Writing

Preprints of my work are posted on the arXiv as much as possible. Highlights include a long but comprehensive introduction to statistical computing and Hamiltonian Monte Carlo targeted at applied researches and a more theoretical treatment of the geometric foundations of Hamiltonian Monte Carlo.

I’ve also been experimenting with a nontraditional introduction to some of the more formal aspects of probability theory and statistical computation, although fair warning that this draft is long overdue for a reorganization. Still, comments are always welcome.

Recently I have been taking advantage of notebook environments such as knitr and Jupyter to develop case studies demonstrating important concepts in statistical workflow and modeling with Stan.

Robust Gaussian Processes in Stan, Part 3

This series of case studies introduces the very basics of Gaussian processes, how to implement them in Stan, and how they can be robustly incorporated into Bayesian models to avoid subtle but pathological behavior.

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betanalpha/knitr_case_studies/gaussian_processes/gp_part3 (GitHub)
Dependences: R, knitr, RStan
Code License: BSD (3 clause)
Text License: CC BY-NC 4.0
Cite As: Betancourt, Michael (2017). Robust Gaussian Processes in Stan, Part 3. Retrieved from https://betanalpha.github.io/assets/case_studies/gp_part3/part3.html.

Robust Gaussian Processes in Stan, Part 2

This series of case studies introduces the very basics of Gaussian processes, how to implement them in Stan, and how they can be robustly incorporated into Bayesian models to avoid subtle but pathological behavior.

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betanalpha/knitr_case_studies/gaussian_processes/gp_part2 (GitHub)
Dependences: R, knitr, RStan
Code License: BSD (3 clause)
Text License: CC BY-NC 4.0
Cite As: Betancourt, Michael (2017). Robust Gaussian Processes in Stan, Part 2. Retrieved from https://betanalpha.github.io/assets/case_studies/gp_part2/part2.html.

Robust Gaussian Processes in Stan, Part 1

This series of case studies introduces the very basics of Gaussian processes, how to implement them in Stan, and how they can be robustly incorporated into Bayesian models to avoid subtle but pathological behavior.

View (HTML)
betanalpha/knitr_case_studies/gaussian_processes/gp_part1 (GitHub)
Dependences: R, knitr, RStan
Code License: BSD (3 clause)
Text License: CC BY-NC 4.0
Cite As: Betancourt, Michael (2017). Robust Gaussian Processes in Stan, Part 1. Retrieved from https://betanalpha.github.io/assets/case_studies/gp_part1/part1.html.

The QR Decomposition for Regression Models

This case study reviews the QR decomposition, a technique for decorrelating covariates and, consequently, the resulting posterior distribution in regression models.

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betanalpha/knitr_case_studies/qr_regression (GitHub)
Dependences: R, knitr, RStan
Code License: BSD (3 clause)
Text License: CC BY-NC 4.0
Cite As: Betancourt, Michael (2017). The QR Decomposition for Regression Models. Retrieved from https://betanalpha.github.io/assets/case_studies/qr_regression.html.

Robust PyStan Workflow

This case study demonstrates a proper PyStan workflow that ensures robust inferences with the default dynamic Hamiltonian Monte Carlo algorithm.

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betanalpha/jupyter_case_studies/pystan_workflow (GitHub)
Dependences: Python, Jupyter, PyStan
Code License: BSD (3 clause)
Text License: CC BY-NC 4.0
Cite As: Betancourt, Michael (2017). Robust PyStan Workflow. Retrieved from https://betanalpha.github.io/assets/case_studies/pystan_workflow.html.

Robust RStan Workflow

This case study demonstrates a proper RStan workflow that ensures robust inferences with the default dynamic Hamiltonian Monte Carlo algorithm.

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betanalpha/knitr_case_studies/rstan_workflow (GitHub)
Dependences: R, knitr, RStan
Code License: BSD (3 clause)
Text License: CC BY-NC 4.0
Cite As: Betancourt, Michael (2017). Robust RStan Workflow. Retrieved from https://betanalpha.github.io/assets/case_studies/rstan_workflow.html.

Diagnosing Biased Inference with Divergences

This case study discusses the subtleties of accurate Markov chain Monte Carlo estimation and how divergences can be used to identify biased estimation in practice.

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betanalpha/knitr_case_studies/divergences_and_bias (GitHub)
Dependences: R, knitr, RStan
Code License: BSD (3 clause)
Text License: CC BY-NC 4.0
Cite As: Betancourt, Michael (2017). Diagnosing Biased Inference with Divergences. Retrieved from https://betanalpha.github.io/assets/case_studies/divergences_and_bias.html.

Identifying Bayesian Mixture Models

This case study discusses the common pathologies of Bayesian mixture models as well as some strategies for identifying and overcoming them.

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betanalpha/knitr_case_studies/identifying_mixture_models (GitHub)
Dependences: R, knitr, RStan
Code License: BSD (3 clause)
Text License: CC BY-NC 4.0
Cite As: Betancourt, Michael (2017). Identifying Bayesian Mixture Models. Retrieved from https://betanalpha.github.io/assets/case_studies/identifying_mixture_models.html.

How the Shape of a Weakly Informative Prior Affects Inferences

This case study reviews the basics of weakly-informative priors and how the choice of a specific shape of such a prior affects the resulting posterior distribution.

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betanalpha/knitr_case_studies/weakly_informative_shapes (GitHub)
Dependences: R, knitr, RStan
Code License: BSD (3 clause)
Text License: CC BY-NC 4.0
Cite As: Betancourt, Michael (2017). How the Shape of a Weakly Informative Prior Affects Inferences. Retrieved from https://betanalpha.github.io/assets/case_studies/weakly_informative_shapes.html.