### Published papers and technical reports

#### 2021+

L. Hong and R. Martin, (202x). Imprecise credibility theory.

Annals of Actuarial Science. [ssrn]L. Hong and R. Martin (202x). Valid model-free prediction of future insurance claims.

North American Actuarial Journal. [researchers.one] [ssrn]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]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]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]

#### 2020

R. Martin and B. Ning (2020). 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]J. Cahoon and R. Martin (2020). Generalized inferential models for meta-analyses based on few studies.

Statistics and Applications. Special issue in honor of Drs. Bikas and Bimal Sinha on their 75th birthday. [researchers.one] [arXiv]L. Hong and R. Martin (2020). Model misspecification, Bayesian versus credibility estimation, and Gibbs posteriors.

Scandinavian Actuarial Journal. [researchers.one] [ssrn]N. Syring and R. Martin (2020). Robust and rate-optimal Gibbs posterior inference on the boundary of a noisy image.

The Annals of Statistics. [arXiv] [R code]R. Martin and Y. Tang (2020). Empirical priors for prediction in sparse high-dimensional linear regression.

Journal of Machine Learning Research.[arXiv] [researchers.one] [R code]Z. Wang and R. Martin (2020). Model-free posterior inference on the area under the receiver operating characteristic curve.

Journal of Statistical Planning and Inference. [arXiv]

#### 2019

R. Martin (2019). False confidence, non-additive beliefs, and valid statistical inference.

International Journal of Approximate Reasoning. [arXiv] [researchers.one]M. S. Balch, R. Martin, and S. Ferson (2019). Satellite conjunction analysis and the false confidence theorem.

Proceedings of the Royal Society, Series A. [arXiv]

- C. Cunen, N. Hjort, and T. Schweder (2020). Comment: Confidence in confidence distributions!
- R. Martin, M. Balch, and S. Ferson (202x). Response to the comment. [researchers.one]
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]N. Syring, L. Hong, and R. Martin (2019). Gibbs posterior inference on value-at-risk.

Scandinavian Actuarial Journal. [researchers.one]L. Cella and R. Martin (2019). Incorporating expert opinion in an inferential model while retaining validity.

Proceedings of the 11th International Symposium on Imprecise Probabilities: Theories and Applications.J. Cahoon and R. Martin (2019). Possibility measures for valid statistical inference based on censored data.

Proceedings of the 11th International Symposium on Imprecise Probabilities: Theories and Applications.R. Martin and N. Syring (2019). Validity-preservation properties of rules for combining inferential models.

Proceedings of the 11th International Symposium on Imprecise Probabilities: Theories and Applications. [researchers.one]R. Martin (2019). On valid uncertainty quantification about a model.

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]Y. Yang, R. Martin, and H. Bondell (2019). Variational approximations using Fisher divergence. [arXiv]

#### 2018

P. R. Hahn, R. Martin, and S. G. Walker (2018). On recursive Bayesian predictive distributions.

Journal of the American Statistical Association. [arXiv]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]R. Martin (2018). On an inferential model construction using generalized associations.

Journal of Statistical Planning and Inference. [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]

#### 2017

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.

#### 2016

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, J. Stufken, and M. Yang (2016). A conversation with Samad Hedayat.

Statistical Science.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]R. Martin, H. Xu, Z. Zhang, and C. Liu (2016). Valid uncertainty quantification about the model in linear regression. [arXiv]

#### 2015

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]

#### 2014

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]

#### 2013

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, L. Hong, and S. G. Walker (2013). A note on Bayesian convergence rates under local prior support conditions. [arXiv]

R. Martin, D. Ermini Leaf, and C. Liu (2013). Optimal inferential models for a Poisson mean. [arXiv] [R code]

#### 2012

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]L. Hong and R. Martin (2012). On convergence rates of Bayesian predictive densities and posterior distributions. [arXiv]

#### 2011

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.O. Tilak, R. Martin, and S. Mukhopadhyay (2011). Decentralized indirect method for learning automata games.

IEEE Transactions on Systems, Man, and Cybernetics, Series B.

#### 2010 and earlier

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 (2009).

Fast Nonparametric Estimation of Mixing Distributions with Application to High-Dimensional Inference.Ph.D. thesis, Purdue University, Department of Statistics. [pdf]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.