Bob Carpenter is an American computer scientist and statistician who led the development of the Stan probabilistic programming language, one of the most important software projects in the history of Bayesian statistics. With a background in computational linguistics and natural language processing, Carpenter brought software engineering discipline and a focus on usability to the challenge of building a general-purpose Bayesian inference platform. His work on Stan's automatic differentiation library, modeling language design, and documentation has enabled researchers across dozens of fields to fit complex Bayesian models efficiently.
Life and Career
Born in the United States. Studies mathematics, computer science, and linguistics.
Earns his Ph.D. in cognitive science from the University of Edinburgh, focusing on computational linguistics and categorial grammar.
Works on natural language processing at various institutions, applying Bayesian methods to problems in text annotation, named entity recognition, and language modeling.
Joins the Stan development team at Columbia University. Becomes the lead developer, designing the language, building the automatic differentiation library, and writing the core inference algorithms.
Co-authors "Stan: A Probabilistic Programming Language" in the Journal of Statistical Software, the canonical reference paper for Stan.
Continues to contribute to Stan development and works on applications of Bayesian methods to data annotation and measurement models.
Building Stan
Stan is a probabilistic programming language that allows users to specify Bayesian models in a declarative syntax and then performs posterior inference using state-of-the-art algorithms, primarily the No-U-Turn Sampler (NUTS), an adaptive form of Hamiltonian Monte Carlo. Carpenter's contributions to Stan were both technical and architectural. He designed and implemented the automatic differentiation library that computes the gradients needed by HMC, built the Stan math library containing hundreds of probability distributions and special functions, and designed the modeling language syntax that balances expressiveness with computational efficiency.
Hamiltonian Monte Carlo requires the gradient of the log posterior density with respect to all parameters. Computing these gradients by hand for each new model would be impractical. Stan's automatic differentiation library computes exact gradients by applying the chain rule to the elementary operations in the model's log density computation. Carpenter's implementation uses reverse-mode automatic differentiation, which computes the full gradient in time proportional to a small constant times the cost of evaluating the log density itself, regardless of the number of parameters.
Computational Linguistics and Bayesian NLP
Before Stan, Carpenter spent years applying Bayesian methods to natural language processing problems. His work on Bayesian approaches to text annotation modeling addressed the challenge of combining judgments from multiple imperfect annotators to estimate true labels and annotator reliability simultaneously. This is a naturally Bayesian problem: each annotator's accuracy is unknown and must be inferred, and the true labels are latent variables that can be integrated over. His annotation models demonstrated the practical value of hierarchical Bayesian thinking in computational linguistics.
Documentation and Community Building
Carpenter recognized that Stan's success depended not just on algorithmic performance but on usability and documentation. He wrote extensive sections of the Stan User's Guide and Reference Manual, providing detailed guidance on model specification, prior selection, and debugging. His efforts to make Stan accessible to non-experts, through clear documentation, example models, and responsive community support, were essential to the platform's adoption across statistics, epidemiology, political science, ecology, pharmacology, and many other fields.
"The goal of Stan is to make it possible to specify a Bayesian model and get reliable posterior inference without having to be an expert in computational statistics." — Bob Carpenter
Legacy
Stan has been cited in tens of thousands of research papers and is used by organizations ranging from academic research groups to pharmaceutical companies to technology firms. Carpenter's vision of a general-purpose Bayesian inference engine that combines mathematical rigor with software engineering quality has been realized. By making the No-U-Turn Sampler, automatic differentiation, and a rich modeling language available in a single platform, he and his collaborators removed the computational barrier that had prevented many researchers from adopting Bayesian methods.