Miracle-dz/UniFAR-FTUs huggingface dataset:
Local inversion-free estimation of spatial Gaussian processes

Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for large number of (possibly) irregularly spaced observations, due to the need to handle the inverse of ill-conditioned and large covariance matrices. Extending the "inversion-free" method of Anitescu, Chen and Stein \cite{anitescu2017inversion}, we investigate a broad class of covariance parameter estimators based on inversion-free surrogate losses and block diagonal approximation schemes of the covariance structure. This class of estimators yields a spectrum for negotiating the trade-off between statistical accuracy and computational cost. We present fixed-domain asymptotic properties of our proposed method, establishing $\sqrt{n}$-consistency and asymptotic normality results for isotropic Matern Gaussian processes observed on a multi-dimensional and irregular lattice. Simulation studies are also presented for assessing the scalability and statistical efficiency of the proposed algorithm for large data sets.
Statistical post-processing of hydrological forecasts using Bayesian model averaging.

Accurate and reliable probabilistic forecasts of hydrological quantities like runoff or water level are beneficial to various areas of society. Probabilistic state-of-the-art hydrological ensemble prediction models are usually driven with meteorological ensemble forecasts. Hence, biases and dispersion errors of the meteorological forecasts cascade down to the hydrological predictions and add to the errors of the hydrological models. The systematic parts of these errors can be reduced by applying statistical post-processing. For a sound estimation of predictive uncertainty and an optimal correction of systematic errors, statistical post-processing methods should be tailored to the particular forecast variable at hand. Former studies have shown that it can make sense to treat hydrological quantities as bounded variables. In this paper, a doubly truncated Bayesian model averaging (BMA) method, which allows for flexible post-processing of (multi-model) ensemble forecasts of water level, is introduced. A case study based on water level for a gauge of river Rhine, reveals a good predictive skill of doubly truncated BMA compared both to the raw ensemble and the reference ensemble model output statistics approach.
Learning Weighted Representations for Generalization Across Designs

Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to machine learning applications. One example is the estimation of treatment effects from observational data, where a subtask is to predict the effect of a treatment on subjects that are systematically different from those who received the treatment in the data. A related kind of distributional shift appears in unsupervised domain adaptation, where we are tasked with generalizing to a distribution of inputs that is different from the one in which we observe labels. We pose both of these problems as prediction under a shift in design. Popular methods for overcoming distributional shift are often heuristic or rely on assumptions that are rarely true in practice, such as having a well-specified model or knowing the policy that gave rise to the observed data. Other methods are hindered by their need for a pre-specified metric for comparing observations, or by poor asymptotic properties. In this work, we devise a bound on the generalization error under design shift, based on integral probability metrics and sample re-weighting. We combine this idea with representation learning, generalizing and tightening existing results in this space. Finally, we propose an algorithmic framework inspired by our bound and verify is effectiveness in causal effect estimation.
Hierarchies for Relatively Hyperbolic Virtually Special Groups

Wise's Quasiconvex Hierarchy Theorem classifying hyperbolic virtually compact special groups in terms of quasiconvex hierarchies played an essential role in Agol's proof of the Virtual Haken Conjecture. Answering a question of Wise, we construct a new virtual quasiconvex hierarchy for relatively hyperbolic virtually compact special groups. We use this hierarchy to prove a generalization of Wise's Malnormal Special Quotient Theorem for relatively hyperbolic virtually compact special groups with arbitrary peripheral subgroups.
Robust Inference Under Heteroskedasticity via the Hadamard Estimator

Drawing statistical inferences from large datasets in a model-robust way is an important problem in statistics and data science. In this paper, we propose methods that are robust to large and unequal noise in different observational units (i.e., heteroskedasticity) for statistical inference in linear regression. We leverage the Hadamard estimator, which is unbiased for the variances of ordinary least-squares regression. This is in contrast to the popular White's sandwich estimator, which can be substantially biased in high dimensions. We propose to estimate the signal strength, noise level, signal-to-noise ratio, and mean squared error via the Hadamard estimator. We develop a new degrees of freedom adjustment that gives more accurate confidence intervals than variants of White's sandwich estimator. Moreover, we provide conditions ensuring the estimator is well-defined, by studying a new random matrix ensemble in which the entries of a random orthogonal projection matrix are squared. We also show approximate normality, using the second-order Poincare inequality. Our work provides improved statistical theory and methods for linear regression in high dimensions.
Improved Measurements of the β-Decay Response of Liquid Xenon with the LUX Detector

The LUX experiment was based on a liquid-xenon time-projection chamber that was located on the 4,850’ level of the Sanford Underground Research Facility until it was decommissioned in 2016. In total, the LUX detector contained about 370 kg of xenon, 250 kg of which was active. LUX was designed primarily to detect WIMP dark matter, and produced world-leading limits on the WIMP scattering cross section. In this presentation, I report results from an extensive set of measurements of the β-decay response in liquid xenon. These measurements are derived from high-statistics calibration data from injected sources of both tritium and carbon-14 in the LUX detector after the WIMP-search runs had been completed. The mean light-to-charge ratio is reported for 13 electric field values ranging from 43 to 491 V/cm, and for energies ranging from 1.5 to 145 keV.
Inter-Rater: Software for analysis of inter-rater reliability by permutating pairs of multiple users.

Inter-Rater quantifies the reliability between multiple raters who evaluate a group of subjects. It calculates the group quantity, Fleiss kappa, and it improves on existing software by keeping information about each user and quantifying how each user agreed with the rest of the group. This is accomplished through permutations of user pairs. The software was written in Python, can be run in Linux, and the code is deposited in Zenodo and GitHub. This software can be used for evaluation of inter-rater reliability in systematic reviews, medical diagnosis algorithms, education applications, and others.
A Simple Algorithm for Scalable Monte Carlo Inference

The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of parameters of exponential family distributions - a family of statistical models, that includes Ising model, Markov Random Field and Exponential Random Graph models. Computational experiments and analysis of empirical data demonstrate that the algorithm increases by orders of magnitude the size of network data amenable to Monte Carlo based inference. We report results suggesting that the applicability of the algorithm may readily be extended to the analysis of large samples of dependent observations commonly found in biology, sociology, astrophysics, and ecology.
The CLT in high dimensions: Quantitative bounds via martingale embedding

We introduce a new method for obtaining quantitative convergence rates for the central limit theorem (CLT) in a high dimensional setting. Using our method, we obtain several new bounds for convergence in transportation distance and entropy, and in particular: (a) We improve the best known bound, obtained by the third named author, for convergence in quadratic Wasserstein transportation distance for bounded random vectors; (b) We derive the first non-asymptotic convergence rate for the entropic CLT in arbitrary dimension, for general log-concave random vectors; (c) We give an improved bound for convergence in transportation distance under a log-concavity assumption and improvements for both metrics under the assumption of strong log-concavity. Our method is based on martingale embeddings and specifically on the Skorokhod embedding constructed by the first named author.
Efficient determination of optimised multi-arm multi-stage experimental designs with control of generalised error-rates

Primarily motivated by the drug development process, several publications have now presented methodology for the design of multi-arm multi-stage experiments with normally distributed outcome variables of known variance. Here, we extend these past considerations to allow the design of what we refer to as an abcd multi-arm multi-stage experiment. We provide a proof of how strong control of the a-generalised type-I familywise error-rate can be ensured. We then describe how to attain the power to reject at least b out of c false hypotheses, which is related to controlling the b-generalised type-II familywise error-rate. Following this, we detail how a design can be optimised for a scenario in which rejection of any d null hypotheses brings about termination of the experiment. We achieve this by proposing a highly computationally efficient approach for evaluating the performance of a candidate design. Finally, using a real clinical trial as a motivating example, we explore the effect of the design's control parameters on the statistical operating characteristics.
Testing for tail behavior using extreme spacings

Methodologies to test hypotheses about the tail-heaviness of an underlying distribution are introduced based on results of Rojo (1996) using the limiting behavior of the extreme spacings. The tests are consistent and have point-wise robust levels in the sense of Lehmann (2005) and Lehmann and Loh (1990). Simulation results based on these new methodologies indicate that the tests exhibit good control of the probability of Type I error and have good power properties for finite sample sizes. The tests are compared with a test proposed by Bryson (1974) and it is seen that, although Bryson's test is competitive with the tests proposed here, Bryson's test does not have point-wise robust levels. The operating characteristics of the tests are also explored when the data is blocked. It turns out that the power increases substantially by blocking. The methodology is illustrated by analyzing various data sets.
Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with applications

A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. The basic idea is to map each pair of data points into a real-valued feature function defined on $[0,1]$. The construction of these feature functions is heavily based on geometric considerations, which has the benefits of enhancing interpretability. Further statistical analysis is then based on the collection of the feature functions. The potential of the method is illustrated by different applications, including classification of high-dimensional and non-Euclidean data. For continuous data in Euclidean space, our feature functions contain information about the underlying density at a given base point (small scale features), and also about the depth of the base point (large scale feature). As shown by our theoretical investigations, the method combats the curse of dimensionality, and also shows some adaptiveness towards sparsity. Connections to other concepts, such as random set theory, localized depth measures and nonlinear multidimensional scaling, are also explored.
Directional differentiability for supremum-type functionals: Statistical applications

We show that various functionals related to the supremum of a real function defined on an arbitrary set or a measure space are Hadamard directionally differentiable. We specifically consider the supremum norm, the supremum, the infimum, and the amplitude of a function. The (usually non-linear) derivatives of these maps adopt simple expressions under suitable assumptions on the underlying space. As an application, we improve and extend to the multidimensional case the results in \cite{Raghavachari} regarding the limiting distributions of Kolmogorov-Smirnov type statistics under the alternative hypothesis. Similar results are obtained for analogous statistics associated with copulas. We additionally solve an open problem about the Berk-Jones statistic proposed by \cite{Jager-Wellner-2004}. Finally, the asymptotic distribution of maximum mean discrepancies over Donsker classes of functions is derived.
Validation of a Computer Code for the Energy Consumption of a Building, with Application to Optimal Electric Bill Pricing

In this paper, we present a case study aimed at determining a billing plan that ensures customer loyalty and provides a profit for the energy company, whose point of view is taken in the paper. The energy provider promotes new contracts for residential buildings, in which customers pay a fixed rate chosen in advance, based on an overall energy consumption forecast. For such a purpose, we consider a practical Bayesian framework for the calibration and validation of a computer code used to forecast the energy consumption of a building. On the basis of power field measurements, collected from an experimental building cell in a given period of time, the code is calibrated, effectively reducing the epistemic uncertainty affecting the most relevant parameters of the code (albedo, thermal bridge factor, and convective coefficient). The validation is carried out by testing the goodness of fit of the code with respect to the field measurements, and then propagating the posterior parametric uncertainty through the code, obtaining probabilistic forecasts of the average electrical power delivered inside the cell in a given period of time. Finally, Bayesian decision-making methods are used to choose the optimal fixed rate (for the energy provider) of the contract, in order to balance short-term benefits with customer retention. We identify three significant contributions of the paper. First of all, the case study data were never analyzed from a Bayesian viewpoint, which is relevant here not only for estimating the parameters but also for properly assessing the uncertainty about the forecasts. Furthermore, the study of optimal policies for energy providers in this framework is new, to the best of our knowledge. Finally, we propose Bayesian posterior predictive p-value for validation.
Spiked covariances and principal components analysis in high-dimensional random effects models

We study principal components analyses in multivariate random and mixed effects linear models, assuming a spherical-plus-spikes structure for the covariance matrix of each random effect. We characterize the behavior of outlier sample eigenvalues and eigenvectors of MANOVA variance components estimators in such models under a high-dimensional asymptotic regime. Our results show that an aliasing phenomenon may occur in high dimensions, in which eigenvalues and eigenvectors of the MANOVA estimate for one variance component may be influenced by the other components. We propose an alternative procedure for estimating the true principal eigenvalues and eigenvectors that asymptotically corrects for this aliasing problem.
Posterior Predictive Treatment Assignment for Estimating Causal Effects with Limited Overlap

Estimating causal effects with propensity scores relies upon the availability of treated and untreated units observed at each value of the estimated propensity score. In settings with strong confounding, limited so-called "overlap" in propensity score distributions can undermine the empirical basis for estimating causal effects and yield erratic finite-sample performance of existing estimators. We propose a Bayesian procedure designed to estimate causal effects in settings where there is limited overlap in propensity score distributions. Our method relies on the posterior predictive treatment assignment (PPTA), a quantity that is derived from the propensity score but serves different role in estimation of causal effects. We use the PPTA to estimate causal effects by marginalizing over the uncertainty in whether each observation is a member of an unknown subset for which treatment assignment can be assumed unconfounded. The resulting posterior distribution depends on the empirical basis for estimating a causal effect for each observation and has commonalities with recently-proposed "overlap weights" of Li et al. (2016). We show that the PPTA approach can be construed as a stochastic version of existing ad-hoc approaches such as pruning based on the propensity score or truncation of inverse probability of treatment weights, and highlight several practical advantages including uncertainty quantification and improved finite-sample performance. We illustrate the method in an evaluation of the effectiveness of technologies for reducing harmful pollution emissions from power plants in the United States.
On the estimation of population size from a dependent triple‐record system

Population size estimation based on a capture–recapture experiment under a triple‐record system is an interesting problem in various fields including epidemiology and population studies. In many real life scenarios, there is inherent dependence between capture and recapture attempts. We propose a novel model that successfully incorporates the possible dependence and the associated parameters have nice interpretations. We provide estimation methodology for the population size and the associated model parameters based on the maximum likelihood method. The model proposed is applied to analyse real data sets from public health and census coverage evaluation studies. The performance of the estimate proposed is evaluated through extensive simulation study and the results are compared with existing competitors. The results exhibit superiority of the model over the existing competitors both in real data analysis and in a simulation study.
MacroPCA: An All-in-One PCA Method Allowing for Missing Values as Well as Cellwise and Rowwise Outliers

Abstract Multivariate data are typically represented by a rectangular matrix (table) in which the rows are the objects (cases) and the columns are the variables (measurements). When there are many variables one often reduces the dimension by principal component analysis (PCA), which in its basic form is not robust to outliers. Much research has focused on handling rowwise outliers, that is, rows that deviate from the majority of the rows in the data (e.g., they might belong to a different population). In recent years also cellwise outliers are receiving attention. These are suspicious cells (entries) that can occur anywhere in the table. Even a relatively small proportion of outlying cells can contaminate over half the rows, which causes rowwise robust methods to break down. In this article, a new PCA method is constructed which combines the strengths of two existing robust methods to be robust against both cellwise and rowwise outliers. At the same time, the algorithm can cope with missing values. As of yet it is the only PCA method that can deal with all three problems simultaneously. Its name MacroPCA stands for PCA allowing for Missingness And Cellwise & Rowwise Outliers. Several simulations and real datasets illustrate its robustness. New residual maps are introduced, which help to determine which variables are responsible for the outlying behavior. The method is well-suited for online process control.
Computationally efficient inference for latent position network models

Latent position models are widely used for the analysis of networks in a variety of research fields. In fact, these models possess a number of desirable theoretical properties, and are particularly easy to interpret. However, statistical methodologies to fit these models generally incur a computational cost which grows with the square of the number of nodes in the graph. This makes the analysis of large social networks impractical. In this paper, we propose a new method characterised by a linear computational complexity, which can be used to fit latent position models on networks of several tens of thousands nodes. Our approach relies on an approximation of the likelihood function, where the amount of noise introduced by the approximation can be arbitrarily reduced at the expense of computational efficiency. We establish several theoretical results that show how the likelihood error propagates to the invariant distribution of the Markov chain Monte Carlo sampler. In particular, we demonstrate that one can achieve a substantial reduction in computing time and still obtain a good estimate of the latent structure. Finally, we propose applications of our method to simulated networks and to a large coauthorships network, highlighting the usefulness of our approach.
THE DEGREE PROFILE AND GINI INDEX OF RANDOM CATERPILLAR TREES

Abstract In this paper, we investigate the degree profile and Gini index of random caterpillar trees (RCTs). We consider RCTs which evolve in two different manners: uniform and nonuniform. The degrees of the vertices on the central path (i.e., the degree profile) of a uniform RCT follows a multinomial distribution. For nonuniform RCTs, we focus on those growing in the fashion of preferential attachment. We develop methods based on stochastic recurrences to compute the exact expectations and the dispersion matrix of the degree variables. A generalized Pólya urn model is exploited to determine the exact joint distribution of these degree variables. We apply the methods from combinatorics to prove that the asymptotic distribution is Dirichlet. In addition, we propose a new type of Gini index to quantitatively distinguish the evolutionary characteristics of the two classes of RCTs. We present the results via several numerical experiments.
Estimating local interactions among many agents who observe their neighbors

In various economic environments, people observe other people with whom they strategically interact. We can model such information‐sharing relations as an information network, and the strategic interactions as a game on the network. When any two agents in the network are connected either directly or indirectly in a large network, empirical modeling using an equilibrium approach can be cumbersome, since the testable implications from an equilibrium generally involve all the players of the game, whereas a researcher's data set may contain only a fraction of these players in practice. This paper develops a tractable empirical model of linear interactions where each agent, after observing part of his neighbors' types, not knowing the full information network, uses best responses that are linear in his and other players' types that he observes, based on simple beliefs about the other players' strategies. We provide conditions on information networks and beliefs such that the best responses take an explicit form with multiple intuitive features. Furthermore, the best responses reveal how local payoff interdependence among agents is translated into local stochastic dependence of their actions, allowing the econometrician to perform asymptotic inference without having to observe all the players in the game or having to know the precise sampling process.