My company recently implemented software that uses an MCMC method. In that program, a handful of randomly generated nuisance parameters are used to calculate expected values in a function modeling experimental data, which are then compared to an observed value from experimental data. A likelihood is calculated by using log(observed/expected) as an x value to plug into the normal probability density function (along with a variance) and used for the likelihood of the current state.
Is log(observed/expected) a typical x value for something like this? I can't seem to find anything on this particular form. Everything I can find on fit and obs/exp uses a chi-square distribution. Is this just a general comparison so we can assume normality?