After having broken the Bayesian eggs and prepared your model in your statistical kitchen the main dish is the posterior. The posterior is the posterior is the posterior, given the model and the data it contains all the information you need and anything else will be a little bit less nourishing. However, taking in the posterior in one gulp can be a bit difficult, in all but the most simple cases it will be multidimensional and difficult to plot. But even if it is one-dimensional and you could plot it (as, say, a density plot) that does not necessary mean that it is easy to see what’s going on.
One way of getting around this is to take a bite at a time and look at summaries of the marginal posteriors of the variables of interest, the two most common type of summaries being point estimates and credible intervals (an interval that covers a certain percentage of the probability distribution). Here one is faced with a choice, which of the many ways of constructing point estimates and credible intervals to choose? This is a perfectly good question that can be given an unhelpful answer (with a predictable follow-up question):
- That depends on your loss function.
- So which loss function should I use?