Multi-Model Probabilistic Programming
This work addresses a foundational problem for probabilistic modelers by providing a novel framework to manage model spaces, potentially mitigating issues like p-hacking and improving model development processes.
The paper tackles the challenge of representing and navigating spaces of alternative probabilistic models, which is central to probabilistic modeling but lacks good methods. It presents an extension of probabilistic programming that allows programs to represent networks of interrelated models, with a formal semantics, efficient algorithms, and an implementation in Stan, enabling applications like automatic model search and development tracking.
Probabilistic programming makes it easy to represent a probabilistic model as a program. Building an individual model, however, is only one step of probabilistic modeling. The broader challenge of probabilistic modeling is in understanding and navigating spaces of alternative models. There is currently no good way to represent these spaces of alternative models, despite their central role. We present an extension of probabilistic programming that lets each program represent a network of interrelated probabilistic models. We give a formal semantics for these multi-model probabilistic programs, a collection of efficient algorithms for network-of-model operations, and an example implementation built on top of the popular probabilistic programming language Stan. This network-of-models representation opens many doors, including search and automation in model-space, tracking and communication of model development, and explicit modeler degrees of freedom to mitigate issues like p-hacking. We demonstrate automatic model search and model development tracking using our Stan implementation, and we propose many more possible applications.