Many common distributional families take the form of *exponential families*.

The functional form of the conditional densities of these families gives them convenient compositional properties, yielding opportunities for powerful reasoning and optimization.

We present a Haskell-based approach for expressing probabilistic models in terms of *free arrows*, over a basis of exponential families. Arrows are more restrictive than the more common monadic approach, but this sacrifice in expressiveness is balanced with broader opportunities for inference, for example in terms of the dependency graph of random variables. Moreover, any monadic inference method is easily applied to arrow-based models.

The extended abstract is available atÂ http://pps2017.soic.indiana.edu/arrow-ppl/.

The free arrow approach is based on a Stack Overflow answer by Sjoerd Visscher, who has kindly pointed me to a recent blog post by Dan Piponi giving some more motivation and details on free arrows:

http://blog.sigfpe.com/2017/01/building-free-arrows-from-components.html