R Statistics Cookbook

How to decide the parameters for a prior

Once the support for the prior distribution has been determined, we need to decide what the actual shape of the prior will look like (by choosing the right parameters). For example, if we think that a certain prior should be a Gaussian distribution, it really matters whether the mean is 4 or 20. In general, these are tuned so the peak/mode of the prior is very near the value that we have in mind. For example, if we expect the promotion effect on sales to be equal to 2, we should put a prior that has a mode near 2.

However, it's not just the mode, but also the asymmetry and the variance. For example, if we think that this promotional variable has an impact around two, but we are equally unsure whether ...