Updated 09/11/2017 |
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]
Applications of an algorithm solving Fredholm equations of the first kind, with M. Chae and S. G. Walker. [arXiv]
A mathematical characterization of confidence as valid beliefs. [arXiv]
Coverage probability fails to ensure reliable inference, with M. S. Balch and S. Ferson. [arXiv]
Validity and the foundations of statistical inference, with C. Liu. [arXiv]
Rethinking probabilistic prediction in the wake of the 2016 U.S. presidential election, with H. Crane. [arXiv] [ssrn]
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]
Calibrating general posterior credible regions, with N. Syring^{s}. [arXiv] [R code]
'Purposely misspecified' posterior inference on the volatility of a jump diffusion process, with C. Ouyang and F. Domagni^{s}. [arXiv]
Online prediction of solvency risk using recursive Bayesian updating, with L. Hong. [ssrn]
Dirichlet process mixture models for insurance loss data, with L. Hong. [ssrn]
On prediction of future insurance claims when the model is uncertain, with L. Hong and T. Kuffner. [ssrn]
P. R. Hahn, R. Martin, and S. G. Walker (2017+). On recursive Bayesian predictive distributions. Journal of the American Statistical Association, to appear. [arXiv]
R. Martin (2017). Comment on the article by van der Pas, Szabo, and van der Vaart. Bayesian Analysis, to appear. [isba]
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+). On an inferential model construction using generalized associations. Journal of Statistical Planning and Inference, to appear. [arXiv]
R. Martin (2017). Inferential models. Wiley StatsRef: Statistics Reference Online, to appear.
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, to appear. [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.
Valid uncertainty quantification about the model in a linear regression setting, 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]
Kullback–Leibler projections, estimation of mixing distributions, and applications, with S. T. Tokdar, 2008. Purdue University, Department of Statistics, Technical Report 08–06. [link]
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()
2nd Workshop on Higher-Order Asymptotics & Post-Selection Inference.
"On valid post-selection prediction in regression."
Washington University in St. Louis, August 13th, 2017.
11th Conference on Bayesian Nonparametrics.
"Model misspecification on purpose."
Paris, France, June 29th, 2017.
4th Bayesian, Fiducial, and Frequentist Conference.
"Confidence, probability, and plausibility."
Harvard University, May 1st, 2017.
Department of Mathematics, Statistics Seminar.
"On valid prior-free probabilistic inference."
Washington University in St Louis, April 7th, 2017.
10th International Conference of the Thailand Econometric Society.
"Valid prior-free probabilistic inference."
Chiang Mai University, Thailand, January 11th, 2017.
Department of Statistics Seminar.
"Posterior inference without (really) using Bayes."
North Carolina State University, December 2nd, 2016. [slides]
Latent Variables Conference.
"A double empirical Bayes approach for high-dimensional problems."
University of South Carolina, October 14th, 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 30th, 2016.
ICSA Applied Statistics Symposium.
"A new double empirical Bayes approach for high-dimensional problems."
Atlanta, GA, June 13th, 2016.
Workshop on Fusion Learning, BFF inferences and Statistical Foundations.
"Beliefs, validity, and the foundations of statistics."
Rutgers University, April 12th, 2016.
Department of Statistics and Biostatistics Seminar.
"Valid prior-free probabilistic inference."
Rutgers University, December 9th, 2015.
Department of Statistics Colloquium.
"Inferential models: a framework for prior-free probabilistic inference."
North Carolina State University, November 3rd, 2015.
Statistics Colloquium.
"High-dimensional posterior inference via double empirical Bayes."
Texas A&M University, February 20th, 2015.
Statistics Seminar.
"Recursive Bayes prediction with copulas."
University of Illinois at Chicago, January 21st, 2015.
Chuanhai Liu's course (Stat 598CL) on Foundations of Statistics and Inferential Models.
"Generalized inferential models: prior-free probabilistic inference using default associations."
Purdue University, November 6th, 2014.
International Conference on Advances in Interdisciplinary Statistics and Combinatorics.
"Empirical Bayes posterior concentration in sparse high-dimensional linear models,"
Greensboro, NC, October 10th, 2014.
Joint Statistical Meetings.
"Optimal prior-free probabilistic variable selection in regression."
Boston, MA, August 5th, 2014.
ICSA Applied Statistics Symposium.
"Generalized inferential models."
Portland, OR, June 17th, 2014.
Statistics Colloquium.
"Plausibility functions and exact frequentist inference."
Northern Illinois University, March 28th, 2014.
MSCS Graduate Student Recruitment Day Talk.
"Bayesian inference on infinite-dimensional parameters."
University of Illinois at Chicago, March 21st, 2014.
Department of Statistics Seminar.
"Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector."
University of Illinois at Urbana–Champaign, September 26th, 2013.
Department of Statistics Seminar.
"A Bayesian test of normality versus a Dirichlet process mixture alternative."
Northwestern University, January 9th, 2013.
Statistical Science Seminar.
"Inferential models: A framework for prior-free posterior probabilistic inference."
Duke University, November 9th, 2012.
ASA Northeastern Illinois Chapter Meeting.
"A nonparametric empirical Bayes framework for large-scale multiple testing."
Northbrook, IL, October 24th, 2012.
Statistics and Probability Seminar.
"Plausibility functions and exact frequentist inference."
Michigan State University, October 9th, 2012.
Purdue Symposium on Statistics.
"Inferential models: A framework for prior-free posterior probabilistic inference."
Purdue University, June 24th, 2012.
Applied Mathematics Department Colloquium.
"A nonparametric empirical Bayes framework for large-scale multiple testing."
Illinois Institute of Technology, January 30th, 2012.
Department of Statistics Research Colloquium.
"Bayesian test of normality versus a Dirichlet process mixture alternative."
Purdue University, November 18th, 2011.
ACMS Department Colloquium.
"Predictive recursion marginal likelihood and application to large-scale simultaneous testing."
University of Notre Dame, January 21st, 2011.
Joint Statistical Meetings
"Predictive Recursion: convergence theory, extensions, and applications."
Vancouver, BC, August 2nd, 2010.
ICSA Applied Statistics Symposium
"On probabilistic inference without priors."
Indianapolis, IN, June 22nd, 2010.