Stephen Berg

Assistant Professor, Penn State University


Efficient Shape Constrained Inference With Applications in Autocovariance Sequence Estimation


I will present a novel shape-constrained estimator of the autocovariance sequence resulting from a reversible Markov chain. A motivating application for studying this problem is the estimation of the asymptotic variance in central limit theorems for Markov chains. Our approach is based on the key observation that the representability of the autocovariance sequence as a moment sequence imposes certain shape constraints, which we can exploit in the estimation procedure. I will discuss the theoretical properties of the proposed estimator and provide strong consistency guarantees for the proposed estimator. Finally, I will empirically demonstrate the effectiveness of our estimator in comparison with other current state-of-the-art methods for Markov chain Monte Carlo variance estimation, including batch means, spectral variance estimators, and the initial convex sequence estimator.


I am an assistant professor in the Department of Statistics at Penn State University. I joined Penn State in 2020 after receiving my PhD in Statistics from the University of Wisconsin-Madison, where I was advised by Jun Zhu and Murray Clayton.

My research focuses on statistical computing problems, particularly related to Markov chain Monte Carlo (MCMC), including asymptotic variance estimation and variance reduction.


Headshot of Stephen Berg