Approaches to Defining Priors
Pablo Inchausti · 2022
Defining priors remains an issue of perennial debate in the Bayesian framework. There is no principled way of defining priors that has gained universal or even widespread acceptance. While this might well be an elusive goal, one would hope that, at least for some large class of commonly used models (e.g., generalized linear mixed models), there ought to be at least a conventional approach to setting priors to guide the data analysts. Those working within the frequentist framework do not have such problems, as we operate in a state of almost complete amnesia as if the world starts again with every data analysis. We may criticize Bayesian statistics all we want, but it is the explicit specification of the assumed priors what allows us to debate their influence on the results. We have pointed out that priors tend to have a larger influence on the results of data analyses when we are trying to detect smaller magnitudes of effects of the explanatory variables with data sets of modest size. Unfortunately, this is the most common situation with experimental and survey data in the life sciences. Effect sizes of large magnitude are likely to have been detected in previous studies. The amount of information contained in large (meaning many hundreds of thousands of data points) data sets is likely to overwhelm most reasonable priors. Priors can also be used to regularize results by reducing the chances of obtaining unrealistically large effect sizes due to chance, as may occur with data sets of modest size.