Miracle-dz/UniFAR-FTUs huggingface dataset:
A new standard for the analysis and design of replication studies

A new standard is proposed for the evidential assessment of replication studies. The approach combines a specific reverse Bayes technique with prior‐predictive tail probabilities to define replication success. The method gives rise to a quantitative measure for replication success, called the sceptical p‐value. The sceptical p‐value integrates traditional significance of both the original and the replication study with a comparison of the respective effect sizes. It incorporates the uncertainty of both the original and the replication effect estimates and reduces to the ordinary p‐value of the replication study if the uncertainty of the original effect estimate is ignored. The framework proposed can also be used to determine the power or the required replication sample size to achieve replication success. Numerical calculations highlight the difficulty of achieving replication success if the evidence from the original study is only suggestive. An application to data from the Open Science Collaboration project on the replicability of psychological science illustrates the methodology proposed.
Identifiability and Consistent Estimation of Nonparametric Translation Hidden Markov Models with General State Space

This paper considers hidden Markov models where the observations are given as the sum of a latent state which lies in a general state space and some independent noise with unknown distribution. It is shown that these fully nonparametric translation models are identifiable with respect to both the distribution of the latent variables and the distribution of the noise, under mostly a light tail assumption on the latent variables. Two nonparametric estimation methods are proposed and we prove that the corresponding estimators are consistent for the weak convergence topology. These results are illustrated with numerical experiments.
A Hierarchical Spatio-Temporal Statistical Model for Physical Systems

In this paper, we extend and analyze a Bayesian hierarchical spatio-temporal model for physical systems. A novelty is to model the discrepancy between the output of a computer simulator for a physical process and the actual process values with a multivariate random walk. For computational efficiency, linear algebra for bandwidth limited matrices is utilized, and first-order emulator inference allows for the fast emulation of a numerical partial differential equation (PDE) solver. A test scenario from a physical system motivated by glaciology is used to examine the speed and accuracy of the computational methods used, in addition to the viability of modeling assumptions. We conclude by discussing how the model and associated methodology can be applied in other physical contexts besides glaciology.
Minimax rates for the covariance estimation of multi-dimensional Lévy processes with high-frequency data

This article studies nonparametric methods to estimate the co-integrated volatility for multi-dimensional Levy processes with high frequency data. We construct a spectral estimator for the co-integrated volatility and prove minimax rates for an appropriate bounded nonparametric class of semimartingales. Given $ n $ observations of increments over intervals of length $1/n$, the rates of convergence are $1 / \sqrt{n} $ if $ r \leq 1 $ and $ (n\log n)^{(r-2)/2} $ if $ r>1 $, which are optimal in a minimax sense. We bound the co-jump index activity from below with the harmonic mean. Finally, we assess the efficiency of our estimator by comparing it with estimators in the existing literature.
Growing simplified vine copula trees: improving Di{\ss}mann's algorithm

Vine copulas are pair-copula constructions enabling multivariate dependence modeling in terms of bivariate building blocks. One of the main tasks of fitting a vine copula is the selection of a suitable tree structure. For this the prevalent method is a heuristic called Di{\ss}mann's algorithm. It sequentially constructs the vine's trees by maximizing dependence at each tree level, where dependence is measured in terms of absolute Kendall's $\tau$. However, the algorithm disregards any implications of the tree structure on the simplifying assumption that is usually made for vine copulas to keep inference tractable. We develop two new algorithms that select tree structures focused on producing simplified vine copulas for which the simplifying assumption is violated as little as possible. For this we make use of a recently developed statistical test of the simplifying assumption. In a simulation study we show that our proposed methods outperform the benchmark given by Di{\ss}mann's algorithm by a great margin. Several real data applications emphasize their practical relevance.
Score Predictor Factor Analysis: Reproducing Observed Covariances by Means of Factor Score Predictors

The non-diagonal elements of the observed covariances are more exactly reproduced by the factor loadings than by the model implied by the corresponding factor score predictors. This is a limitation to the validity of factor score predictors. It is therefore investigated whether it is possible to estimate factor loadings for which the model implied by the factor score predictors optimally reproduces the non-diagonal elements of the observed covariance matrix. Accordingly, loading estimates are proposed for which the model implied by the factor score predictors allows for a least-squares approximation of the non-diagonal elements of the observed covariance matrix. This estimation method is termed score predictor factor analysis and algebraically compared with Minres factor analysis as well as principal component analysis. A population-based and a sample-based simulation study was performed in order to compare score predictor factor analysis, Minres factor analysis, and principal component analysis. It turns out that the non-diagonal elements of the observed covariance matrix can more exactly be reproduced from the factor score predictors computed from score predictor factor analysis than from the factor score predictors computed from Minres factor analysis and from principal components.
Exponential weights in multivariate regression and a low-rankness favoring prior

We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with fixed design and bounded noise. The first new feature uncovered by our guarantees is that it is not necessary to require independence of the observations: a symmetry condition on the noise distribution alone suffices to get a sharp risk bound. This result needs the regression vectors to be bounded. A second curious finding concerns the case of unbounded regression vectors but independent noise. It turns out that applying exponential weights to the label vectors perturbed by a uniform noise leads to an estimator satisfying a sharp oracle inequality. The last contribution is the instantiation of the proposed oracle inequalities to problems in which the unknown parameter is a matrix. We propose a low-rankness favoring prior and show that it leads to an estimator that is optimal under weak assumptions.
Construction of Non-asymptotic Confidence Sets in 2-Wasserstein Space

In this paper, we consider a probabilistic setting where the probability measures are considered to be random objects. We propose a procedure of construction non-asymptotic confidence sets for empirical barycenters in 2-Wasserstein space and develop the idea further to construction of a non-parametric two-sample test that is then applied to the detection of structural breaks in data with complex geometry. Both procedures mainly rely on the idea of multiplier bootstrap (Spokoiny and Zhilova (2015), Chernozhukov et al. (2014)). The main focus lies on probability measures that have commuting covariance matrices and belong to the same scatter-location family: we proof the validity of a bootstrap procedure that allows to compute confidence sets and critical values for a Wasserstein-based two-sample test.
Very Highly Skilled Individuals Do Not Choke Under Pressure: Evidence from Professional Darts

Understanding and predicting how individuals perform in high-pressure situations is of importance in designing and managing workplaces, but also in other areas of society such as disaster management or professional sports. For simple effort tasks, an increase in the pressure experienced by an individual, e.g. due to incentive schemes in a workplace, will increase the effort put into the task and hence in most cases also the performance. For the more complex and usually harder to capture case of skill tasks, there exists a substantial body of literature that fairly consistently reports a choking phenomenon under pressure. However, we argue that many of the corresponding studies have crucial limitations, such as neglected interaction effects or insufficient numbers of observations to allow within-individual analysis. Here, we investigate performance under pressure in professional darts as a near-ideal setting with no direct interaction between players and a high number of observations per subject. We analyze almost one year of tournament data covering 23,192 dart throws, hence a data set that is very much larger than those used in most previous studies. Contrary to what would be expected given the evidence in favor of a choking phenomenon, we find strong evidence for an overall improved performance under pressure, for nearly all 83 players in the sample. These results could have important consequences for our understanding of how highly skilled individuals deal with high-pressure situations.
Two-sample Test of Community Memberships of Weighted Stochastic Block Models.

Suppose two networks are observed for the same set of nodes, where each network is assumed to be generated from a weighted stochastic block model. This paper considers the problem of testing whether the community memberships of the two networks are the same. A test statistic based on singular subspace distance is developed. Under the weighted stochastic block models with dense graphs, the limiting distribution of the proposed test statistic is developed. Simulation results show that the test has correct empirical type 1 errors under the dense graphs. The test also behaves as expected in empirical power, showing gradual changes when the intra-block and inter-block distributions are close and achieving 1 when the two distributions are not so close, where the closeness of the two distributions is characterized by Renyi divergence of order 1/2. The Enron email networks are used to demonstrate the proposed test.
On the Asymptotics of Maronna's Robust PCA

The eigenvalue decomposition (EVD) parameters of the second order statistics are ubiquitous in statistical analysis and signal processing. Notably, the EVD of the <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula>-estimators of the scatter matrix is a popular choice to perform robust probabilistic PCA or other dimension reduction related applications. Towards the goal of characterizing this process, this paper derives new asymptotics for the EVD parameters (i.e. eigenvalues, eigenvectors, and principal subspace) of <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula>-estimators in the context of complex elliptically symmetric distributions. First, their Gaussian asymptotic distribution is obtained by extending standard results on the sample covariance matrix in the Gaussian context. Second, their convergence towards the EVD parameters of a Gaussian-Core Wishart Equivalent is derived. This second result represents the main contribution in the sense that it quantifies when it is acceptable to directly rely on well-established results on the EVD of Wishart-distributed matrix for characterizing the EVD of <inline-formula><tex-math notation="LaTeX">$M$</tex-math></inline-formula>-estimators. Finally, some examples (intrinsic bias analysis, rank estimation, and low-rank adaptive filtering) illustrate where the obtained results can be leveraged.
Classification of functional fragments by regularized linear classifiers with domain selection

We consider the problem of classification of functional data into two groups by linear classifiers based on one-dimensional projections of functions. We reformulate the task to find the best classifier as an optimization problem and solve it by regularization techniques, namely the conjugate gradient method with early stopping, the principal component method and the ridge method. We study the empirical version with finite training samples consisting of incomplete functions observed on different subsets of the domain and show that the optimal, possibly zero, misclassification probability can be achieved in the limit along a possibly non-convergent empirical regularization path. Being able to work with fragmentary training data we propose a domain extension and selection procedure that finds the best domain beyond the common observation domain of all curves. In a simulation study we compare the different regularization methods and investigate the performance of domain selection. Our methodology is illustrated on a medical data set, where we observe a substantial improvement of classification accuracy due to domain extension.
Tree-Based Bayesian Treatment Effect Analysis

The inclusion of the propensity score as a covariate in Bayesian regression trees for causal inference can reduce the bias in treatment effect estimations, which occurs due to the regularization-induced confounding phenomenon. This study advocate for the use of the propensity score by evaluating it under a full-Bayesian variable selection setting, and the use of Individual Conditional Expectation Plots, which is a graphical tool that can improve treatment effect analysis on tree-based Bayesian models and others "black box" models. The first one, even if poorly estimated, can lead to bias reduction on the estimated treatment effects, while the latter can be used to found groups of individuals which have different responses to the applied treatment, and analyze the impact of each variable in the estimated treatment effect.
Measuring religious morality using very limited poll responses: Implementing "big-data analytics" to small data.

Opinion polls remain among the most efficient and widespread methods to capture psycho-social data at large scales. However, there are limitations on the logistics and structure of opinion polls that restrict the amount and type of information that can be collected. As a consequence, data from opinion polls are often reported in simple percentages and analyzed non-parametrically. In this paper, response data on just four questions from a national opinion poll were used to demonstrate that a parametric scale can be constructed using item response modeling approaches. Developing a parametric scale yields interval-level measures which are more useful than the strictly ordinal-level measures obtained from Likert-type scales common in opinion polls. The metric that was developed in this paper, a measure of religious morality, can be processed and used in a wider range of statistical analyses compared to conventional approaches of simply reporting percentages at item-level. Finally, this paper reports the item parameters so that researchers can adopt these items to future instruments and place their own results on the same scale, thereby allowing responses from future samples to be compared to the results from the representative data in this paper.
Distributed learning with compressed gradients

Asynchronous computation and gradient compression have emerged as two key techniques for achieving scalability in distributed optimization for large-scale machine learning. This paper presents a unified analysis framework for distributed gradient methods operating with staled and compressed gradients. Non-asymptotic bounds on convergence rates and information exchange are derived for several optimization algorithms. These bounds give explicit expressions for step-sizes and characterize how the amount of asynchrony and the compression accuracy affect iteration and communication complexity guarantees. Numerical results highlight convergence properties of different gradient compression algorithms and confirm that fast convergence under limited information exchange is indeed possible.
A framework for posterior consistency in model selection

We develop a theoretical framework for the frequentist assessment of Bayesian model selection, specifically its ability to select the (Kullback-Leibler) optimal model and to portray the corresponding uncertainty. The contribution is not proving consistency for a specific prior, but giving a general strategy for such proofs. Its basis applies to any model, prior, sample size, parameter dimensionality and (although only briefly exploited here) under model misspecification. As an immediate consequence the framework also characterizes a strong form of convergence for $L_0$ penalties and associated pseudo-posterior probabilities of potential interest for uncertainty quantification. The main advantage of the framework is that, instead of studying complex high-dimensional stochastic sums, it suffices to bound certain Bayes factor tails and use standard tools to determine the convergence of deterministic series. As a second contribution we deploy the framework to canonical linear regression. These findings give a high-level description of when one can achieve consistency and at what rate for a wide class of priors as a function of the data-generating truth, sample size and dimensionality. They also indicate when it is possible to use less sparse priors to improve inherent sparsity vs. power trade-offs that are not adequately captured by studying asymptotically optimal rates. Our empirical illustrations align with these findings, underlining the importance of considering the problem at hand's characteristics to judge the quality of model selection procedures, rather than relying purely on asymptotics.
Quasi Markov Chain Monte Carlo Methods

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior densities within the Bayesian framework, in particular for inverse problems. We introduce a general parallel Markov chain Monte Carlo (MCMC) framework, for which we prove a law of large numbers and a central limit theorem. In that context, non-reversible transitions are investigated. We then extend this approach to the use of adaptive kernels and state conditions, under which ergodicity holds. As a further extension, an importance sampling estimator is derived, for which asymptotic unbiasedness is proven. We consider the use of completely uniformly distributed (CUD) numbers within the above mentioned algorithms, which leads to a general parallel quasi-MCMC (QMCMC) methodology. We prove consistency of the resulting estimators and demonstrate numerically that this approach scales close to $n^{-2}$ as we increase parallelisation, instead of the usual $n^{-1}$ that is typical of standard MCMC algorithms. In practical statistical models we observe multiple orders of magnitude improvement compared with pseudo-random methods.
Ordinal Probit Functional Regression Models with Application to Computer-Use Behavior in Rhesus Monkeys

Research in functional regression has made great strides in expanding to non-Gaussian functional outcomes, however the exploration of ordinal functional outcomes remains limited. Motivated by a study of computer-use behavior in rhesus macaques (\emph{Macaca mulatta}), we introduce the Ordinal Probit Functional Regression Model or OPFRM to perform ordinal function-on-scalar regression. The OPFRM is flexibly formulated to allow for the choice of different basis functions including penalized B-splines, wavelets, and O'Sullivan splines. We demonstrate the operating characteristics of the model in simulation using a variety of underlying covariance patterns showing the model performs reasonably well in estimation under multiple basis functions. We also present and compare two approaches for conducting posterior inference showing that joint credible intervals tend to out perform point-wise credible. Finally, in application, we determine demographic factors associated with the monkeys' computer use over the course of a year and provide a brief analysis of the findings.
On the Anatomy of MCMC-based Maximum Likelihood Learning of Energy-Based Models

This study investigates the effects of Markov chain Monte Carlo (MCMC) sampling in unsupervised Maximum Likelihood (ML) learning. Our attention is restricted to the family of unnormalized probability densities for which the negative log density (or energy function) is a ConvNet. We find that many of the techniques used to stabilize training in previous studies are not necessary. ML learning with a ConvNet potential requires only a few hyper-parameters and no regularization. Using this minimal framework, we identify a variety of ML learning outcomes that depend solely on the implementation of MCMC sampling. On one hand, we show that it is easy to train an energy-based model which can sample realistic images with short-run Langevin. ML can be effective and stable even when MCMC samples have much higher energy than true steady-state samples throughout training. Based on this insight, we introduce an ML method with purely noise-initialized MCMC, high-quality short-run synthesis, and the same budget as ML with informative MCMC initialization such as CD or PCD. Unlike previous models, our energy model can obtain realistic high-diversity samples from a noise signal after training. On the other hand, ConvNet potentials learned with non-convergent MCMC do not have a valid steady-state and cannot be considered approximate unnormalized densities of the training data because long-run MCMC samples differ greatly from observed images. We show that it is much harder to train a ConvNet potential to learn a steady-state over realistic images. To our knowledge, long-run MCMC samples of all previous models lose the realism of short-run samples. With correct tuning of Langevin noise, we train the first ConvNet potentials for which long-run and steady-state MCMC samples are realistic images.
Statistical thresholds for tensor PCA

We study the statistical limits of testing and estimation for a rank one deformation of a Gaussian random tensor. We compute the sharp thresholds for hypothesis testing and estimation by maximum likelihood and show that they are the same. Furthermore, we find that the maximum likelihood estimator achieves the maximal correlation with the planted vector among measurable estimators above the estimation threshold. In this setting, the maximum likelihood estimator exhibits a discontinuous BBP-type transition: below the critical threshold the estimator is orthogonal to the planted vector, but above the critical threshold, it achieves positive correlation which is uniformly bounded away from zero.
Empirical likelihood for linear structural equation models with dependent errors

We consider linear structural equation models that are associated with mixed graphs. The structural equations in these models only involve observed variables, but their idiosyncratic error terms are allowed to be correlated and non‐Gaussian. We propose empirical likelihood procedures for inference and suggest several modifications, including a profile likelihood, in order to improve tractability and performance of the resulting methods. Through simulations, we show that when the error distributions are non‐Gaussian, the use of empirical likelihood and the proposed modifications may increase statistical efficiency and improve assessment of significance. Copyright © 2017 John Wiley & Sons, Ltd.