Tags: Colloquium Series

The Statistics Department hosts weekly colloquia on a variety of statistcal subjects, bringing in speakers from around the world.


Parameter estimation for linear Gaussian covariance models

Linear Gaussian covariance models are Gaussian models with linear constraints on the covariance matrix. Such models arise in stochastic processes from repeated time series data, Brownian motion tree models of phylogenetic data and network tomography models used for analyzing connections in the Internet. Maximum likelihood estimation in this class of models leads to a non-convex optimization problem that typically has many local maxima. Using…


Unknown Sparsity in Compressed Sensing: Denoising and Inference

The theory of Compressed Sensing (CS) asserts that an unknown p-dimensional signal can be accurately recovered from an underdetermined set of n linear measurements with n<p, provided that x is sufficiently sparse. However, in applications, the degree of sparsity ||x||_0 is typically unknown, and the problem of directly estimating ||x||_0 has been a longstanding gap between theory and practice. A closely…


A simple way to incorporate prior information on margins in Bayesian latent class models

I present an approach to incorporating informative prior beliefs about marginal probabilities into Bayesian latent class models for categorical data. The basic idea is to append synthetic observations to the original data such that (i) the empirical distributions of the desired margins match those of the prior beliefs, and (ii) the values of the remaining variables are left missing. The degree of prior uncertainty is controlled by the number of…


Optimal Subsampling for Large Sample Logistic Regression

For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least squares estimate in linear regression, where statistical leverage scores are often used to define subsampling probabilities. In this paper, we propose fast subsampling algorithms to efficiently approximate the maximum likelihood estimate in logistic regression.…


Small Area Estimation with Uncertain Random Effects

Random effects models play an important role in model-based small area estimation. Random effects account for any lack of fit of a regression model for the population means of small areas on a set of explanatory variables. In Datta, Hall and Mandal (2011, JASA), we showed that if the random effects can be dispensed with through a statistical test, then the model parameters and the small area means can be estimated substantially accurately. This…


Prediction Summary Measures for a Nonlinear Model and for Right-Censored Time-to-Event Data

The R-squared statistic, or coefficient of determination, is commonly used to measure the predictive power of a linear model.  It is interpreted as the fraction of variation in the response explained by the predictors. Despite its popularity, a direct equivalent measure is not available for nonlinear regression models and for right-censored time-to-event data. In this talk, I will show that in addition to a measure of explained variation,…


Regression with Covariate Subject to Limit of Detection

We consider generalized linear regression with left-censored covariate due to the lower limit of detection. The complete case analysis by eliminating observations with values below limit of detection yields valid estimates for regression coefficients, but loses efficiency. Substitution methods are biased; and maximum likelihood method relies on parametric models for the unobservable tail probability, thus may suffer from model misspecification.…


Risk Analysis in Banking: Opportunities and Challenges for Statisticians

Data-based decision making has always been a fundamental part of banking and finance. This has become even more so after the 2008 crisis and the heightened regulatory environment. In this presentation, I will describe the role of statistics in risk modeling and management in large banks, covering model development and model assessment. The talk will give a glimpse into different types of data structures, computing/data platforms used for big…


Statistical Analysis of Big Data and Structured Data with Application to Neuroscience

In this talk, we consider two types of data from neuroscience: neuromorphology data and neuron activity data. First, we focus on  data extracted from brain neuron cells of rodents and model each neuron as a data object with topological and geometric properties characterizing the branching structure, connectedness and orientation of a neuron. We define the notions of topological and geometric medians as well as quantiles based on newly…


Extreme Quantile Determination for Manufacturing Process Parameters

Monitoring the control and capability of process parameters is a continual and mammoth task for today’s manufacturers. The importance of simple, efficient, and automated approaches cannot be overstated. Paramount in this endeavor is the determination of extreme quantiles. I will review approaches for determining these quantile from the last 25 years of literature, as well as current usage at Eli Lilly and Company. A number of candidate…
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