Linear regression models which account for skewed error distributions with fat tails have been previously studied. These two important features, skewness, and fat tails, are often observed in real data analyses. Covariates measured with an error also happen frequently in the observational data set-up. As a motivating example, wind speed as a covariate is usually used, among other covariates, to estimate the particulate matter (PM) which is one of the most critical air pollutants and has a major impact on human health and on the environment. However, the wind speed is measured with error and the distribution of PM is neither symmetric nor normally distributed (see Section "PM data application in Canada" for more details). Ignoring the issue of measurement error in covariates may produce bias in model parameters estimate and lead to wrong conclusions. In this paper, we propose an approach to study properly linear regression models where the covariates are measured with error and the error distribution is skewed with fat tails. We use a hierarchical Bayesian approach for inference, addressing also sensitivity of the results to priors. Performance of the proposed approach is evaluated through a simulation study and also by a real data application (PM in Canada).

In this paper we propose a new methodology for solving a discrete time stochastic Markovian control problem under model uncertainty. By utilizing the Dirichlet process, we model the unknown distribution of the underlying stochastic process as a random probability measure and achieve online learning in a Bayesian manner. Our approach integrates optimizing and dynamic learning. When dealing with model uncertainty, the nonparametric framework allows us to avoid model misspecification that usually occurs in other classical control methods. Then, we develop a numerical algorithm to handle the infinitely dimensional state space in this setup and utilizes Gaussian process surrogates to obtain a functional representation of the value function in the Bellman recursion. We also build separate surrogates for optimal control to eliminate repeated optimizations on out-of-sample paths and bring computational speed-ups. Finally, we demonstrate the financial advantages of the nonparametric Bayesian framework compared to parametric approaches such as strong robust and time consistent adaptive.

Small area models handling area level data typically assume normality of random effects. This assumption does not always work. The present paper introduces a new small area model with t random effects. Along with this, this paper also considers joint modeling of small area means and variances. The present approach is shown to perform better than other methods.

Nonparametric Bayes and empirical Bayes estimators of the population median are provided under Dirichlet process priors. The finite-population sampling is used to estimate the finite-population median under Dirichlet process priors. The asymptotic properties of the estimators are obtained from a frequentist perspective.

s 5 Valid Post-Selection Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Computationally Efficient Minimax Adaptive Estimation of Large Covariance Matrices with Low Dimensional Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Ensemble Subsampling for Imbalanced Multivariate Two-Sample Tests . . . . . . . . . . 6 Prediction in Abundant High-dimensional Linear Regression . . . . . . . . . . . . . . . . 6 On an Additive Semi-Graphoid Model for Statistical Networks with Application to Pathway Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Tensor Regression, Regularization, and Neuroimaging Data Analysis . . . . . . . . . . . . 7 On Estimation Efficiency in Dimension Reduction . . . . . . . . . . . . . . . . . . . . . . 8 Properties of Optimizations Used in Penalized Gaussian Likelihood Inverse Covariance Matrix Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Optimal Detection of Sparse Signal Segments . . . . . . . . . . . . . . . . . . . . . . . . 8 Asymptotic Normality and Efficiency In Estimation of High-dimensional Graphical Models 9 Poster Abstracts 10 Interpolation of Computationally Expensive Posterior Densities with Variable Parameter Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Modeling Financial Volatility: An Exogenous Log-GARCH Approach . . . . . . . . . . . 10 Identification of Important Regressor Groups, Subgroups, and Individuals via Regularization Methods: Application to Gut Microbiome Data . . . . . . . . . . . . . . . . . . 11 Making the Cut: Ranking and Selection Procedures for Large-Scale Inference . . . . . . . 11 Covariance Estimation for Multivariate Longitudinal Data . . . . . . . . . . . . . . . . . . 12 Meta-Analysis Based Variable Selection for Gene Expression Data . . . . . . . . . . . . . 12 Assessing Protein Conformational Sampling Methods Based on Bivariate Lag-Distributions of Backbone Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Dimension Reduction Using Inverse Spline Regression . . . . . . . . . . . . . . . . . . . 13