Probabilistic Programming#

What is probabilistics programming#

Probabilistic programming (PP) is a paradigm in computer programming that enables the creation of models and algorithms capable of handling uncertainty and randomness. It combines principles from probability theory and programming to build systems that can reason about uncertain data and make informed decisions. This approach allows practitioners to express complex models in a natural and intuitive way, aloowing the Bayesian inference process to be performed more effectively.

Probabilistic programming lies at the intersection of machine learning algorithms, statistics, and programming laguages, and its golas are to simplify the inference process and automate inference.

You can think of the overall logic hierarchy as

Inference → Probabilistic Programming System → Probabilistic Programming Language → Models → Applications

Why do we need probabilistic programming#

Because writing your own sampler for Bayesian inference in hard! It involves complex mathematics, knoweldge and understanding of sampling algorithms (both MCMC and approximate). There are potential issues with numeric stability and computational cost. Hence, one needs to be both an excellent developer, as well as an expert statistician to succeed at this task.

Wouldn’t it be wonderful to oursouce all these tasks to someone, so that we could focus on solving scientific problems?

Probabilistic programming languages (PPLs)#

In this section we will give an overview of the modern landscape of probabilistic programming languages (PPLs) and in the next section we will explore abilities of one of them: NumPyro.

A PPL allows us to formalize a Bayesian model and perform inference with the help of powerful algorithms. A user needs to only formulate the model, maybe chose a sampler, and “press the inference button”.

In general, what is required from a probabilistic programm, are the ability to draw values at random from distributions, and the ability to condition values of variables in a program via observations.

Some (relatively) early Probabilistic programming languages and tools, such as BUGS and WinBUGS, showed the way. They had the three key capabiltiies:

  • random to make random variables

  • constraint to constraint variables e.g. to data

  • infer - returns the distribution of a variable

The list of currently existing PPLs is overwhelmingly long and only keeps growing:


  • Stan,

  • PyMC3, PyMC4, PyMC,

  • Nimble,

  • Pyro, Numpyro,

  • Edward, TensorFlow Probability, Edward 2,

  • Gen,

  • Turing,

  • Stheno, = SOSS,

  • Omega,

  • Infer.NET

to name a few.

How to chose a PPL?#

From the practical point of view, how can we decide which of the PPLs to choose?

  • Functionality: evaluate the language’s functionality by examining the availability of a wide range of probability distributions and samplers,

  • Oppenness to Customization: consider whether the PPL allows you to define custom probability distributions and samplers,

  • Performance: some PPLs may offer optimizations or parallel processing capabilities to improve performance,

  • Documentation: the availability of well-documented resources, including official documentation, tutorials, and guides, can significantly impact your learning curve and productivity. A well-documented PPL makes it easier to understand and use its features effectively.

  • Community Support: an active and supportive community can be an invaluable resource when you encounter challenges or have questions while working with the PPL. Community forums, discussion groups, and user-contributed content can provide guidance and solutions. Dedicated meetups and conferences.

  • Integration: consider whether the PPL can easily integrate with other tools and frameworks you may need for your project. Compatibility with libraries for data manipulation, visualization, or machine learning can streamline your workflow.