1.2k citations · 3.1k across the 36 of their papers we have counts for
37 papers
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…
Efficient Automatic Differentiation of Implicit Functions
Charles C. Margossian, Michael Betancourt
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate the…
A Short Review of Ergodicity and Convergence of Markov chain Monte Carlo Estimators
Michael Betancourt
This short note reviews the basic theory for quantifying both the asymptotic and preasymptotic convergence of Markov chain Monte Carlo estimators.
A Unifying and Canonical Description of Measure-Preserving Diffusions
Alessandro Barp, So Takao, Michael Betancourt +2
A complete recipe of measure-preserving diffusions in Euclidean space was recently derived unifying several MCMC algorithms into a single framework. In this paper, we develop a geo…
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…
The Discrete Adjoint Method: Efficient Derivatives for Functions of Discrete Sequences
Michael Betancourt, Charles C. Margossian, Vianey Leos-Barajas
Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimatel…
Bregman dynamics, contact transformations and convex optimization
Alessandro Bravetti, Maria L. Daza-Torres, Hugo Flores-Arguedas +1
Recent research on accelerated gradient methods of use in optimization has demonstrated that these methods can be derived as discretizations of dynamical systems. This, in turn, ha…
Incomplete Reparameterizations and Equivalent Metrics
Michael Betancourt
Reparameterizing a probabilisitic system is common advice for improving the performance of a statistical algorithm like Markov chain Monte Carlo, even though in theory such reparam…
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…
A Geometric Theory of Higher-Order Automatic Differentiation
Michael Betancourt
First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, how…
Reassembling the English novel, 1789-1919
Allen Riddell, Michael Betancourt
The absence of an exhaustive bibliography of novels published in the British Isles and Ireland during the 19th century blocks several lines of research in sociologically-inclined l…
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…
On Symplectic Optimization
Michael Betancourt, Michael I. Jordan, Ashia C. Wilson
Accelerated gradient methods have had significant impact in machine learning -- in particular the theoretical side of machine learning -- due to their ability to achieve oracle low…
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…
Hierarchical inference of the relationship between Concentration and Mass in Galaxy Groups and Clusters
Maggie Lieu, Will M. Farr, Michael Betancourt +3
Mass is a fundamental property of galaxy groups and clusters. In theory weak gravitational lensing will enable an approximately unbiased measurement of mass, but parametric methods…
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…
Bayesian aggregation of average data: An application in drug development
Sebastian Weber, Andrew Gelman, Daniel Lee +3
Throughout the different phases of a drug development program, randomized trials are used to establish the tolerability, safety, and efficacy of a candidate drug. At each stage one…
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…
On the Geometric Ergodicity of Hamiltonian Monte Carlo
Samuel Livingstone, Michael Betancourt, Simon Byrne +1
We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations wit…
The Stan Math Library: Reverse-Mode Automatic Differentiation in C++
Bob Carpenter, Matthew D. Hoffman, Marcus Brubaker +3
As computational challenges in optimization and statistical inference grow ever harder, algorithms that utilize derivatives are becoming increasingly more important. The implementa…