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Modifying Survival Models To Accommodate Thresholding Behavior
Michael Betancourt
Survival models capture the relationship between an accumulating hazard and the occurrence of a singular event stimulated by that accumulation. When the model for the hazard is suf…
Workflow Techniques for the Robust Use of Bayes Factors
Daniel J. Schad, Bruno Nicenboim, Paul-Christian Bürkner +2
Inferences about hypotheses are ubiquitous in the cognitive sciences. Bayes factors provide one general way to compare different hypotheses by their compatibility with the observed…
Toward a principled Bayesian workflow in cognitive science
Daniel J. Schad, Michael Betancourt, Shravan Vasishth
Experiments in research on memory, language, and in other areas of cognitive science are increasingly being analyzed using Bayesian methods. This has been facilitated by the develo…
Validating Bayesian Inference Algorithms with Simulation-Based Calibration
Sean Talts, Michael Betancourt, Daniel Simpson +2
Verifying the correctness of Bayesian computation is challenging. This is especially true for complex models that are common in practice, as these require sophisticated model imple…
Calibrating Model-Based Inferences and Decisions
Michael Betancourt
As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations w…
Visualization in Bayesian workflow
Jonah Gabry, Daniel Simpson, Aki Vehtari +2
Bayesian data analysis is about more than just computing a posterior distribution, and Bayesian visualization is about more than trace plots of Markov chains. Practical Bayesian da…
The prior can generally only be understood in the context of the likelihood
Andrew Gelman, Daniel Simpson, Michael Betancourt
A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, refe…
The Convergence of Markov chain Monte Carlo Methods: From the Metropolis method to Hamiltonian Monte Carlo
Michael Betancourt
From its inception in the 1950s to the modern frontiers of applied statistics, Markov chain Monte Carlo has been one of the most ubiquitous and successful methods in statistical co…
A Conceptual Introduction to Hamiltonian Monte Carlo
Michael Betancourt
Hamiltonian Monte Carlo has proven a remarkable empirical success, but only recently have we begun to develop a rigorous understanding of why it performs so well on difficult probl…
Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo
Michael Betancourt
When properly tuned, Hamiltonian Monte Carlo scales to some of the most challenging high-dimensional problems at the frontiers of applied statistics, but when that tuning is subopt…
Identifying the Optimal Integration Time in Hamiltonian Monte Carlo
Michael Betancourt
By leveraging the natural geometry of a smooth probabilistic system, Hamiltonian Monte Carlo yields computationally efficient Markov Chain Monte Carlo estimation. At least provided…
A Unified Treatment of Predictive Model Comparison
Michael Betancourt
The predictive performance of any inferential model is critical to its practical success, but quantifying predictive performance is a subtle statistical problem. In this paper I sh…
The Fundamental Incompatibility of Hamiltonian Monte Carlo and Data Subsampling
M. J. Betancourt
Leveraging the coherent exploration of Hamiltonian flow, Hamiltonian Monte Carlo produces computationally efficient Monte Carlo estimators, even with respect to complex and high-di…
Optimizing The Integrator Step Size for Hamiltonian Monte Carlo
M. J. Betancourt, Simon Byrne, Mark Girolami
Hamiltonian Monte Carlo can provide powerful inference in complex statistical problems, but ultimately its performance is sensitive to various tuning parameters. In this paper we u…
The Geometric Foundations of Hamiltonian Monte Carlo
M. J. Betancourt, Simon Byrne, Samuel Livingstone +1
Although Hamiltonian Monte Carlo has proven an empirical success, the lack of a rigorous theoretical understanding of the algorithm has in many ways impeded both principled develop…
Adiabatic Monte Carlo
M. J. Betancourt
A common strategy for inference in complex models is the relaxation of a simple model into the more complex target model, for example the prior into the posterior in Bayesian infer…
Hamiltonian Monte Carlo for Hierarchical Models
M. J. Betancourt, Mark Girolami
Hierarchical modeling provides a framework for modeling the complex interactions typical of problems in applied statistics. By capturing these relationships, however, hierarchical…
Generalizing the No-U-Turn Sampler to Riemannian Manifolds
M. J. Betancourt
Hamiltonian Monte Carlo provides efficient Markov transitions at the expense of introducing two free parameters: a step size and total integration time. Because the step size contr…
A General Metric for Riemannian Manifold Hamiltonian Monte Carlo
M. J. Betancourt
Markov Chain Monte Carlo (MCMC) is an invaluable means of inference with complicated models, and Hamiltonian Monte Carlo, in particular Riemannian Manifold Hamiltonian Monte Carlo…
The Geometry of Hamiltonian Monte Carlo
Michael Betancourt, Leo C. Stein
With its systematic exploration of probability distributions, Hamiltonian Monte Carlo is a potent Markov Chain Monte Carlo technique; it is an approach, however, ultimately conting…