The Hotelling Lectures are an annual event in the Department of Statistics & Operations Research at the University of North Carolina – Chapel Hill, honoring the memory of Professor Harold Hotelling (first chairman of the “Department of Mathematical Statistics”, as it was originally named at the time of its inception in 1946). A distinguished guest speaker presents a series of talks (which are open to the public) and remains in residence at the Department for several days. The inaugural Hotelling Lectures were given by David R. Cox in 1980, followed in subsequent years by these other distinguished speakers: Herman Chernoff, Ole Barndorff-Nielsen, Frank Hampel, David Brillinger, David Kendall, Persi Diaconis, Pal Revesz, Willem van Zwet, C.R. Rao, Bradley Efron, Lucien LeCam, Peter Bickel, Ulf Grenander, Larry Shepp, David Donoho, David Siegmund, Herbert Robbins, Lawrence D. Brown, Nancy Reid, S.R.S. Varadhan, Stuart Geman, Iain Johnstone, Peter Hall, Ruth J. Williams, Terry Speed, Thomas Kurtz, Peter McCullagh, Richard Davis, Yuval Peres and Dimitris Bertsimas.

Machine Learning and Statistics via a modern optimization lens The field of Statistics has historically been linked with Probability Theory. However, some of the central problems of classification, regression and estimation can naturally be written as optimization problems. While continuous optimization approaches has had a significant impact in Statistics, mixed integer optimization (MIO) has played a very limited role, primarily based on the belief that MIO models are computationally intractable. The period 1991–2015 has witnessed a) algorithmic advances in mixed…

From Predictive to Prescriptive Analytics Operations Research and Management Science (OR/MS) as a field typically starts with models and aims to obtain decisions. Data by enlarge is rarely present. Machine learning (ML)/ Statistics (S) as a field typically starts with data and aims to make predictions. Decisions are rarely addressed. In this work, we combine ideas from ML/S and OR/MS in developing a framework, along with specific methods, for using data to prescribe optimal decisions in OR/MS problems. In a…

Nonparametric Bayesian methods: frequentist analysis Aad van der Vaart Leiden University We present an overview of Bayesian methods to estimate functions or high-dimensional parameter vectors, and discuss the validity (or not) of these methods from a non-Bayesian point of view. For instance, we consider using a Gaussian process as a prior for a regression function or (after exponentiation and normalisation) for a density function. We characterise the rate at which the corresponding posterior distribution can recover a true function as…

Nonparametric Bayesian methods: frequentist analysis Aad van der Vaart Leiden University A more detailed view of Bayesian methods to estimate functions or high-dimensional parameter vectors, and discuss the validity (or not) of these methods from a non-Bayesian point of view. For instance, we consider using a Gaussian process as a prior for a regression function or (after exponentiation and normalisation) for a density function. We characterise the rate at which the corresponding posterior distribution can recover a true function as…

Steven N. Evans, Departments of Mathematics and Statistics, University of California at Berkeley Title: Some mathematical insights into aging and mortality Abstract: In 1825 Benjamin Gompertz noted that, to a reasonable approximation, mortality rates after maturity in the British population increased exponentially with age. This unexpected yet simple relationship has since been seen in many multi-cellular organisms. Recently, it has been observed that this exponential increase appears to level off in extreme old age. I will discuss ongoing work…

The fundamental theorem of arithmetic for metric measure spaces A metric measure space (mms) is a complete, separable metric space equipped with a probability measure that has full support. A fundamental insight of Gromov is that the space of such objects is much ``tamer'' than the space of complete, separable metric spaces per se because mms carry within themselves a canonical family of approximations by finite structures: one takes the random mms that arises from picking some number of points…

Hunting for Invisible Hands Monday, April 8th, 2019 In this talk, we discuss several optimization algorithms deeply incorporated in our daily life. In accordance to the standard Microeconomic Theory, we are surrounded by many invisible hands (Adam Smith, 1776), which are responsible for keeping the balanced production and ensuring the rationality of consumers. The main goal of this talk is to make some of these hands visible. We show that they correspond to several efficient optimization algorithms with provable efficiency…

Soft clustering by convex electoral model Wednesday, April 10th, 2019 In this talk, we analyze an electoral model based on random preferences of participants. Each voter can choose a party with certain probability depending on the divergence between his personal preferences and current position of the party. Our model represents a rare example of a community detection model (or, soft clustering) with unique equilibrium state. This is achieved by allowing the flexible positions for the parties (centers of clusters). We…