Publications (114)
Convergence rate for predictive recursion estimation of finite mixtures
Ryan Martin
Predictive recursion (PR) is a fast stochastic algorithm for nonparametric estimation of mixing distributions in mixture models. It is known that the PR estimates of both the mixin…
A note on Bayesian convergence rates under local prior support conditions
Ryan Martin, Liang Hong, Stephen G. Walker
Bounds on Bayesian posterior convergence rates, assuming the prior satisfies both local and global support conditions, are now readily available. In this paper we explore, in the c…
Optimal inferential models for a Poisson mean
Ryan Martin, Duncan Ermini Leaf, Chuanhai Liu
Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisso…
Valid and efficient imprecise-probabilistic inference with partial priors, I. First results
Ryan Martin
Between Bayesian and frequentist inference, it's commonly believed that the former is for cases where one has a prior and the latter is for cases where one has no prior. But the pr…
Validity, consonant plausibility measures, and conformal prediction
Leonardo Cella, Ryan Martin
Prediction of future observations is an important and challenging problem. The two mainstream approaches for quantifying prediction uncertainty use prediction regions and predictiv…
Bayesian test of normality versus a Dirichlet process mixture alternative
Surya T. Tokdar, Ryan Martin
We propose a Bayesian test of normality for univariate or multivariate data against alternative nonparametric models characterized by Dirichlet process mixture distributions. The a…
On epsilon-optimality of the pursuit learning algorithm
Ryan Martin, Omkar Tilak
Estimator algorithms in learning automata are useful tools for adaptive, real-time optimization in computer science and engineering applications. This paper investigates theoretica…
Permutation-based uncertainty quantification about a mixing distribution
Vaidehi Dixit, Ryan Martin
Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantifica…
Semiparametric inference in mixture models with predictive recursion marginal likelihood
Ryan Martin, Surya T. Tokdar
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, ho…
Computationally efficient variational-like approximations of possibilistic inferential models
Leonardo Cella, Ryan Martin
Inferential models (IMs) offer provably reliable, data-driven, possibilistic statistical inference. But despite the IM framework's theoretical and foundational advantages, efficien…
Asymptotically optimal inference in sparse sequence models with a simple data-dependent measure
Ryan Martin
For high-dimensional inference problems, statisticians have a number of competing interests. On the one hand, procedures should provide accurate estimation, reliable structure lear…
A nonparametric empirical Bayes framework for large-scale multiple testing
Ryan Martin, Surya T. Tokdar
We propose a flexible and identifiable version of the two-groups model, motivated by hierarchical Bayes considerations, that features an empirical null and a semiparametric mixture…
Exact prior-free probabilistic inference in a class of non-regular models
Ryan Martin, Yi Lin
The use of standard statistical methods, such as maximum likelihood, is often justified based on their asymptotic properties. For suitably regular models, this theory is standard b…
Discussion: Foundations of Statistical Inference, Revisited
Ryan Martin, Chuanhai Liu
This is an invited contribution to the discussion on Professor Deborah Mayo's paper, "On the Birnbaum argument for the strong likelihood principle," to appear in Statistical Scienc…
Stochastic Approximation and Newton's Estimate of a Mixing Distribution
Ryan Martin, Jayanta K. Ghosh
Many statistical problems involve mixture models and the need for computationally efficient methods to estimate the mixing distribution has increased dramatically in recent years.…
Valid and efficient possibilistic structure learning in Gaussian linear regression
Ryan Martin, Naomi Singer, Jonathan Williams
A crucial step in fitting a regression model to data is determining the model's structure, i.e., the subset of explanatory variables to be included. However, the uncertainty in thi…
Dempster--Shafer Theory and Statistical Inference with Weak Beliefs
Ryan Martin, Jianchun Zhang, Chuanhai Liu
The Dempster--Shafer (DS) theory is a powerful tool for probabilistic reasoning based on a formal calculus for combining evidence. DS theory has been widely used in computer scienc…
No-prior Bayes reIMagined: probabilistic approximations of inferential models
Ryan Martin
When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generali…
On an inferential model construction using generalized associations
Ryan Martin
The inferential model (IM) approach, like fiducial and its generalizations, depends on a representation of the data-generating process. Here, a particular variation on the IM const…
Universal Inference for model selection on networks
Eric Yanchenko, Jonathan P. Williams, Ryan Martin
Model selection and hypothesis testing are important tasks on networks. A key challenge lies in the inherent dependence in network data, as well as the fact that typically only a s…
Valid and efficient imprecise-probabilistic inference with partial priors, II. General framework
Ryan Martin
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world…
False confidence, non-additive beliefs, and valid statistical inference
Ryan Martin
Statistics has made tremendous advances since the times of Fisher, Neyman, Jeffreys, and others, but the fundamental and practically relevant questions about probability and infere…
An efficient Monte Carlo method for valid prior-free possibilistic statistical inference
Ryan Martin
Inferential models (IMs) offer prior-free, Bayesian-like posterior degrees of belief designed for statistical inference, which feature a frequentist-like calibration property that…
Asymptotically optimal nonparametric empirical Bayes via predictive recursion
Ryan Martin
An empirical Bayes problem has an unknown prior to be estimated from data. The predictive recursion (PR) algorithm provides fast nonparametric estimation of mixing distributions an…
Regularized e-processes: anytime valid inference with knowledge-based efficiency gains
Ryan Martin
Classical statistical methods have theoretical justification when the sample size is predetermined. In applications, however, it's often the case that sample sizes are data-depende…
A note on p-values interpreted as plausibilities
Ryan Martin, Chuanhai Liu
P-values are a mainstay in statistics but are often misinterpreted. We propose a new interpretation of p-value as a meaningful plausibility, where this is to be interpreted formall…
A PRticle filter algorithm for nonparametric estimation of multivariate mixing distributions
Vaidehi Dixit, Ryan Martin
Predictive recursion (PR) is a fast, recursive algorithm that gives a smooth estimate of the mixing distribution under the general mixture model. However, the PR algorithm requires…
On the edit distance from -free graphs II: Cases
Ryan Martin, Tracy McKay
The edit distance between two graphs on the same vertex set is defined to be size of the symmetric difference of their edge sets. The edit distance function of a hereditary propert…
Variational empirical Bayes variable selection in high-dimensional logistic regression
Yiqi Tang, Ryan Martin
Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariat…
Fiducial inference viewed through a possibility-theoretic inferential model lens
Ryan Martin
Fisher's fiducial argument is widely viewed as a failed version of Neyman's theory of confidence limits. But Fisher's goal -- Bayesian-like probabilistic uncertainty quantification…
Model-free posterior inference on the area under the receiver operating characteristic curve
Zhe Wang, Ryan Martin
The area under the receiver operating characteristic curve (AUC) serves as a summary of a binary classifier's performance. Methods for estimating the AUC have been developed under…
Ultra-Low Noise Mechanically Cooled Germanium Detector
Paul Barton, Mark Amman, Ryan Martin +1
Low capacitance, large volume, high purity germanium (HPGe) radiation detectors have been successfully employed in low-background physics experiments. However, some physical proces…
Decision-making with possibilistic inferential models
Ryan Martin, Shih-Ni Prim, Jonathan Williams
Inferential models (IMs) are data-dependent, imprecise-probabilistic structures designed to quantify uncertainty about unknowns. As the name suggests, the focus has been on uncerta…
Turning the information-sharing dial: efficient inference from different data sources
Emily C. Hector, Ryan Martin
A fundamental aspect of statistics is the integration of data from different sources. Classically, Fisher and others were focused on how to integrate homogeneous (or only mildly he…
Inferential models and possibility measures
Chuanhai Liu, Ryan Martin
The inferential model (IM) framework produces data-dependent, non-additive degrees of belief about the unknown parameter that are provably valid. The validity property guarantees,…
Generalized Bayes inference on a linear personalized minimum clinically important difference
Pei-Shien Wu, Ryan Martin
Inference on the minimum clinically important difference, or MCID, is an important practical problem in medicine. The basic idea is that a treatment being statistically significant…
Inferential models: A framework for prior-free posterior probabilistic inference
Ryan Martin, Chuanhai Liu
Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and B…
Calibrating general posterior credible regions
Nicholas Syring, Ryan Martin
An advantage of methods that base inference on a posterior distribution is that credible regions are readily obtained. Except in well-specified situations, however, there is no gua…
Fisher's underworld and the behavioral-statistical reliability balance in scientific inference
Ryan Martin
That science and other domains are now largely data-driven means virtually unlimited opportunities for statisticians. With great power comes responsibility, so it's imperative that…
Conditional inferential models: combining information for prior-free probabilistic inference
Ryan Martin, Chuanhai Liu
The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference c…
Plausibility functions and exact frequentist inference
Ryan Martin
In the frequentist program, inferential methods with exact control on error rates are a primary focus. The standard approach, however, is to rely on asymptotic approximations, whic…
Advances in Bayesian model selection consistency for high-dimensional generalized linear models
Jeyong Lee, Minwoo Chae, Ryan Martin
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of…
Simulating from a gamma distribution with small shape parameter
Chuanhai Liu, Ryan Martin, Nick Syring
Simulating from a gamma distribution with small shape parameter is a challenging problem. Towards an efficient method, we obtain a limiting distribution for a suitably normalized g…
Consistency of a recursive estimate of mixing distributions
Surya T. Tokdar, Ryan Martin, Jayanta K. Ghosh
Mixture models have received considerable attention recently and Newton [SankhyÄ Ser. A 64 (2002) 306--322] proposed a fast recursive algorithm for estimating a mixing distributio…
Gibbs posterior inference on a Levy density under discrete sampling
Zhe Wang, Ryan Martin
In mathematical finance, Levy processes are widely used for their ability to model both continuous variation and abrupt, discontinuous jumps. These jumps are practically relevant,…
Gibbs posterior inference on multivariate quantiles
Indrabati Bhattacharya, Ryan Martin
Bayesian and other likelihood-based methods require specification of a statistical model and may not be fully satisfactory for inference on quantities, such as quantiles, that are…
Lower bounds for identifying codes in some infinite grids
Ryan Martin, Brendon Stanton
An -identifying code on a graph is a set such that for every vertex in , the intersection of the radius- closed neighborhood with is nonempty an…
Results from the Neutral Current Detector phase of the Sudbury Neutrino Observatory
Ryan Martin
The Sudbury Neutrino Observatory (SNO) was a heavy water Cerenkov detector designed to solve the long-standing ``solar neutrino problem''; a discrepancy between the measured and pr…
A comparison of learning rate selection methods in generalized Bayesian inference
Pei-Shien Wu, Ryan Martin
Generalized Bayes posterior distributions are formed by putting a fractional power on the likelihood before combining with the prior via Bayes's formula. This fractional power, whi…
An empirical -Wishart prior for sparse high-dimensional Gaussian graphical models
Chang Liu, Ryan Martin
In Gaussian graphical models, the zero entries in the precision matrix determine the dependence structure, so estimating that sparse precision matrix and, thereby, learning this un…
Empirical priors and posterior concentration in a piecewise polynomial sequence model
Chang Liu, Ryan Martin, Weining Shen
Inference on high-dimensional parameters in structured linear models is an important statistical problem. This paper focuses on the case of a piecewise polynomial Gaussian sequence…
Anytime valid and asymptotically optimal inference driven by predictive recursion
Vaidehi Dixit, Ryan Martin
Distinguishing two candidate models is a fundamental and practically important statistical problem. Error rate control is crucial to the testing logic but, in complex nonparametric…
On recursive Bayesian predictive distributions
P. Richard Hahn, Ryan Martin, Stephen G. Walker
A Bayesian framework is attractive in the context of prediction, but a fast recursive update of the predictive distribution has apparently been out of reach, in part because Monte…
Robust and rate-optimal Gibbs posterior inference on the boundary of a noisy image
Nicholas Syring, Ryan Martin
Detection of an image boundary when the pixel intensities are measured with noise is an important problem in image segmentation, with numerous applications in medical imaging and e…
An imprecise-probabilistic characterization of frequentist statistical inference
Ryan Martin
Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigoro…
Elucidating Inferential Models with the Cauchy Distribution
Chuanhai Liu, Ryan Martin
Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been a…
Possibility-theoretic statistical inference offers performance and probativeness assurances
Leonardo Cella, Ryan Martin
Statisticians are largely focused on developing methods that perform well in a frequentist sense -- even the Bayesians. But the widely-publicized replication crisis suggests that t…
Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector
Ryan Martin, Stephen G. Walker
For the important classical problem of inference on a sparse high-dimensional normal mean vector, we propose a novel empirical Bayes model that admits a posterior distribution with…
Direct Gibbs posterior inference on risk minimizers: construction, concentration, and calibration
Ryan Martin, Nicholas Syring
Real-world problems, often couched as machine learning applications, involve quantities of interest that have real-world meaning, independent of any statistical model. To avoid pot…
Generalized inferential models for meta-analyses based on few studies
Joyce Cahoon, Ryan Martin
Meta-analysis based on only a few studies remains a challenging problem, as an accurate estimate of the between-study variance is apparently needed, but hard to attain, within this…
Empirical priors and coverage of posterior credible sets in a sparse normal mean model
Ryan Martin, Bo Ning
Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution. But is this uncertainty quan…
Generalized inferential models for censored data
Joyce Cahoon, Ryan Martin
Inferential challenges that arise when data are censored have been extensively studied under the classical frameworks. In this paper, we provide an alternative generalized inferent…
Stochastic optimization for numerical evaluation of imprecise probabilities
Nicholas Syring, Ryan Martin
In applications of imprecise probability, analysts must compute lower (or upper) expectations, defined as the infimum of an expectation over a set of parameter values. Monte Carlo…
Data-driven priors and their posterior concentration rates
Ryan Martin, Stephen G. Walker
In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs t…
On optimal designs for non-regular models
Yi Lin, Ryan Martin, Min Yang
Classically, Fisher information is the relevant object in defining optimal experimental designs. However, for models that lack certain regularity, the Fisher information does not e…
Empirical priors and posterior concentration rates for a monotone density
Ryan Martin
In a Bayesian context, prior specification for inference on monotone densities is conceptually straightforward, but proving posterior convergence theorems is complicated by the fac…
A mathematical characterization of confidence as valid belief
Ryan Martin
Confidence is a fundamental concept in statistics, but there is a tendency to misinterpret it as probability. In this paper, I argue that an intuitively and mathematically more app…
On overfitting and post-selection uncertainty assessments
Liang Hong, Todd A. Kuffner, Ryan Martin
In a regression context, when the relevant subset of explanatory variables is uncertain, it is common to use a data-driven model selection procedure. Classical linear model theory,…
On nonparametric estimation of a mixing density via the predictive recursion algorithm
Ryan Martin
Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast,…
Bayesian inference in high-dimensional linear models using an empirical correlation-adaptive prior
Chang Liu, Yue Yang, Howard Bondell +1
In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor…
The typicality principle and its implications for statistics and data science
Yiran Jiang, Zeyu Zhang, Ryan Martin +1
A central focus of data science is the transformation of empirical evidence into knowledge. As such, the key insights and scientific attitudes of deep thinkers like Fisher, Popper,…
Powers of Hamiltonian cycles in multipartite graphs
Louis DeBiasio, Ryan Martin, Theodore Molla
We prove that if is a -partite graph on vertices in which all of the parts have order at most and every vertex is adjacent to at least a proportion of…
Random sets and exact confidence regions
Ryan Martin
An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence r…
Prior-free probabilistic prediction of future observations
Ryan Martin, Rama Lingham
Prediction of future observations is a fundamental problem in statistics. Here we present a general approach based on the recently developed inferential model (IM) framework. We em…
On convergence rates of Bayesian predictive densities and posterior distributions
Ryan Martin, Liang Hong
Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In…
Gibbs posterior concentration rates under sub-exponential type losses
Nicholas Syring, Ryan Martin
Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance pa…
Gibbs posterior inference on the minimum clinically important difference
Nick Syring, Ryan Martin
IIt is known that a statistically significant treatment may not be clinically significant. A quantity that can be used to assess clinical significance is called the minimum clinica…
Generalized Universal Inference on Risk Minimizers
Neil Dey, Ryan Martin, Jonathan P. Williams
A common goal in statistics and machine learning is estimation of unknowns. Point estimates alone are of little value without an accompanying measure of uncertainty, but traditiona…
Valid model-free spatial prediction
Huiying Mao, Ryan Martin, Brian Reich
Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in non-stationary…
Exact prior-free probabilistic inference on the heritability coefficient in a linear mixed model
Qianshun Cheng, Xu Gao, Ryan Martin
Linear mixed-effect models with two variance components are often used when variability comes from two sources. In genetics applications, variation in observed traits can be attrib…
Empirical Bayes inference in sparse high-dimensional generalized linear models
Yiqi Tang, Ryan Martin
High-dimensional linear models have been widely studied, but the developments in high-dimensional generalized linear models, or GLMs, have been slower. In this paper, we propose an…
On weighted Ramsey numbers
Maria Axenovich, Ryan Martin
The weighted Ramsey number, , is the minimum such that there is an assignment of nonnegative real numbers (weights) to the edges of with the total sum of t…
Marginal inferential models: prior-free probabilistic inference on interest parameters
Ryan Martin, Chuanhai Liu
The inferential models (IM) framework provides prior-free, frequency-calibrated, posterior probabilistic inference. The key is the use of random sets to predict unobservable auxili…
Applications of an algorithm for solving Fredholm equations of the first kind
Minwoo Chae, Ryan Martin, Stephen G. Walker
In this paper we use an iterative algorithm for solving Fredholm equations of the first kind. The basic algorithm is known and is based on an EM algorithm when involved functions a…
Frameworks for prior-free posterior probabilistic inference
Chuanhai Liu, Ryan Martin
The development of statistical methods for valid and efficient probabilistic inference without prior distributions has a long history. Fisher's fiducial inference is perhaps the mo…
Revisiting consistency of a recursive estimator of mixing distributions
Vaidehi Dixit, Ryan Martin
Estimation of the mixing distribution under a general mixture model is a very difficult problem, especially when the mixing distribution is assumed to have a density. Predictive re…
Multiple Testing in Generalized Universal Inference
Neil Dey, Ryan Martin, Jonathan P. Williams
Compared to p-values, e-values provably guarantee safe, valid inference. If the goal is to test multiple hypotheses simultaneously, one can construct e-values for each individual t…
Valid inferential models for prediction in supervised learning problems
Leonardo Cella, Ryan Martin
Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guaran…
An approximate Bayesian marginal likelihood approach for estimating finite mixtures
Ryan Martin
Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the…
Fast nonparametric near-maximum likelihood estimation of a mixing density
Minwoo Chae, Ryan Martin, Stephen G. Walker
Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood pr…
Direct and approximately valid probabilistic inference on a class of statistical functionals
Leonardo Cella, Ryan Martin
Existing frameworks for probabilistic inference assume the quantity of interest is the parameter of a posited statistical model. In machine learning applications, however, often th…
Empirical priors for prediction in sparse high-dimensional linear regression
Ryan Martin, Yiqi Tang
In this paper we adopt the familiar sparse, high-dimensional linear regression model and focus on the important but often overlooked task of prediction. In particular, we consider…
A statistical inference course based on p-values
Ryan Martin
Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sam…
Efficient posterior inference on the volatility of a jump diffusion process
Ryan Martin, Cheng Ouyang, Francois Domagni
Jump diffusion processes are widely used to model asset prices over time, mainly for their ability to capture complex discontinuous behavior, but inference on the model parameters…
Status Update of the MAJORANA DEMONSTRATOR Neutrinoless Double Beta Decay Experiment
Julieta Gruszko, Nicolas Abgrall, Isaac Arnquist +67
Neutrinoless double beta decay searches play a major role in determining neutrino properties, in particular the Majorana or Dirac nature of the neutrino and the absolute scale of t…
Possibilistic inferential models: a review
Ryan Martin
An inferential model (IM) is a model describing the construction of provably reliable, data-driven uncertainty quantification and inference about relevant unknowns. IMs and Fisher'…
Estimating a mixing distribution on the sphere using predictive recursion
Vaidehi Dixit, Ryan Martin
Mixture models are commonly used when data show signs of heterogeneity and, often, it is important to estimate the distribution of the latent variable responsible for that heteroge…
Asymptotic efficiency of inferential models and a possibilistic Bernstein--von Mises theorem
Ryan Martin, Jonathan P. Williams
The inferential model (IM) framework offers an alternative to the classical probabilistic (e.g., Bayesian and fiducial) uncertainty quantification in statistical inference. A key d…
Valid uncertainty quantification about the model in a linear regression setting
Ryan Martin, Huiping Xu, Zuoyi Zhang +1
In scientific applications, there often are several competing models that could be fit to the observed data, so quantification of the model uncertainty is of fundamental importance…
A possibility-theoretic solution to Basu's Bayesian--frequentist via media
Ryan Martin
Basu's via media is what he referred to as the middle road between the Bayesian and frequentist poles. He seemed skeptical that a suitable via media could be found, but I disagree.…