To calculate the pre-exponential factor from the Arrhenius equation see: https://socratic.org/questions/how-do-you-calculate-the-pre-exponential-factor-from-the-arrhenius-equation

The chemical reaction sequence which takes place in the thermal oxidation of benzene is a complicated process. Several intermediate products often appear before the benzene is completely oxidized.

See refferences:

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19790020088.pdf

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19880002393.pdf

http://www.tandfonline.com/doi/pdf/10.1080/00022470.1979.10470861

Linearise the Arrhenius equation using natural logarithm on both sides and intercept of linear equation shoud be equal to ln (A) and take exponential of ln (A) which is equal to your pre-exponential coefficient

If you have a non-linear estimation  statistical software you directly calculate the value of A    

Go through the document Method How to determine order and activation energy: Kinetics of li...

Hope you get the answer.

From which perspective, experimentalist or theoreticians point of view?

https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/06%3A_Modeling_Reaction_Kinetics/6.02%3A_Temperature_Dependence_of_Reaction_Rates/6.2.03%3A_The_Arrhenius_Law/6.2.3.06%3A_The_Arrhenius_Law_-_Pre-exponential_Factors

The only problem is the numerical correlation between A and E.