My question results from the subjectivity of priors, and if there are bodies of work that help to create a more objective approach towards prior choices.
My question specifically is to do in the realm of spectroscopic/experimental data, where prior information of the system beforehand is limited. For example, concerning the amplitude of a peak: it is quite difficult to know much prior information about this beforehand.
Other features such as the FWHM and the peak positions have some prior information about them in databanks for known materials, however for newer materials this is also not known. In this case, would you simply assign uniform priors to all parameters? Even with the danger of generating an improper posterior?
Are there alternatives to uniform priors when weakly informative information is known about a parameter, for example the amplitude must be positive, or a certain other parameter must be bounded between 0 and 1. How can you express this in your prior choices?