Miracle-dz/UniFAR-FTUs huggingface dataset:
A Supremum-Norm Based Test for the Equality of Several Covariance Functions

In this paper, we propose a new test for the equality of several covariance functions for functional data. Its test statistic is taken as the supremum value of the sum of the squared differences between the estimated individual covariance functions and the pooled sample covariance function, hoping to obtain a more powerful test than some existing tests for the same testing problem. The asymptotic random expression of this test statistic under the null hypothesis is obtained. To approximate the null distribution of the proposed test statistic, we describe a parametric bootstrap method and a non-parametric bootstrap method. The asymptotic random expression of the proposed test is also studied under a local alternative and it is shown that the proposed test is root-$n$ consistent. Intensive simulation studies are conducted to demonstrate the finite sample performance of the proposed test and it turns out that the proposed test is indeed more powerful than some existing tests when functional data are highly correlated. The proposed test is illustrated with three real data examples.
Semi-Parametric Survival Estimation for pedigrees

Mendelian diseases are determined by a single mutation in a given gene. However, in the case of diseases with late onset, the age at onset is variable; it can even be the case that the onset is not observed in a lifetime. Estimating the survival function of the mutation carriers and the effect of modifying factors such as the sex, mutation, origin, etc, is a task of importance, both for management of mutation carriers and for prevention. In this work, we present a semi-parametric method based on a proportional to estimate the survival function using pedigrees ascertained through affected individuals (probands). Not all members of the pedigree need to be genotyped. The ascertainment bias is corrected by using only the phenotypic information from the relatives of the proband, and not of the proband himself. The method manage ungenotyped individuals through belief propagation in Bayesian networks and uses an EM algorithm to compute a Kaplan-Meier estimator of the survival function. The method is illustrated on simulated data and on a samples of families with transthyretin-related hereditary amyloidosis, a rare autosomal dominant disease with highly variable age of onset.
Elicitability and its Application in Risk Management

Elicitability is a property of $\mathbb{R}^k$-valued functionals defined on a set of distribution functions. These functionals represent statistical properties of a distribution, for instance its mean, variance, or median. They are called elicitable if there exists a scoring function such that the expected score under a distribution takes its unique minimum at the functional value of this distribution. If such a scoring function exists, it is called strictly consistent for the functional. Motivated by the recent findings of Fissler and Ziegel concerning higher order elicitability, this thesis reviews the most important results, examples, and applications which are found in the relevant literature. Moreover, we also contribute our own examples and findings in order to give the reader a well-founded overview of the topic as well as of the most used tools and techniques. We include necessary and sufficient conditions for strictly consistent scoring functions, several elicitable as well as non-elicitable functionals and the use of elicitability in forecast comparison, regression, and estimation. Special emphasis is placed on quantitative risk management and the result that Value at Risk and Expected Shortfall are jointly elicitable.
Informed Proposals for Local MCMC in Discrete Spaces

Abstract There is a lack of methodological results to design efficient Markov chain Monte Carlo ( MCMC) algorithms for statistical models with discrete-valued high-dimensional parameters. Motivated by this consideration, we propose a simple framework for the design of informed MCMC proposals (i.e., Metropolis–Hastings proposal distributions that appropriately incorporate local information about the target) which is naturally applicable to discrete spaces. Using Peskun-type comparisons of Markov kernels, we explicitly characterize the class of asymptotically optimal proposal distributions under this framework, which we refer to as locally balanced proposals. The resulting algorithms are straightforward to implement in discrete spaces and provide orders of magnitude improvements in efficiency compared to alternative MCMC schemes, including discrete versions of Hamiltonian Monte Carlo. Simulations are performed with both simulated and real datasets, including a detailed application to Bayesian record linkage. A direct connection with gradient-based MCMC suggests that locally balanced proposals can be seen as a natural way to extend the latter to discrete spaces. Supplementary materials for this article are available online.
Dmos and Tourism Product Development: Accesible Destinations, the Case of Monterrey, Mexico

Introduction The evolving role of Destination Management Organizations (DMO) is highlighted through a case study related to accessible tourism development in Monterrey, Mexico. Specifically, it allows the future DMO professional to understand the characteristics, market potential and travel and service needs of the segment of more than one billion people with disabilities in the world, as well as the requirements of an accessible destination. The benefits, training needs and challenges that arise in developing and promoting accessible tourist infrastructure and services for this market segment will be discussed.
On the Data Augmentation Algorithm for Bayesian Multivariate Linear Regression with Non-Gaussian Errors

Let $\pi$ denote the intractable posterior density that results when the likelihood from a multivariate linear regression model with errors from a scale mixture of normals is combined with the standard non-informative prior. There is a simple data augmentation algorithm (based on latent data from the mixing density) that can be used to explore $\pi$. Hobert et al. (2015) [arXiv:1506.03113v1] recently performed a convergence rate analysis of the Markov chain underlying this MCMC algorithm in the special case where the regression model is univariate. These authors provide simple sufficient conditions (on the mixing density) for geometric ergodicity of the Markov chain. In this note, we extend Hobert et al.'s (2015) result to the multivariate case.
Acceleration and Averaging in Stochastic Mirror Descent Dynamics

We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a stochastic variant in which the gradient is contaminated by noise, and study the resulting stochastic differential equation. We prove a bound on the rate of change of an energy function associated with the problem, then use it to derive estimates of convergence rates of the function values, (a.s. and in expectation) both for persistent and asymptotically vanishing noise. We discuss the interaction between the parameters of the dynamics (learning rate and averaging weights) and the covariation of the noise process, and show, in particular, how the asymptotic rate of covariation affects the choice of parameters and, ultimately, the convergence rate.
Bayesian adaptive lasso with variational Bayes for variable selection in high-dimensional generalized linear mixed models

ABSTRACT This article describes a full Bayesian treatment for simultaneous fixed-effect selection and parameter estimation in high-dimensional generalized linear mixed models. The approach consists of using a Bayesian adaptive Lasso penalty for signal-level adaptive shrinkage and a fast Variational Bayes scheme for estimating the posterior mode of the coefficients. The proposed approach offers several advantages over the existing methods, for example, the adaptive shrinkage parameters are automatically incorporated, no Laplace approximation step is required to integrate out the random effects. The performance of our approach is illustrated on several simulated and real data examples. The algorithm is implemented in the R package glmmvb and is made available online.
Change Point Detection with Optimal Transport and Geometric Discrepancy

We present novel retrospective change point detection approach based on optimal transport and geometric discrepancy. The method does not require any parametric assumptions about distributions separated by change points. It can be used both for single and multiple change point detection and estimation, while the number of change points is either known or unknown. This result is achieved by construction of a certain sliding window statistic from which change points can be derived with elementary convex geometry in a specific Hilbert space. The work is illustrated with computational examples, both artificially constructed and based on actual data.
Kernel Method for Detecting Higher Order Interactions in multi-view Data: An Application to Imaging, Genetics, and Epigenetics

In this study, we tested the interaction effect of multimodal datasets using a novel method called the kernel method for detecting higher order interactions among biologically relevant mulit-view data. Using a semiparametric method on a reproducing kernel Hilbert space (RKHS), we used a standard mixed-effects linear model and derived a score-based variance component statistic that tests for higher order interactions between multi-view data. The proposed method offers an intangible framework for the identification of higher order interaction effects (e.g., three way interaction) between genetics, brain imaging, and epigenetic data. Extensive numerical simulation studies were first conducted to evaluate the performance of this method. Finally, this method was evaluated using data from the Mind Clinical Imaging Consortium (MCIC) including single nucleotide polymorphism (SNP) data, functional magnetic resonance imaging (fMRI) scans, and deoxyribonucleic acid (DNA) methylation data, respectfully, in schizophrenia patients and healthy controls. We treated each gene-derived SNPs, region of interest (ROI) and gene-derived DNA methylation as a single testing unit, which are combined into triplets for evaluation. In addition, cardiovascular disease risk factors such as age, gender, and body mass index were assessed as covariates on hippocampal volume and compared between triplets. Our method identified $13$-triplets ($p$-values $\leq 0.001$) that included $6$ gene-derived SNPs, $10$ ROIs, and $6$ gene-derived DNA methylations that correlated with changes in hippocampal volume, suggesting that these triplets may be important in explaining schizophrenia-related neurodegeneration. With strong evidence ($p$-values $\leq 0.000001$), the triplet ({\bf MAGI2, CRBLCrus1.L, FBXO28}) has the potential to distinguish schizophrenia patients from the healthy control variations.
Recovering covariance from functional fragments

&NA; We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is observed only on a subinterval of length Symbol, one has no statistical information on the unknown covariance outside a δ‐band around the diagonal. The problem seems unidentifiable without parametric assumptions, but we show that nonparametric estimation is feasible under suitable smoothness and rank conditions on the unknown covariance. This remains true even when the observations are discrete, and we give precise deterministic conditions on how fine the observation grid needs to be relative to the rank and fragment length for identifiability to hold true. We show that our conditions translate the estimation problem to a low‐rank matrix completion problem, construct a nonparametric estimator in this vein, and study its asymptotic properties. We illustrate the numerical performance of our method on real and simulated data. Symbol. No caption available.
Automatic Inference of the Quantile Parameter

Supervised learning is an active research area, with numerous applications in diverse fields such as data analytics, computer vision, speech and audio processing, and image understanding. In most cases, the loss functions used in machine learning assume symmetric noise models, and seek to estimate the unknown function parameters. However, loss functions such as quantile and quantile Huber generalize the symmetric $\ell_1$ and Huber losses to the asymmetric setting, for a fixed quantile parameter. In this paper, we propose to jointly infer the quantile parameter and the unknown function parameters, for the asymmetric quantile Huber and quantile losses. We explore various properties of the quantile Huber loss and implement a convexity certificate that can be used to check convexity in the quantile parameter. When the loss if convex with respect to the parameter of the function, we prove that it is biconvex in both the function and the quantile parameters, and propose an algorithm to jointly estimate these. Results with synthetic and real data demonstrate that the proposed approach can automatically recover the quantile parameter corresponding to the noise and also provide an improved recovery of function parameters. To illustrate the potential of the framework, we extend the gradient boosting machines with quantile losses to automatically estimate the quantile parameter at each iteration.
Entropy-based inhomogeneity detection in porous media

We study a change-point problem for random fields based on a univariate detection of outliers via the $3\sigma$-rule in order to recognize inhomogeneities in porous media. In particular, we focus on fibre reinforced polymers modeled by stochastic fibre processes with high fibre intensity and search for abrupt changes in the direction of the fibres. As a measure of change, the entropy of the directional distribution is locally estimated within a window that scans the region to be analyzed.
Simple Rules for Complex Decisions

From doctors diagnosing patients to judges setting bail, experts often base their decisions on experience and intuition rather than on statistical models. While understandable, relying on intuition over models has often been found to result in inferior outcomes. Here we present a new method-select-regress-and-round-for constructing simple rules that perform well for complex decisions. These rules take the form of a weighted checklist, can be applied mentally, and nonetheless rival the performance of modern machine learning algorithms. Our method for creating these rules is itself simple, and can be carried out by practitioners with basic statistics knowledge. We demonstrate this technique with a detailed case study of judicial decisions to release or detain defendants while they await trial. In this application, as in many policy settings, the effects of proposed decision rules cannot be directly observed from historical data: if a rule recommends releasing a defendant that the judge in reality detained, we do not observe what would have happened under the proposed action. We address this key counterfactual estimation problem by drawing on tools from causal inference. We find that simple rules significantly outperform judges and are on par with decisions derived from random forests trained on all available features. Generalizing to 22 varied decision-making domains, we find this basic result replicates. We conclude with an analytical framework that helps explain why these simple decision rules perform as well as they do.
A Nonlinear Differential Equation for Generating Warping Function

Given set of functions $y_i(t)$ and $x(t)$ such that $y_i(t) = a_i x\left[h_i(t)\right]$ with $a_i$ being an unknown amplitude with low changes in time (or $\frac{\Delta a_i}{a^2_i} << 1$) and $h_i(t)$ an unknown warping function, the paper shows that $h_i(t)$ can be described using a non-linear differential equation. The differential equation then can be utilized to estimate the warping function $h_i(t)$ using a nonlinear least-squares optimization. This differential equation can also be useful for reducing and analyzing phase variability in data sequences. Results, obtained on synthetic curves, showed that the proposed method is effective in aligning the curves. The obtained aligned curves exhibit variation only in amplitude, and phase variation can be removed efficiently.
Gaussian variational approximation for high-dimensional state space models

Our article considers variational approximations of the posterior distribution in a high-dimensional state space model. The variational approximation is a multivariate Gaussian density, in which the variational parameters to be optimized are a mean vector and a covariance matrix. The number of parameters in the covariance matrix grows as the square of the number of model parameters, so it is necessary to find simple yet effective parametrizations of the covariance structure when the number of model parameters is large. The joint posterior distribution over the high-dimensional state vectors is approximated using a dynamic factor model, with Markovian dependence in time and a factor covariance structure for the states. This gives a reduced dimension description of the dependence structure for the states, as well as a temporal conditional independence structure similar to that in the true posterior. We illustrate our approach in two high-dimensional applications which are challenging for Markov chain Monte Carlo sampling. The first is a spatio-temporal model for the spread of the Eurasian Collared-Dove across North America. The second is a multivariate stochastic volatility model for financial returns via a Wishart process.
Consistency of survival tree and forest models: splitting bias and correction

Random survival forest and survival trees are popular models in statistics and machine learning. However, there is a lack of general understanding regarding consistency, splitting rules and influence of the censoring mechanism. In this paper, we investigate the statistical properties of existing methods from several interesting perspectives. First, we show that traditional splitting rules with censored outcomes rely on a biased estimation of the within-node failure distribution. To exactly quantify this bias, we develop a concentration bound of the within-node estimation based on non i.i. d. samples and apply it to the entire forest. Second, we analyze the entanglement between the failure and censoring distributions caused by univariate splits, and show that without correcting the bias at an internal node, survival tree and forest models can still enjoy consistency under suitable conditions. In particular, we demonstrate this property under two cases: a finite-dimensional case where the splitting variables and cutting points are chosen randomly, and a high-dimensional case where the covariates are weakly correlated. Our results can also degenerate into an independent covariate setting, which is commonly used in the random forest literature for high-dimensional sparse models. However, it may not be avoidable that the convergence rate depends on the total number of variables in the failure and censoring distributions. Third, we propose a new splitting rule that compares bias-corrected cumulative hazard functions at each internal node. We show that the rate of consistency of this new model depends only on the number of failure variables, which improves from non-bias-corrected versions. We perform simulation studies to confirm that this can substantially benefit the prediction error.
Estimation of Kullback-Leibler losses for noisy recovery problems within the exponential family

We address the question of estimating Kullback-Leibler losses rather than squared losses in recovery problems where the noise is distributed within the exponential family. Inspired by Stein unbiased risk estimator (SURE), we exhibit conditions under which these losses can be unbiasedly estimated or estimated with a controlled bias. Simulations on parameter selection problems in applications to image denoising and variable selection with Gamma and Poisson noises illustrate the interest of Kullback-Leibler losses and the proposed estimators.
An Efficient Surrogate Model for Emulation and Physics Extraction of Large Eddy Simulations

ABSTRACT In the quest for advanced propulsion and power-generation systems, high-fidelity simulations are too computationally expensive to survey the desired design space, and a new design methodology is needed that combines engineering physics, computer simulations, and statistical modeling. In this article, we propose a new surrogate model that provides efficient prediction and uncertainty quantification of turbulent flows in swirl injectors with varying geometries, devices commonly used in many engineering applications. The novelty of the proposed method lies in the incorporation of known physical properties of the fluid flow as simplifying assumptions for the statistical model. In view of the massive simulation data at hand, which is on the order of hundreds of gigabytes, these assumptions allow for accurate flow predictions in around an hour of computation time. To contrast, existing flow emulators which forgo such simplifications may require more computation time for training and prediction than is needed for conducting the simulation itself. Moreover, by accounting for coupling mechanisms between flow variables, the proposed model can jointly reduce prediction uncertainty and extract useful flow physics, which can then be used to guide further investigations. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
Discovering Effect Modification and Randomization Inference in Air Pollution Studies

Studies have shown that exposure to air pollution, even at low levels, significantly increases mortality. As regulatory actions are becoming prohibitively expensive, robust evidence to guide the development of targeted interventions to reduce air pollution exposure is needed. In this paper, we introduce a novel statistical method that splits the data into two subsamples: (a) Using the first subsample, we consider a data-driven search for $\textit{de novo}$ discovery of subgroups that could have exposure effects that differ from the population mean; and then (b) using the second subsample, we quantify evidence of effect modification among the subgroups with nonparametric randomization-based tests. We also develop a sensitivity analysis method to assess the robustness of the conclusions to unmeasured confounding bias. Via simulation studies and theoretical arguments, we demonstrate that since we discover the subgroups in the first subsample, hypothesis testing on the second subsample can focus on theses subgroups only, thus substantially increasing the statistical power of the test. We apply our method to the data of 1,612,414 Medicare beneficiaries in New England region in the United States for the period 2000 to 2006. We find that seniors aged between 81-85 with low income and seniors aged above 85 have statistically significant higher causal effects of exposure to PM$_{2.5}$ on 5-year mortality rate compared to the population mean.