Updated 03/29/2020 |
R. Martin and C. Liu (2015). Inferential Models: Reasoning with Uncertainty. Monographs in Statistics and Applied Probability Series, Chapman & Hall/CRC Press. [Publisher] [Google books] [companion website]
R. Martin (2009). Fast Nonparametric Estimation of Mixing Distributions with Application to High-Dimensional Inference. Ph.D. thesis. [pdf]
Lecture Notes on Advanced Statistical Theory, 145 pages, version 01/03/2017. [pdf]
Lecture Notes on Statistical Theory, 117 pages, version 01/08/2015. [pdf]
Gibbs posterior inference on multivariate quantiles, with I. Bhattacharya. [arXiv]
Valid distribution-free inferential models for prediction, with L. Cella. [researchers.one] [arXiv]
An empirical G-Wishart prior for sparse high-dimensional Gaussian graphical models, with C. Liu. [arXiv]
Generalized inferential models for censored data, with J. Cahoon. [researchers.one] [arXiv]
Valid model-free prediction of future insurance claims, with L. Hong. [researchers.one] [ssrn]
Generalized inferential models for meta-analyses based on few studies, with J. Cahoon. [researchers.one] [arXiv]
Permutation-based uncertainty quantification about a mixing distribution, with V. Dixit. [arXiv]
Variational approximations using Fisher divergence, with Y. Yang and H. Bondell. [arXiv]
Empirical priors for prediction in sparse high-dimensional linear regression, with Y. Tang. [arXiv] [researchers.one] [R code]
In peer review we (don't) trust: How peer review's filtering poses a systemic risk to science, with H. Crane. [researchers.one]
Is statistics meeting the needs of science?, with H. Crane. [researchers.one]
Asymptotically optimal empirical Bayes inference in a piecewise constant sequence model, with W. Shen. [arXiv] [R code]
A mathematical characterization of confidence as valid beliefs. [arXiv]
Valid uncertainty quantification about the model in linear regression, with H. Xu, Z. Zhang, and C. Liu. [arXiv]
A note on Bayesian convergence rates under local prior support conditions, with L. Hong and S. G. Walker. [arXiv]
Optimal inferential models for a Poisson mean, with D. Ermini Leaf and C. Liu. [arXiv] [R code]
On convergence rates of Bayesian predictive densities and posterior distributions, with L. Hong. [arXiv]
Z. Wang and R. Martin (202x). Model-free posterior inference on the area under the receiver operating characteristic curve. Journal of Statistical Planning and Inference. [arXiv]
C. Liu, Y. Yang, H. Bondell, and R. Martin (202x). Bayesian inference in high-dimensional linear models using an empirical correlation-adaptive prior. Statistica Sinica. [arXiv]
L. Hong and R. Martin (202x). Discussion on "q-Credibility" by O. Le Courtois, Variance: Journal of the Casualty Actuarial Society. [ssrn]
L. Hong and R. Martin (202x). Model misspecification, Bayesian versus credibility estimation, and Gibbs posteriors. Scandinavian Actuarial Journal. [researchers.one] [ssrn]
R. Martin and B. Ning (202x). Empirical priors and coverage of posterior credible sets in a sparse normal mean model. Sankhya A. Special issue in memory of Professor J.K. Ghosh. [arXiv] [researchers.one]
S. T. Tokdar and R. Martin (202x). Bayesian test of normality versus a Dirichlet process mixture alternative. Sankhya B. Special issue in memory of Professor J.K. Ghosh. [arXiv]
R. Martin (202x). A survey of nonparametric mixing density estimation via the predictive recursion algorithm. Sankhya B. Special issue in memory of Professor J.K. Ghosh. [arXiv] [researchers.one]
N. Syring and R. Martin (202x). Robust and rate-optimal Gibbs posterior inference on the boundary of a noisy image. The Annals of Statistics. [arXiv] [R code]
Y. Lin, R. Martin, and M. Yang (2019). On optimal designs for non-regular models. The Annals of Statistics. [arXiv]
R. Martin (2019). Empirical priors and posterior concentration rates for a monotone density. Sankhya A. [arXiv] [researchers.one] [R code]
H. Crane and R. Martin (2019). Rethinking probabilistic prediction: lessons learned from the 2016 U.S. presidential election. Researchers.One.
R. Martin and S. G. Walker (2019). Data-driven priors and their posterior concentration rates. Electronic Journal of Statistics. [arXiv]
R. Martin (2019). False confidence, non-additive beliefs, and valid statistical inference. International Journal of Approximate Reasoning. Special issue for papers presented at the BELIEF 2018 conference in Compiegne, France. [arXiv] [researchers.one]
M. Balch, R. Martin, and S. Ferson (2019). Satellite conjunction analysis and the false confidence theorem. Proceedings of the Royal Society, Series A. [arXiv]
N. Syring, L. Hong, and R. Martin (2019). Gibbs posterior inference on value-at-risk. Scandinavian Actuarial Journal. [researchers.one]
R. Martin (2019). Discussion of "Nonparametric generalized fiducial inference for survival functions under censoring". Biometrika.
L. Cella and R. Martin (2019). Incorporating expert opinion in an inferential model while retaining validity. In Proceedings of Machine Learning Research (2019 International Symposium on Imprecise Probabilities: Theory & Applications).
J. Cahoon and R. Martin (2019). Possibility measures for valid statistical inference based on censored data. In Proceedings of Machine Learning Research (2019 International Symposium on Imprecise Probabilities: Theory & Applications).
R. Martin and N. Syring (2019). Validity-preservation properties of rules for combining inferential models. In Proceedings of Machine Learning Research (2019 International Symposium on Imprecise Probabilities: Theory & Applications). [researchers.one]
R. Martin (2019). On valid uncertainty quantification about a model. In Proceedings of Machine Learning Research (2019 International Symposium on Imprecise Probabilities: Theory & Applications). [researchers.one]
M. Chae, R. Martin, and S. G. Walker (2019). On an algorithm for solving Fredholm equations of the first kind. Statistics and Computing. [arXiv]
N. Syring and R. Martin (2019). Calibrating general posterior credible regions. Biometrika. [arXiv] [R code]
L. Hong and R. Martin (2019). Real-time Bayesian nonparametric prediction of solvency risk. Annals of Actuarial Science. [ssrn] [R code]
H. Crane and R. Martin (2018). Academia's case of Stockholm syndrome. Quillette.
H. Crane and R. Martin (2018). The researchers.one mission. Researchers.One.
L. Hong, T. Kuffner, and R. Martin (2018). On prediction of future insurance claims when the model is uncertain. Variance: Journal of the Casualty Actuarial Society. [ssrn] [R code]
P. R. Hahn, R. Martin, and S. G. Walker (2018). On recursive Bayesian predictive distributions. Journal of the American Statistical Association. [arXiv]
M. Chae, R. Martin, and S. G. Walker (2018). Convergence of an iterative algorithm to the nonparametric MLE of a mixing distribution. Statistics & Probability Letters. [arXiv]
L. Hong, T. Kuffner, and R. Martin (2018). On overfitting and post-selection uncertainty assessments. Biometrika. [arXiv]
R. Martin, C. Ouyang, and F. Domagni (2018). 'Purposely misspecified' posterior inference on the volatility of a jump diffusion process. Statistics & Probability Letters. [arXiv]
L. Hong and R. Martin (2018). Dirichlet process mixture models for insurance loss data. Scandinavian Actuarial Journal. [ssrn]
R. Martin (2018). On an inferential model construction using generalized associations. Journal of Statistical Planning and Inference. Special issue on Confidence Distributions and Related Themes. [arXiv]
R. Martin (2017). Invited comment on the article—"Uncertainty quantification for the horseshoe"—by van der Pas, Szabo, and van der Vaart. Bayesian Analysis.
R. Martin, R. Mess, and S. G. Walker (2017). Empirical Bayes posterior concentration in sparse high-dimensional linear models. Bernoulli. [arXiv] [R code] (Some minor corrections are given in the arXiv version.)
N. Syring and R. Martin (2017). Gibbs posterior inference on the minimum clinically important difference. Journal of Statistical Planning and Inference. [arXiv]
R. Martin (2017). A statistical inference course based on p-values. The American Statistician. [arxiv]
R. Martin (2017). Inferential models. Wiley StatsRef: Statistics Reference Online.
L. Hong and R. Martin (2017). A review of Bayesian asymptotics in general insurance applications. European Actuarial Journal. [ssrn]
L. Hong and R. Martin (2017). A flexible Bayesian nonparametric model for predicting future insurance claims. North American Actuarial Journal. [ssrn] [R code]
C. Liu, R. Martin, and N. Syring (2017). Efficient simulation from a gamma distribution with small shape parameter. Computational Statistics. [arXiv] [R code]
R. Martin (2017). Prior-free probabilistic inference for econometricians. In Robustness in Econometrics, Kreinovich, Sriboonchitta, and Huynh, Eds.
R. Martin, J. Stufken, and M. Yang (2016). A conversation with Samad Hedayat. Statistical Science.
R. Martin and R. Lingham (2016). Prior-free probabilistic prediction of future observations. Technometrics. [arXiv] [R code]
R. Martin and Y. Lin (2016). Exact prior-free probabilistic inference in a class of non-regular models. Stat. [arXiv]
R. Martin and Z. Han (2016). A semiparametric scale-mixture regression model and predictive recursion maximum likelihood. Computational Statistics and Data Analysis. [arXiv] [R code]
L. Hong and R. Martin (2016). Discussion on "Credibility estimation of distribution functions with applications to experience rating in general insurance". North American Actuarial Journal. [ssrn]
R. Martin (2015). Plausibility functions and exact frequentist inference. Journal of the American Statistical Association. [arXiv]
R. Martin and C. Liu (2015). Marginal inferential models: prior-free probabilistic inference on interest parameters. Journal of the American Statistical Association. [arXiv]
R. Martin and C. Liu (2015). Conditional inferential models: combining information for prior-free probabilistic inference. Journal of the Royal Statistical Society–Series B. [arXiv]
R. V. Ramamoorthi, K. Sriram, and R. Martin (2015). On posterior concentration in misspecified models. Bayesian Analysis. [arXiv]
C. Liu and R. Martin (2015). Frameworks for prior-free posterior probabilistic inference. WIREs: Computational Statistics. [arXiv]
R. Martin (2015). Asymptotically optimal nonparametric empirical Bayes via predictive recursion. Communications in Statistics–Theory & Methods. [arXiv]
Q. Cheng, X. Gao, and R. Martin (2014). Exact prior-free probabilistic inference on the heritability coefficient in a linear mixed effect model. Electronic Journal of Statistics. [arXiv] [R code]
R. Martin and S. G. Walker (2014). Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector. Electronic Journal of Statistics. [arXiv] [R code]
R. Martin (2014). Random sets and exact confidence regions. Sankhya A. [arXiv]
R. Martin and C. Liu (2014). A note on p-values interpreted as plausibilities. Statistica Sinica. [arXiv]
R. Martin and C. Liu (2014). Discussion: Foundations of statistical inference, revisited. Statistical Science. [arXiv]
R. Martin and C. Liu (2013). Inferential models: A framework for prior-free posterior probabilistic inference. Journal of the American Statistical Association. [arXiv] [R code] (Small correction and some extensions in the arXiv version, also published in the journal here.)
R. Martin (2013). An approximate Bayesian marginal likelihood approach for estimating finite mixtures. Communications in Statistics–Simulation & Computation. [arXiv] [R code]
R. Martin and O. Tilak (2012). On ε-optimality of the pursuit learning algorithm. Journal of Applied Probability. [arXiv]
R. Martin and S. T. Tokdar (2012). A nonparametric empirical Bayes framework for large-scale multiple testing. Biostatistics. [arXiv]
R. Martin (2012). Convergence rate for predictive recursion estimation of finite mixtures. Statistics & Probability Letters. [arXiv]
R. Martin and S. T. Tokdar (2011). Semiparametric inference in mixture models with predictive recursion marginal likelihood. Biometrika. [arXiv]
Z. Zhang, H. Xu, R. Martin, and C. Liu (2011). Inferential models for linear regression. Pakistan Journal of Statistics and Operations Research. Special issue on "Variable Selection in Regression".
O. Tilak, R. Martin, and S. Mukhopadhyay (2011). Decentralized indirect method for learning automata games. IEEE Transactions on Systems, Man, and Cybernetics–Part B.
R. Martin, J. Zhang, and C. Liu (2010). Dempster–Shafer theory and statistical inference with weak beliefs. Statistical Science. [arXiv]
R. Martin and S. T. Tokdar (2009). Asymptotic properties of predictive recursion: robustness and rate of convergence. Electronic Journal of Statistics.
S. T. Tokdar, R. Martin, and J. K. Ghosh (2009). Consistency of a recursive estimate of mixing distributions. The Annals of Statistics. [arXiv]
R. Martin and J. K. Ghosh (2008). Stochastic approximation and Newton's estimate of a mixing distribution. Statistical Science. [arXiv]
J. K. Ghosh and R. Martin (2008). On two fast algorithms for estimating the mixing distribution in mixture models. In Frontiers in Applied and Computational Mathematics, D. Blackmore, A. Bose and P. Petropoulos, Eds.
Paper: "Empirical priors for prediction in sparse high-dimensional linear regression".
Downloadable file: ebpred.R
There is now an R package available here (developed by Yiqi Tang).
Paper: "Empirical priors and posterior concentration rates for a monotone density".
Downloadable file: ebmono.R
Paper: "Asymptotically optimal empirical Bayes inference in a piecewise constant sequence model".
Downloadable file: ebpiece.R
Paper: "On an algorithm for solving Fredholm equations of the first kind".
Downloadable file: fredholm.R
Paper: "On prediction of future insurance claims when the model is uncertain".
Downloadable file: pred.R
Paper: "Real-time Bayesian nonparametric prediction of solvency risk".
Downloadable file: dpmrec.R dpmrec.Rd
Paper: "Empirical Bayes posterior concentration in sparse high-dimensional linear models".
Downloadable file: ebreg.R
Paper: "Asymptotically minimax empirical Bayes estimation of a sparse normal mean"
Downloadable file: ebsparse.R
Paper: "A flexible Bayesian nonparametric model for predicting future insurance claims"
Downloadable file: dpmslice.R
Paper: "Simulating from gamma distribution with small shape parameter"
Downloadable file: rgamss.R
Paper: "Exact prior-free probabilistic inference on the heritability coefficient in a linear mixed model" .
Downloadable files: imvch.R assay.Rd
Paper: "Prior-free probabilistic inference of future observations"
Downloadable file: impred.R
Paper: "Optimal inferential models for a Poisson mean"
Downloadable file: impois.R
Paper: "Inferential models: A framework for prior-free posterior probabilistic inference"
Downloadable file: imbasics.R
Paper: "Robust regression via predictive recursion maximum likelihood"
Downloadable file: prreg.R
Downloadable files: pr.R pr.c
Contains R and R+C versions of predictive recursion (PR).
Instructions provided in the .R file.
PR marginal likelihood can be defined easily using output of PR.
Paper: "An approximate Bayesian marginal likelihood approach for estimating finite mixtures".
Downloadable files: sasa.R sasa.c galaxy.txt
Instructions in the .R file.
Examples with galaxy data: in R, type:source("sasa.R")
gal.loc.mix <- galaxy.known()
gal.locscale.mix <- galaxy.lsmix()
BayesComp 2020
Gibbs posterior distributions. [slides]
University of Florida, January 2020.
ISIPTA 2019
--On valid uncertainty quantification about a model. [slides] [poster]
--Possibility measures for valid statistical inference based on censored data. [slides]
--Incorporating expert opinion in an inferential model while maintaining validity. [slides]
Ghent University, Belgium, July 2019.
O'Bayes 2019
Objective data-dependent distributions. [slides]
University of Warwick, UK, June 2019.
6th African International Conference on Statistics
--False confidence, non-additive beliefs, and valid statistical inference. [slides]
--Construction, concentration, and calibration of Gibbs posteriors. [slides]
Arsi University, Ethiopia, May 2019.
Jessie Jeng's ST790: High-Dimensional Statistical Inference course
Empirical priors for high-dimensional problems. [slides]
North Carolina State University, March 2019.
Applied and Computational Mathematics and Statistics Department Colloquium
False confidence, non-additive beliefs, and valid statistical inference. [slides]
University of Notre Dame, February 2019.
BELIEF 2018/SMPS 2018
Belief functions and valid statistical inference (keynote).
Compiegne, France, September 2018.
2018 IMS Annual Meeting
Construction, concentration, and calibration of Gibbs posteriors.
(Also presented in the session on open-access e-journals [slides])
Vilnius, Lithuania, July 2018.
2018 ISBA World Meeting
Empirical priors for wranglin' with structured high-dimensional problems.
(Editor's choice session: "Lassos and horseshoes for the sparse Bayesian cowboy")
Edinburgh, Scotland, June 2018.
2018 IISA International Conference on Statistics
Fast nonparametric estimation of a smooth mixing density.
(Memorial session for Professor J.K. Ghosh)
University of Florida, May 2018.
5th Bayesian, Fiducial, and Frequentist Conference
Probability dilution, false confidence, and non-additive beliefs.
University of Michigan, May 2018.
12th UMBC Probability and Statistics Day
Fast nonparametric estimation of a smooth mixing density.
(Keynote/Memorial session for Professor J.K. Ghosh)
University of Maryland Baltimore County, April 2018.
Foundations of Probability Seminar
Probability dilution, false confidence, and non-additive beliefs.
Rutgers University, April 2018.
CMStatistics 2017
Posterior concentration rates via empirical priors.
London, UK, December 2017.
2nd Workshop on Higher-Order Asymptotics & Post-Selection Inference
On valid post-selection prediction in regression.
Washington University in St. Louis, August 2017.
11th Conference on Bayesian Nonparametrics
Model misspecification on purpose.
Paris, France, June 2017.
4th Bayesian, Fiducial, and Frequentist Conference
Confidence, probability, and plausibility.
(Also presented in the "Views from Rising Stars" panel discussion)
Harvard University, May 2017.
Department of Mathematics, Statistics Seminar
On valid prior-free probabilistic inference.
Washington University in St Louis, April 2017.
10th International Conference of the Thailand Econometric Society
Valid prior-free probabilistic inference.
(Plenary Session invited talk)
Chiang Mai University, Thailand, January 2017.
Department of Statistics Seminar
Posterior inference without (really) using Bayes. [slides]
North Carolina State University, December 2016.
Latent Variables Conference
A double empirical Bayes approach for high-dimensional problems.
University of South Carolina, October 2016.
Workshop on Higher-Order Asymptotics and Post-Selection Inference
A new double empirical Bayes approach for high-dimensional problems.
Washington University at St. Louis, September 2016.
ICSA Applied Statistics Symposium
A new double empirical Bayes approach for high-dimensional problems.
Atlanta, GA, June 2016.
Workshop on Fusion Learning, BFF inferences and Statistical Foundations
Beliefs, validity, and the foundations of statistics.
Rutgers University, April 2016.
Department of Statistics and Biostatistics Seminar
Valid prior-free probabilistic inference.
Rutgers University, December 2015.
Department of Statistics Colloquium
Inferential models: a framework for prior-free probabilistic inference.
North Carolina State University, November 2015.
Statistics Colloquium
High-dimensional posterior inference via double empirical Bayes.
Texas A&M University, February 2015.
International Conference on Advances in Interdisciplinary Statistics and Combinatorics
Empirical Bayes posterior concentration in sparse high-dimensional linear models,
Greensboro, NC, October 2014.
Department of Statistics Seminar
Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector.
University of Illinois at Urbana–Champaign, September 2013.
Department of Statistics Seminar
A Bayesian test of normality versus a Dirichlet process mixture alternative.
Northwestern University, January 2013.
Statistical Science Seminar
Inferential models: A framework for prior-free posterior probabilistic inference.
Duke University, November 2012.
ASA Northeastern Illinois Chapter Meeting
A nonparametric empirical Bayes framework for large-scale multiple testing.
Northbrook, IL, October 2012.
Statistics and Probability Seminar
Plausibility functions and exact frequentist inference.
Michigan State University, October 2012.
Purdue Symposium on Statistics
Inferential models: A framework for prior-free posterior probabilistic inference.
Purdue University, June 2012.
Applied Mathematics Department Colloquium
"A nonparametric empirical Bayes framework for large-scale multiple testing."
Illinois Institute of Technology, January 2012.
ACMS Department Colloquium
"Predictive recursion marginal likelihood and application to large-scale simultaneous testing."
University of Notre Dame, January 2011.