Continuing our example, suppose our prior beliefs about the mean count of fire calls

To get some sense about the best sampling model, I’ve plotted a histogram of the fire call counts below. I’ve overlaid fitted exponential, Poisson, and normal distributions where I estimate

I think it is pretty clear from the graph that the exponential model is a poor fit. The fits of the Poisson and normal (sd = 12) models are similar, although I’d give a slight preference to the normal model.

For each model, I compute the logarithm of the predictive probability

Here are the results:

Model

————————–

Poisson -148.0368

exponential -194.3483

normal(12) -144.3027

—————————

The exponential model is a clear loser and the Poisson and normal(12) models are close. The Bayes factor in support of the normal(12) model is