jaxspec and xspec fitting results ?¶
If you want to check that jaxspec gives correct values compared to xspec, you need to make sure that the results of
both solutions are comparable. To do this, make sure you do a blind fit with xspec and use Cstat as the fit statistic.
Also with jaxspec, make sure that you explicitly use a uniform prior for each of your parameters.
Why is there no \(\chi^2\) statistic ?¶
When it comes to define the fitting statistic, the question of either using \(\chi^2\) or C-stat arises pretty often. In a Bayesian approach, this is perfectly equivalent to assume either a Gaussian or a Poisson likelihood for the data you are observing. As the acquisition of an X-ray spectrum is in practice a counting process, it is natural to study it under a Poisson likelihood. However, in older times, the computation of associated errors, goodness of fit and other stats was much simpler and faster using a Gaussian likelihood or \(\chi^2\) since most of the expression can be analytically derived. Moreover, the Poisson distribution in high counts is well approximated by a Gaussian distribution when the rate is high enough (\(\lambda \gtrsim 1000\)). Since most of the studied sources were bright enough, this was no issue, but we are now studying fainter sources. Most recent publications on the subject agree that using the C-stat at all count rates is necessary to ensure an unbiased estimate of the parameters.(e.g. Kaastra, 2017 or Buchner & Boorman, 2023).
This figure shows a comparison of true error on the parameters \((A, \Gamma)\) of a power-law recovered by fitting under \(\chi^2\) or C-statistic (Adapted from Buchner & Boorman, 2023) and highlights the systematic biases that arise at low counts.
As we are working in a Bayesian framework, and not computing directly the errors but rather getting samples of the posterior distributions of our parameters, using Poisson likelihood is not an issue. The samples will be distributed accordingly to their intrinsic dispersions, in a representative way of the error in the parameter space. Because of this, we choose to ensure a Poisson likelihood in every situation, which is equivalent to fit under C-stat.