@article{syring_martin_2023, title={Gibbs posterior concentration rates under sub-exponential type losses}, volume={29}, ISSN={["1573-9759"]}, DOI={10.3150/22-BEJ1491}, abstractNote={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 parameters that require prior distributions and posterior computations, plus a potentially serious risk of model misspecification bias. Gibbs posterior distributions, on the other hand, offer direct, principled, probabilistic inference on quantities of interest through a loss function, not a model-based likelihood. Here we provide simple sufficient conditions for establishing Gibbs posterior concentration rates when the loss function is of a sub-exponential type. We apply these general results in a range of practically relevant examples, including mean regression, quantile regression, and sparse high-dimensional classification. We also apply these techniques in an important problem in medical statistics, namely, estimation of a personalized minimum clinically important difference.}, number={2}, journal={BERNOULLI}, author={Syring, Nicholas and Martin, Ryan}, year={2023}, month={May}, pages={1080–1108} }
 @article{martin_syring_2022, title={Direct Gibbs posterior inference on risk minimizers: Construction, concentration, and calibration}, volume={47}, ISSN={["0169-7161"]}, DOI={10.1016/bs.host.2022.06.004}, abstractNote={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 potential model misspecification bias or over-complicating the problem formulation, a direct, model-free approach is desired. The traditional Bayesian framework relies on a model for the data-generating process so, apparently, the desired direct, model-free, posterior-probabilistic inference is out of reach. Fortunately, likelihood functions are not the only means of linking data and quantities of interest. Loss functions provide an alternative link, where the quantity of interest is defined, or at least could be defined, as a minimizer of the corresponding risk, or expected loss. In this case, one can obtain what is commonly referred to as a Gibbs posterior distribution by using the empirical risk function directly. This manuscript explores the Gibbs posterior construction, its asymptotic concentration properties, and the frequentist calibration of its credible regions. By being free from the constraints of model specification, Gibbs posteriors create new opportunities for probabilistic inference in modern statistical learning problems.}, journal={ADVANCEMENTS IN BAYESIAN METHODS AND IMPLEMENTATION}, author={Martin, Ryan and Syring, Nicholas}, year={2022}, pages={1–41} }
 @article{syring_martin_2020, title={ROBUST AND RATE-OPTIMAL GIBBS POSTERIOR INFERENCE ON THE BOUNDARY OF A NOISY IMAGE}, volume={48}, ISSN={["0090-5364"]}, DOI={10.1214/19-AOS1856}, abstractNote={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 engineering. From a statistical point of view, the challenge is that likelihood-based methods require modeling the pixel intensities inside and outside the image boundary, even though these are typically of no practical interest. Since misspecification of the pixel intensity models can negatively affect inference on the image boundary, it would be desirable to avoid this modeling step altogether. Towards this, we develop a robust Gibbs approach that constructs a posterior distribution for the image boundary directly, without modeling the pixel intensities. We prove that, for a suitable prior on the image boundary, the Gibbs posterior concentrates asymptotically at the minimax optimal rate, adaptive to the boundary smoothness. Monte Carlo computation of the Gibbs posterior is straightforward, and simulation experiments show that the corresponding inference is more accurate than that based on existing Bayesian methodology.}, number={3}, journal={ANNALS OF STATISTICS}, author={Syring, Nicholas and Martin, Ryan}, year={2020}, month={Jun}, pages={1498–1513} }
 @article{syring_hong_martin_2019, title={Gibbs posterior inference on value-at-risk}, ISSN={["1651-2030"]}, DOI={10.1080/03461238.2019.1573754}, abstractNote={ABSTRACT Accurate estimation of value-at-risk (VaR) and assessment of associated uncertainty is crucial for both insurers and regulators, particularly in Europe. Existing approaches link data and VaR indirectly by first linking data to the parameter of a probability model, and then expressing VaR as a function of that parameter. This indirect approach exposes the insurer to model misspecification bias or estimation inefficiency, depending on whether the parameter is finite- or infinite-dimensional. In this paper, we link data and VaR directly via what we call a discrepancy function, and this leads naturally to a Gibbs posterior distribution for VaR that does not suffer from the aforementioned biases and inefficiencies. Asymptotic consistency and root-n concentration rate of the Gibbs posterior are established, and simulations highlight its superior finite-sample performance compared to other approaches.}, number={7}, journal={SCANDINAVIAN ACTUARIAL JOURNAL}, author={Syring, Nicholas and Hong, Liang and Martin, Ryan}, year={2019}, month={Aug}, pages={548–557} }
 @article{syring_martin_2019, title={Miscellanea Calibrating general posterior credible regions}, volume={106}, ISSN={["1464-3510"]}, DOI={10.1093/biomet/asy054}, abstractNote={
 Calibration of credible regions derived from under- or misspecified models is an important and challenging problem. In this paper, we introduce a scalar tuning parameter that controls the posterior distribution spread, and develop a Monte Carlo algorithm that sets this parameter so that the corresponding credible region achieves the nominal frequentist coverage probability.}, number={2}, journal={BIOMETRIKA}, author={Syring, Nicholas and Martin, Ryan}, year={2019}, month={Jun}, pages={479–486} }
 @article{liu_martin_syring_2017, title={Efficient simulation from a gamma distribution with small shape parameter}, volume={32}, ISSN={["1613-9658"]}, DOI={10.1007/s00180-016-0692-0}, number={4}, journal={COMPUTATIONAL STATISTICS}, author={Liu, Chuanhai and Martin, Ryan and Syring, Nick}, year={2017}, month={Dec}, pages={1767–1775} }
 @article{syring_martin_2017, title={Gibbs posterior inference on the minimum clinically important difference}, volume={187}, ISSN={["1873-1171"]}, DOI={10.1016/j.jspi.2017.03.001}, abstractNote={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 clinically important difference (MCID), and inference on the MCID is an important and challenging problem. Modeling for the purpose of inference on the MCID is non-trivial, and concerns about bias from a misspecified parametric model or inefficiency from a nonparametric model motivate an alternative approach to balance robustness and efficiency. In particular, a recently proposed representation of the MCID as the minimizer of a suitable risk function makes it possible to construct a Gibbs posterior distribution for the MCID without specifying a model. We establish the posterior convergence rate and show, numerically, that an appropriately scaled version of this Gibbs posterior yields interval estimates for the MCID which are both valid and efficient even for relatively small sample sizes.}, journal={JOURNAL OF STATISTICAL PLANNING AND INFERENCE}, author={Syring, Nicholas and Martin, Ryan}, year={2017}, month={Aug}, pages={67–77} }