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Why priors matter, and when they don't
When the data are abundant and informative, the likelihood is sharply peaked and the posterior is almost independent of any reasonable prior. In that limit a Bayesian fit and a maximum-likelihood fit agree to within the precision of the sampler. When the data are sparse or the model has many parameters per bin — low signal-to-noise sources, partially degenerate components, broad-band CCD spectra with strong absorption — the prior carries real weight and the posterior depends on what was assumed. Reporting the prior choice alongside the result is then mandatory; choosing it carelessly is just as problematic as ignoring background subtraction.
Two practical consequences follow. First, every parameter that the user is genuinely uncertain about must have a prior set explicitly. The default of a constant (flat) prior over the parameter's full allowed range is rarely appropriate when the allowed range spans many decades, because most of the prior mass then sits in the exponentially unlikely regions and pulls the inference towards them. Second, the prior interacts with the parameter's hard limits set through the newpar command. Setting an absurd hard upper limit “just to be safe” is harmless under maximum likelihood, but it can dominate a posterior that has heavy tails.