Related papers: Possibilistic Inferential Models for Post-Selectio…
An inferential model (IM) is a model describing the construction of provably reliable, data-driven uncertainty quantification and inference about relevant unknowns. IMs and Fisher's fiducial argument have similar objectives, but a…
We study the asymptotic frequentist coverage of credible sets based on a novel Bayesian approach for a multiple linear regression model under variable selection. We initially ignore the issue of variable selection, which allows us to put a…
Variable selection in ultra-high dimensional linear regression is often preceded by a screening step to significantly reduce the dimension. Here we develop a Bayesian variable screening method (BITS) guided by the posterior model…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
Integrative analyses based on statistically relevant associations between genomics and a wealth of intermediary phenotypes (such as imaging) provide vital insights into their clinical relevance in terms of the disease mechanisms. Estimates…
We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…
We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…
This article is about estimation and inference methods for high dimensional sparse (HDS) regression models in econometrics. High dimensional sparse models arise in situations where many regressors (or series terms) are available and the…
We propose a likelihood ratio based inferential framework for high dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high dimensional data analysis, including incomplete…
We propose a residual randomization procedure designed for robust Lasso-based inference in the high-dimensional setting. Compared to earlier work that focuses on sub-Gaussian errors, the proposed procedure is designed to work robustly in…
We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…
In this paper, we introduce a novel high-dimensional Factor-Adjusted sparse Partially Linear regression Model (FAPLM), to integrate the linear effects of high-dimensional latent factors with the nonparametric effects of low-dimensional…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…
A popular method for variance reduction in observational causal inference is propensity-based trimming, the practice of removing units with extreme propensities from the sample. This practice has theoretical grounding when the data are…
Conformal inference is a popular tool for constructing prediction intervals (PI). We consider here the scenario of post-selection/selective conformal inference, that is PIs are reported only for individuals selected from an unlabeled test…
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…
This paper describes a method for performing inference on models chosen by cross-validation. When the test error being minimized in cross-validation is a residual sum of squares it can be written as a quadratic form. This allows us to apply…