Research

Monographs

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

These are notes based on the Stat 411 (Statistical Theory) and Stat 511/512 (Advanced Statistical Theory) courses that I taught several times while I was at the University of Illinois at Chicago, between 2011 and 2016. Both documents are technically still “works in progress” but they are readable and useable. Several instructors have asked if they can use these materials and I am happy to share them. If you’re an instructor and would like to use these notes as a reference for your own course, that’s great; but please contact me ahead of time, as I have a few very minor requests.

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]

Unpublished papers

Superscript “s” indicates a co-author who was/is a student advisee.

Satellite conjunction analysis and the false confidence theorem, with M. S. Balch and S. Ferson. [arXiv]

On optimal designs for non-regular models, with Y. Lin^s and M. Yang. [arXiv]

Is statistics meeting the needs of science?, with H. Crane. [psyarxiv]

Calibrating general posterior credible regions, with N. Syring^s. [arXiv] [R code]

Asymptotically optimal empirical Bayes inference in a piecewise constant sequence model, with W. Shen. [arXiv] [R code]

An algorithm for solving Fredholm equations of the first kind, with M. Chae and S. G. Walker. [arXiv]

A mathematical characterization of confidence as valid beliefs. [arXiv]

Empirical priors for target posterior concentration rates, with S. G. Walker. [arXiv]

Empirical priors and posterior concentration rates for a monotone density. [arXiv]

Robust and rate-optimal Gibbs posterior inference on the boundary of a noisy image, with N. Syring^s. [arXiv] [R code]

Rethinking probabilistic prediction in the wake of the 2016 U.S. presidential election, with H. Crane. [arXiv] [ssrn]

Validity and the foundations of statistical inference, with C. Liu. [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]

Bayesian test of normality versus a Dirichlet process mixture alternative, with S. T. Tokdar. [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]

Published papers

Superscript “s” indicates a co-author who was/is a student advisee.

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, volume 140, pages 142–146. [arXiv]
L. Hong, T. Kuffner, and R. Martin (201x). On prediction of future insurance claims when the model is uncertain. Variance, to appear. [ssrn] [R code]
L. Hong and R. Martin (201x). Real-time Bayesian nonparametric prediction of solvency risk. Annals of Actuarial Science, to appear. [ssrn] [R code]
P. R. Hahn, R. Martin, and S. G. Walker (201x). On recursive Bayesian predictive distributions. Journal of the American Statistical Association, to appear. [arXiv]
L. Hong, T. Kuffner, and R. Martin (2018). On overfitting and post-selection uncertainty assessments. Biometrika, volume 105, pages 221–224. [arXiv]
R. Martin, C. Ouyang, and F. Domagni^s (2018). ‘Purposely misspecified’ posterior inference on the volatility of a jump diffusion process. Statistics & Probability Letters, volume 134, pages 106–113. [arXiv]
L. Hong and R. Martin (201x). Dirichlet process mixture models for insurance loss data. Scandinavian Actuarial Journal, to appear. [ssrn]
R. Martin (2018). On an inferential model construction using generalized associations. Journal of Statistical Planning and Inference, volume 195, pages 105–115; special issue on Confidence Distributions and Related Themes. [arXiv]
R. Martin (2017). Comment on the article—“Uncertainty quantification for the horseshoe”—by van der Pas, Szabo, and van der Vaart. Bayesian Analysis, volume 12, pages 1254–1258. [isba news]
R. Martin, R. Mess^s, and S. G. Walker (2017). Empirical Bayes posterior concentration in sparse high-dimensional linear models. Bernoulli, volume 23, pages 1822–1847. [arXiv] [R code] (Some minor corrections are given in the arXiv version.)
N. Syring^s and R. Martin (2017). Gibbs posterior inference on the minimum clinically important difference. Journal of Statistical Planning and Inference, volume 187, pages 67–77. [arXiv]
R. Martin (2017). A statistical inference course based on p-values. The American Statistician, volume 71, pages 128–136. [arxiv]
R. Martin (2017). Inferential models. Wiley StatsRef: Statistics Reference Online, pages 1–8.
L. Hong and R. Martin (2017). A review of Bayesian asymptotics in general insurance applications. European Actuarial Journal, volume 7, pages 231–255. [ssrn]
L. Hong and R. Martin (2017). A flexible Bayesian nonparametric model for predicting future insurance claims. North American Actuarial Journal, volume 21, pages 228–241. [ssrn] [R code]
C. Liu, R. Martin, and N. Syring^s (2017). Efficient simulation from a gamma distribution with small shape parameter. Computational Statistics, volume 32, pages 1767–1775. [arXiv] [R code]
R. Martin (2017). <!––>Prior-free probabilistic inference for econometricians. In Robustness
in Econometrics, Kreinovich, Sriboonchitta, and Huynh, Eds. Springer International, Studies in Computational Intelligence, volume 692, pages 169–186.
R. Martin, J. Stufken, and M. Yang (2016). A conversation with Samad Hedayat. Statistical Science, volume 31, pages 637–647.
R. Martin and R. Lingham (2016). Prior-free probabilistic prediction of future observations. Technometrics, volume 58, pages 225–235. [arXiv] [R code]
R. Martin and Y. Lin^s (2016). Exact prior-free probabilistic inference in a class of non-regular models. Stat, volume 5, pages 312–321. [arXiv]
R. Martin and Z. Han^s (2016). A semiparametric scale-mixture regression model and predictive recursion maximum likelihood. Computational Statistics and Data Analysis, volume 94, pages 75–85. [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, volume 20, pages 95–98. [ssrn]
R. Martin (2015). Plausibility functions and exact frequentist inference. Journal of the American Statistical Association, volume 110, pages 1552–1561. [arXiv]
R. Martin and C. Liu (2015). Marginal inferential models: prior-free probabilistic inference on interest parameters. Journal of the American Statistical Association, volume 110, pages 1621–1631. [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, volume 77, pages 195–217. [arXiv]
R. V. Ramamoorthi, K. Sriram, and R. Martin (2015). On posterior concentration in misspecified models. Bayesian Analysis, volume 10, pages 759–789. [arXiv]
C. Liu and R. Martin (2015). Frameworks for prior-free posterior probabilistic inference. WIREs: Computational Statistics, volume 7, pages 77–85; invited review paper. [arXiv]
R. Martin (2015). Asymptotically optimal nonparametric empirical Bayes via predictive recursion. Communications in Statistics–Theory & Methods, volume 44, pages 286–299. [arXiv]
Q. Cheng^s, X. Gao^s, and R. Martin (2014). Exact prior-free probabilistic inference on the heritability coefficient in a linear mixed effect model. Electronic Journal of Statistics, volume 8, pages 3062–3076. [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, volume 8, pages 2188–2206. [arXiv] [R code]
R. Martin (2014). Random sets and exact confidence regions. Sankhya A, volume 76, pages 288–304. [arXiv]
R. Martin and C. Liu (2014). A note on p-values interpreted as plausibilities. Statistica Sinica, volume 24, pages 1703–1716. [arXiv]
R. Martin and C. Liu (2014). Discussion: Foundations of statistical inference, revisited. Statistical Science, volume 29, pages 247–251. [arXiv]
R. Martin and C. Liu (2013). Inferential models: A framework for prior-free posterior probabilistic inference. Journal of the American Statistical Association, volume 108, pages 301–313. [arXiv] [R code]

Correction. Journal of the American Statistical Association, volume 108, pages 1138–1139.
R. Martin (2013). An approximate Bayesian marginal likelihood approach for estimating finite mixtures. Communications in Statistics–Simulation & Computation, volume 42, pages 1533–1548. [arXiv] [R code]
R. Martin and O. Tilak^s (2012). On ε-optimality of the pursuit learning algorithm. Journal of Applied Probability, volume 49, pages 795–805. [arXiv]
R. Martin and S. T. Tokdar (2012). A nonparametric empirical Bayes framework for large-scale multiple testing. Biostatistics, volume 13, pages 427–439. (Earlier version won ASA–SBSS Student Paper Award.) [arXiv]
R. Martin (2012). Convergence rate for predictive recursion estimation of finite mixtures. Statistics & Probability Letters, volume 82, pages 378–384. [arXiv]
R. Martin and S. T. Tokdar (2011). Semiparametric inference in mixture models with predictive recursion marginal likelihood. Biometrika, volume 98, pages 567–582. [arXiv]
Z. Zhang, H. Xu, R. Martin, and C. Liu (2011). Inferential models for linear regression. Pakistan Journal of Statistics and Operations Research, volume 7, pages 413–432; special issue on “Variable Selection in Regression”.
O. Tilak^s, R. Martin, and S. Mukhopadhyay (2011). Decentralized indirect method for learning automata games. IEEE Transactions on Systems, Man, and Cybernetics–Part B, volume 41, pages 1213–1223.
R. Martin, J. Zhang, and C. Liu (2010). Dempster–Shafer theory and statistical inference with weak beliefs. Statistical Science, volume 25, pages 72–87. [arXiv]
R. Martin and S. T. Tokdar (2009). Asymptotic properties of predictive recursion: robustness and rate of convergence. Electronic Journal of Statistics, volume 3, pages 1455–1472.
S. T. Tokdar, R. Martin, and J. K. Ghosh (2009). Consistency of a recursive estimate of mixing distributions. The Annals of Statistics, volume 37, pages 2502–2522. [arXiv]
R. Martin and J. K. Ghosh (2008). Stochastic approximation and Newton’s estimate of a mixing distribution. Statistical Science, volume 23, pages 365–382. [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. World Scientific, Hackensack, NJ, pages 154–161.

Software

Empirical Bayes inference in high-dimensional piecewise constant models.

Paper: “Asymptotically optimal empirical Bayes inference in a piecewise constant sequence model”.
Downloadable file: ebpiece.R
Post-selection performance of prediction intervals in regression.

Paper: “On prediction of future insurance claims when the model is uncertain”.
Downloadable file: pred.R
Recursive Bayesian nonparametric predictive distribution.

Paper: “Real-time Bayesian nonparametric prediction of solvency risk”.
Downloadable file: dpmrec.R dpmrec.Rd
Empirical Bayes variable selection and inference in a sparse linear regression model.

Paper: “Empirical Bayes posterior concentration in sparse high-dimensional linear models”.
Downloadable file: ebreg.R
Empirical Bayes estimation of a sparse normal mean vector.

Paper: “Asymptotically minimax empirical Bayes estimation of a sparse normal mean”
Downloadable file: ebsparse.R
Dirichlet process mixture of log-normal distributions.

Paper: “A flexible Bayesian nonparametric model for predicting future insurance claims”
Downloadable file: dpmslice.R
Gamma distribution with small shape parameter.

Paper: “Simulating from gamma distribution with small shape parameter”
Downloadable file: rgamss.R
Inferential models—heritability coefficient in mixed effect models.

Paper: “Exact prior-free probabilistic inference on the heritability coefficient in a linear mixed model” .
Downloadable files: imvch.R assay.Rd
Inferential models—prediction.

Paper: “Prior-free probabilistic inference of future observations”
Downloadable file: impred.R
Inferential models—Poisson distribution.

Paper: “Optimal inferential models for a Poisson mean”
Downloadable file: impois.R
Inferential models—the basics.

Paper: “Inferential models: A framework for prior-free posterior probabilistic inference”
Downloadable file: imbasics.R
Robust regression via a hybrid predictive recursion-EM algorithm

Paper: “Robust regression via predictive recursion maximum likelihood”
Downloadable file: prreg.R
Predictive recursion and predictive recursion marginal likelihood.

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.
Stochastic approximation–simulated annealing (SASA) method for finite mixtures.

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()

Some presentations

BELIEF 2018/SMPS 2018.
TBD (keynote).
Compiegne, France, September 2018.

2018 IMS Annual Meeting.
Construction, concentration, and calibration of Gibbs posteriors.
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.
(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, England, 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.
North Carolina State University, December 2016. [slides]

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.