Numerical values for priors

[Tiny]

I am not a statistician but a food scientist that applies Bayesian modeling to predict changes in foods. So, my question was not meant to provoke a statistical debate, but rather to get some practical advice. From the Gelman papers I learn that it is OK to also look at the experiments when deciding about priors. But I still struggle how far I can go in that. Suppose I have a student that comes to me with experimental results. I study the results and come to the conclusion that a nonlinear exponential decay model could be a candidate, c=c0exp(-kt) with two parameters c0 (initial concentration) and k (rate constant): I can only do that by looking at the data. Because the experiments are chemical measurements I decide for a normal likelihood, and a zero-bounded normal, or lognormal or exponential for the two parameters. What parameter values do I give these priors if I want to make the priors weakly informative (for noninformative priors it is easily solved but I learned that I’d better not do that) ? That depends on the scales of the measurements. Was time measured in seconds, days, months? I can only find out by looking at the data before setting the priors. So, what I considered a practical solution is to run a quick least-squares regression to get an idea about the order of magnitude of the parameter values, and then increase the standard deviation of the prior parameter values to avoid dominating priors. So, I find that an easy way but I do realize the danger of working towards a solution comparable to p-hacking (I try to avoid that by making the priors much wider than the least squares results suggest). On the other hand, by choosing prior parameter values that lead to crazy results because I did not look at the data beforehand forces me to reconsider new prior values and again I can only do that by looking at the data to find more sensible values than in the first attempt (The example of the exponential decay is just trivial, in practice I have more complicated models.) So, it is a very practical question for which I seek some advice whether or not it is a feasible way of working like this. In any case, I would like to thank the respondents because it already helped me a lot.