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<h2 id="stephen-berg">Stephen Berg</h2>
<img src="department-photo.jpg" width="200"/>
<h2 id="about-me">About Me</h2>
<p>I am an Assistant Professor of Statistics at Penn State University. My research explores the intersection of statistical computing, numerical analysis, and machine learning. I joined Penn State in 2020 after earning my PhD in Statistics from the University of Wisconsin-Madison, advised by Jun Zhu and Murray Clayton.</p>
<p>A central focus of my work is advancing the theory and methodology of Markov chain Monte Carlo (MCMC) simulations. I develop variance reduction techniques to improve MCMC efficiency, alongside methods to robustly estimate the variability of simulation output. I also develop new theory and methods for fitting nonparametric mixture models.</p>
<p>Recently, I have been applying modern machine learning techniques to classical statistical problems. My current projects include using deep learning and neural networks to approximate solutions to the Poisson equation resulting from Markov transition kernels. Beyond algorithm development, I am highly interested in the rigorous mathematical foundations of statistical computing.</p>
<p><strong>Email:</strong> <a href="mailto:sqb6128@psu.edu">sqb6128@psu.edu</a></p>
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<p><strong>Statistical computing</strong></p>
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<p>My current work revolves around variance estimation and variance reduction for MCMC simulations.</p>
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<li>Recently I have worked with Hyebin Song at PSU on nonparametric variance estimation for reversible Markov chains, using similar ideas to classic shape-constrained regression approaches like isotonic regression.</li>
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<p>&ndash; <a href="https://arxiv.org/abs/2408.03024">Weighted shape-constrained estimation for the autocovariance sequence from a reversible Markov chain</a>
&ndash; <a href="https://arxiv.org/abs/2310.06330">Multivariate moment least-squares estimators for reversible Markov chains</a>
&ndash; <a href="https://arxiv.org/abs/2207.12705">Efficient shape-constrained inference for the autocovariance sequence from a reversible Markov chain</a></p>
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<li>I am also interested in variance reduction for Markov chains using control variate and conditioning approaches.</li>
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<p>&ndash; <a href="https://arxiv.org/abs/1912.06926">Control variates and Rao-Blackwellization for deterministic sweep Markov chains</a></p>
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<p><strong>Spatial-temporal statistics</strong></p>
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<li>I am interested in application problems in landscape ecology and in modeling chronic wasting disease (CWD) in Wisconsin deer, and in constructing realistic models of natural phenomena in order to do inference and forecasting. Methodologically, I am interested in differential equation and partial differential equation models, and addressing statistical and computational challenges for these models. <a href="https://doi.org/10.1214/19-AOAS1259">A latent discrete Markov random field approach to identifying and classifying historical forest communities based on spatial multivariate tree species counts</a></li>
<li>On the theory side, I am interested in using nonparametric mixture models for estimating spatial covariance functions.</li>
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<!-- <span style="font-size:1.5em;">**Research opportunities**</span>  -->
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<h2 id="research-opportunities">Research opportunities</h2>
<p>I have funding for motivated PhD students with an interest in statistical computing, spatial statistics, and/or nonparametric statistics problems. Please contact me by email to discuss potential research opportunities.</p>
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