Model notation and visualization

If you want to communicate the results of an analysis, you should also communicate the model you used. A common notation to succinctly represent probabilistic models is:

This is just the model we use for the coin-flip example. As you may remember, the  symbol indicates that the variable, on the left of it, is a random variable distributed according to the distribution on the right. In many contexts, this symbol is used to indicate that a variable takes approximately some value, but when talking about probabilistic models, we will read this symbol out loud saying is distributed as. Thus, we can say  is distributed as a beta distribution with  and  parameters, and  is distributed as a binomial with  and  parameters. The very same model can be represented graphically using Kruschke's diagrams:

On the first level, we have the prior that generates the values for , then the likelihood, and on the last line the data, . Arrows indicate the relationship between variables, and the  symbol indicates the stochastic nature of the variables. All Kruschke's diagrams in the book were made using the templates provided by Rasmus Bååth (http://www.sumsar.net/blog/2013/10/diy-kruschke-style-diagrams/).