[Paper Review] Bambi: A simple interface for fitting Bayesian linear models in Python

Tomás Capretto, Camen Piho+4 more|arXiv (Cornell University)|Dec 19, 2020

Statistical Methods and Bayesian Inference38 citations

TL;DR

Bambi provides a Python-based, formula-driven interface for fitting Bayesian generalized linear multilevel models on top of PyMC, enabling easy specification, fitting, diagnostics, and predictions, including regression, logistic, and hierarchical models.

ABSTRACT

The popularity of Bayesian statistical methods has increased dramatically in recent years across many research areas and industrial applications. This is the result of a variety of methodological advances with faster and cheaper hardware as well as the development of new software tools. Here we introduce an open source Python package named Bambi (BAyesian Model Building Interface) that is built on top of the PyMC probabilistic programming framework and the ArviZ package for exploratory analysis of Bayesian models. Bambi makes it easy to specify complex generalized linear hierarchical models using a formula notation similar to those found in R. We demonstrate Bambi's versatility and ease of use with a few examples spanning a range of common statistical models including multiple regression, logistic regression, and mixed-effects modeling with crossed group specific effects. Additionally we discuss how automatic priors are constructed. Finally, we conclude with a discussion of our plans for the future development of Bambi.

Motivation & Objective

• Promote widespread adoption of Bayesian methods by lowering the barrier to fitting GLMMs.
• Provide an intuitive, formula-based interface similar to R’s lme4 for specifying complex models.
• Integrate with PyMC and ArviZ to enable efficient sampling, diagnostics, and visualization of Bayesian models.
• Demonstrate versatility through examples: multiple regression, logistic regression, and hierarchical models with random effects.
• Discuss default priors, inference workflows, and future development of the Bambi package.

Proposed method

• Introduce a Python package (Bambi) built on PyMC and ArviZ for Bayesian GLMMs.
• Use a formula interface (similar to R) to specify fixed and random effects with a Model class.
• Employ adaptive dynamic Hamiltonian Monte Carlo for posterior sampling and multiple chains for diagnostics.
• Provide default priors when not specified, with mechanisms to inspect priors via plot_priors().
• Support various families (Gaussian, Bernoulli, etc.) and link functions via a Family class.
• Enable posterior predictive checks and predictions through a .predict() method and ArviZ visualizations.

Figure 1: Density estimates based on 5000 samples from the prior distribution for all the regression coefficients. If the user does not explicitly state the priors to be used for the model parameters, Bambi will choose default prior distributions sensible in a wide range of use cases.

Experimental results

Research questions

• RQ1 How can Bayesian generalized linear multilevel models be specified conveniently in Python using a formula-like interface?
• RQ2 What priors are used by default in Bambi, and how can users customize them?
• RQ3 How does Bambi facilitate model fitting, diagnostics, and posterior predictive checks for different model families (e.g., Gaussian, Bernoulli)?
• RQ4 Can users perform complex hierarchical models with crossed random effects and inspect model outputs easily?
• RQ5 What is the workflow for making in-sample and out-of-sample predictions with posterior uncertainty?

Key findings

• Bambi enables quick specification and fitting of GLMMs with sensible defaults and a familiar formula syntax.
• The package leverages PyMC’s adaptive dynamic Hamiltonian Monte Carlo to sample from the joint posterior.
• Users can inspect priors, diagnostics, and posterior summaries via ArviZ, including trace plots and summary statistics.
• The .predict() function allows generating posterior mean predictions and posterior predictive samples for new data.
• Hierarchical models with multiple random effects (intercepts and slopes) can be specified and fit with custom priors.
• Examples demonstrate regression, logistic regression, and crossed random effects, illustrating both usability and modeling flexibility.

Figure 2: HTML representation of an InferenceData object. We can see information is stored into four groups: posterior , log_likelihood , sample_stats , and observed_data. Other groups not shown here are also possible. The posterior group is unfolded showing information like the Dimensions (4 chains