How do I learn when to apply which statistical distributions? I am learning Bayesian modeling and having trouble keeping straight when it is most appropriate to apply the various statistical distributions beyond the basic ones like the beta, binomial, and Gaussian. 
Are there resources out there that provide overviews of the practical applications of various distributions, in particular less commonly used ones? I am aware of the 2011 by Catherine Forbes et al., which does a great job of presenting the mathematical properties of the various statistical distribution, but I want something that helps me with application. I would appreciate any references to books, articles, or websites. 
 A: I don't think there is any general answer, besides telling you to look into the literature about the kind of data you are analyzing. I am aware at least of some cases where the question about the underlying distribution is still subject to debate, so for these cases, one cannot know what distribution to pick.
For example, for response times there is this paper, which discusses that they may be described by either log-normal, inverse-normal (Wald), ex-Gaussian, or Weibull distribution. Also, it mentions that the most common approach is to use an ex-Gaussian distribution. On the other hand, an ex-Gaussian is clearly wrong, because it has some support in the negative values, which cannot be the case for response times, which always must be positive.
Thus, this question can be very hard to answer. The usual approach I take is, that I try not to be to wrong ("all models are wrong") and use something that has been debated in the literature and gives me the properties I want.
For example, for RTs I usually use a log-normal, because log transformations are most common on RTs in other fields as well and also I can then use the mode or the mean of the log-normal as a hyperparameter in a hierarchical model (i.e. I can estimate mean and sd separately). While an ex-Gaussian would probably be better given the literature, I would have more parameters and I cannot easily just estimate the mean independently of other parameters (mean is $\mu+\nu$, so I have to pick one of those to get the other). If I had some intuition about the meaning of $\mu$ and $\nu$ in the ex-Gaussian for some experiments, I would probably use that one.
