arXiv subjects

Stephen Berg

Publications and source records attributed to Stephen Berg.

9 recordsLinked to original sources

arXiv2026

Mixture-based Nonparametric Estimation of Spatial Covariance Functions with Applications to HIV Key Population Size Estimation across Sub-Saharan Africa

Consistent data on the sizes of key populations, such as female sex workers (FSWs), are often scarce, particularly at the sub-national level. Accurate size estimates are critical to effectively allocate resources and achieve HIV targets. Since FSW population sizes may be spatially correlated across areas, models that account for spatial dependence can improve estimation. An important component of such models is the covariance function, which characterizes the spatial dependence structure of the underlying process. In this work, we study spatial covariance functions to estimate FSW population sizes in Sub-Saharan Africa (SSA). Many spatial models rely on parametric covariance functions. However, parametric estimation can suffer from model mis-specification, potentially leading to inefficient or biased predictions. We therefore develop a robust non-parametric approach for estimating the covariance function of a stationary isotropic process in $\mathbb{R}^d$. We focus on a class of covariance functions that are valid in all dimensions, which includes popular kernels such as the exponential and Mat\'{e}rn kernels. Leveraging the fact that such covariance functions can be represented as infinite mixtures of scaled Gaussian kernels, we propose two estimation methods: weighted least squares and nonparametric maximum likelihood estimation to estimate the mixing measure of scaled Gaussian kernels. We also develop computationally efficient methods to solve these optimization problems using non-negative least squares and second-order descent updates. We evaluate the proposed methods through simulations and apply them to estimate the FSW population sizes at the sub-national level in SSA.

stat.ME↗

arXiv2026

Bayesian inference for the automultinomial model with an application to landcover data

Multicategory lattice data arise in a wide variety of disciplines such as image analysis, biology, and forestry. We consider modeling such data with the automultinomial model, which can be viewed as a natural extension of the autologistic model to multicategory responses, or equivalently as an extension of the Potts model that incorporates covariate information into a pure-intercept model. The automultinomial model has the advantage of having a unique parameter that controls the spatial correlation. However, the model's likelihood involves an intractable normalizing function of the model parameters that poses serious computational problems for likelihood-based inference. We address this difficulty by performing Bayesian inference through the Double-Metropolis Hastings algorithm, and implement diagnostics to assess the convergence to the target posterior distribution. Through simulation studies and an application to land cover data, we find that the automultinomial model is flexible across a wide range of spatial correlations while maintaining a relatively simple specification. For large data sets we find it also has advantages over spatial generalized linear mixed models. To make this model practical for scientists, we provide recommendations for its specification and computational implementation.

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arXiv2025

Modeling discrete lattice data using the Potts and tapered Potts models

The Ising and Potts models, among the most important models in statistical physics, have been used for modeling binary and multinomial data on lattices in a wide variety of disciplines such as psychology, image analysis, biology, and forestry. However, these models have several well known shortcomings: (i) they can result in poorly fitting models, that is, simulations from fitted models often do not produce realizations that look like the observed data; (ii) phase transitions and the presence of ground states introduce significant challenges for statistical inference, model interpretation, and goodness of fit; (iii) intractable normalizing constants that are functions of the model parameters pose serious computational problems for likelihood-based inference. Here we develop a tapered version of the Ising and Potts models that addresses issues (i) and (ii). We develop efficient Markov Chain Monte Carlo Maximum Likelihood Estimation (MCMCMLE) algorithms that address issue (iii). We perform an extensive simulation study for the classical and Tapered Potts models that provide insights regarding the issues generated by the phase transition and ground states. Finally, we offer practical recommendations for modeling and computation based on applications of our approach to simulated data as well as data from the 2021 National Land Cover Database.

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arXiv2024

Weighted shape-constrained estimation for the autocovariance sequence from a reversible Markov chain

We present a novel weighted $\ell_2$ projection method for estimating autocovariance sequences and spectral density functions from reversible Markov chains. Berg and Song (2023) introduced a least-squares shape-constrained estimation approach for the autocovariance function by projecting an initial estimate onto a shape-constrained space using an $\ell_2$ projection. While the least-squares objective is commonly used in shape-constrained regression, it can be suboptimal due to correlation and unequal variances in the input function. To address this, we propose a weighted least-squares method that defines a weighted norm on transformed data. Specifically, we transform an input autocovariance sequence into the Fourier domain and apply weights based on the asymptotic variance of the sample periodogram, leveraging the asymptotic independence of periodogram ordinates. Our proposal can equivalently be viewed as estimating a spectral density function by applying shape constraints to its Fourier series. We demonstrate that our weighted approach yields strongly consistent estimates for both the spectral density and the autocovariance sequence. Empirical studies show its effectiveness in uncertainty quantification for Markov chain Monte Carlo estimation, outperforming the unweighted moment LS estimator and other state-of-the-art methods.

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arXiv2023

Multivariate moment least-squares estimators for reversible Markov chains

Markov chain Monte Carlo (MCMC) is a commonly used method for approximating expectations with respect to probability distributions. Uncertainty assessment for MCMC estimators is essential in practical applications. Moreover, for multivariate functions of a Markov chain, it is important to estimate not only the auto-correlation for each component but also to estimate cross-correlations, in order to better assess sample quality, improve estimates of effective sample size, and use more effective stopping rules. Berg and Song [2022] introduced the moment least squares (momentLS) estimator, a shape-constrained estimator for the autocovariance sequence from a reversible Markov chain, for univariate functions of the Markov chain. Based on this sequence estimator, they proposed an estimator of the asymptotic variance of the sample mean from MCMC samples. In this study, we propose novel autocovariance sequence and asymptotic variance estimators for Markov chain functions with multiple components, based on the univariate momentLS estimators from Berg and Song [2022]. We demonstrate strong consistency of the proposed auto(cross)-covariance sequence and asymptotic variance matrix estimators. We conduct empirical comparisons of our method with other state-of-the-art approaches on simulated and real-data examples, using popular samplers including the random-walk Metropolis sampler and the No-U-Turn sampler from STAN.

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arXiv2023

Introducing the Condor Array Telescope. II. Deep imaging observations of the edge-on spiral galaxy NGC 5907 and the NGC 5866 Group: yet another view of the iconic stellar stream

We used the Condor Array Telescope to obtain deep imaging observations through the luminance filter of the entirety of the NGC 5866 Group, including a very extended region surrounding the galaxy NGC 5907 and its stellar stream. We find that the stellar stream consists of a single curved structure that stretches $220$ kpc from a brighter eastern stream to a fainter western stream that bends to the north and then curls back toward the galaxy. This result runs contrary to a previous claim of a second loop of the stellar stream but is consistent with another previous description of the overall morphology of the stream. We further find that: (1) an extension of the western stream appears to bifurcate near its apex, (2) there is an apparent gap of $\approx 6$ kpc in the western stream due east of the galaxy, (3) contrary to a previous claim, there is no evidence of the remnant of a progenitor galaxy within the eastern stream, although (4) there are many other possible progenitor galaxies, (5) there is another structure that, if it is at the distance of the galaxy, stretches 240 kpc and contains two very large, very low-surface-brightness "patches" of emission, one of which was noted previously and another of which was not. We note the number and variety of stellar streams in the vicinity of NGC 5907 and the apparent gap in the western stream, which may be indicative of a dark subhalo or satellite in the vicinity of the galaxy.

astro-ph.GA↗

arXiv2023

Introducing the Condor Array Telescope. 1. Motivation, Configuration, and Performance

The "Condor Array Telescope" or "Condor" is a high-performance "array telescope" comprised of six apochromatic refracting telescopes of objective diameter 180 mm, each equipped with a large-format, very low-read-noise ($\approx 1.2$ e$^-$), very rapid-read-time ($< 1$ s) CMOS camera. Condor is located at a very dark astronomical site in the southwest corner of New Mexico, at the Dark Sky New Mexico observatory near Animas, roughly midway between (and more than 150 km from either) Tucson and El Paso. Condor enjoys a wide field of view ($2.29 \times 1.53$ deg$^2$ or 3.50 deg$^2$), is optimized for measuring both point sources and extended, very low-surface-brightness features, and for broad-band images can operate at a cadence of 60 s (or even less) while remaining sky-noise limited with a duty cycle near 100\%. In its normal mode of operation, Condor obtains broad-band exposures of exposure time 60 s over dwell times spanning dozens or hundreds of hours. In this way, Condor builds up deep, sensitive images while simultaneously monitoring tens or hundreds of thousands of point sources per field at a cadence of 60 s. Condor is also equipped with diffraction gratings and with a set of He II 468.6 nm, [O III] 500.7 nm, He I 587.5 nm, H$\alpha$ 656.3 nm, [N II] 658.4 nm, and [S II] 671.6 nm narrow-band filters, allowing it to address a variety of broad- and narrow-band science issues. Given its unique capabilities, Condor can access regions of "astronomical discovery space" that have never before been studied. Here we introduce Condor and describe various aspects of its performance.

astro-ph.IM↗

arXiv2022

Efficient shape-constrained inference for the autocovariance sequence from a reversible Markov chain

In this paper, we study the problem of estimating 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. We propose a novel shape-constrained estimator of the autocovariance sequence, which is based on the key observation that the representability of the autocovariance sequence as a moment sequence imposes certain shape constraints. We examine the theoretical properties of the proposed estimator and provide strong consistency guarantees for our estimator. In particular, for geometrically ergodic reversible Markov chains, we show that our estimator is strongly consistent for the true autocovariance sequence with respect to an $\ell_2$ distance, and that our estimator leads to strongly consistent estimates of the asymptotic variance. Finally, we perform empirical studies to illustrate the theoretical properties of the proposed estimator as well as to 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.

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arXiv2019

Control variates and Rao-Blackwellization for deterministic sweep Markov chains

We study control variate methods for Markov chain Monte Carlo (MCMC) in the setting of deterministic sweep sampling using $K\geq 2$ transition kernels. New variance reduction results are provided for MCMC averages based on sweeps over general transition kernels, leading to a particularly simple control variate estimator in the setting of deterministic sweep Gibbs sampling. Theoretical comparisons of our proposed control variate estimators with existing literature are made, and a simulation study is performed to examine the amount of variance reduction in some example cases. We also relate control variate approaches to approaches based on conditioning (or Rao-Blackwellization), and show that the latter can be viewed as an approximation of the former. Our theoretical results hold for Markov chains under standard geometric drift assumptions.

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