Miracle-dz/UniFAR-FTUs huggingface dataset:
Information bounds for inverse problems with application to deconvolution and L\'evy models

If a functional in an inverse problem can be estimated with parametric rate, then the minimax rate gives no information about the ill-posedness of the problem. To have a more precise lower bound, we study semiparametric efficiency in the sense of H\'ajek-Le Cam for functional estimation in regular indirect models. These are characterized as models that can be locally approximated by a linear white noise model that is described by the generalized score operator. A convolution theorem for regular indirect models is proved. This applies to a large class of statistical inverse problems, which is illustrated for the prototypical white noise and deconvolution model. It is especially useful for nonlinear models. We discuss in detail a nonlinear model of deconvolution type where a L\'evy process is observed at low frequency, concluding an information bound for the estimation of linear functionals of the jump measure.
A solution in small area estimation problems

We present a new method in problems where estimates are needed for finite population domains with small or even zero sample sizes. In contrast to known estimation methods, an auxiliary information is used to model sizes of population units instead of a direct prediction of their values of interest. In particular, via an additional characterization of regression models, we incorporate a scatter and variabilities of the units sizes into an estimator, and then it uses an information of the whole sample by taking into an account a location of the estimation domain inside the population. To reduce an impact of the introduced domain total estimator bias to the mean square error, we construct also a regression type version of the estimator. An efficiency of the method proposed is shown in a simulation study.
Optimal Robustness Results for Some Bayesian Procedures and the Relationship to Prior-Data Conflict

The robustness to the prior of Bayesian inference procedures based on a measure of statistical evidence are considered. These inferences are shown to have optimal properties with respect to robustness. Furthermore, a connection between robustness and prior-data conflict is established. In particular, the inferences are shown to be effectively robust when the choice of prior does not lead to prior-data conflict. When there is prior-data conflict, however, robustness may fail to hold.
On some generalized orderings: In the spirit of relative ageing

ABSTRACT We introduce some new generalized stochastic orderings (in the spirit of relative ageing) which compare probability distributions with the exponential distribution. These orderings are useful to understand the phenomenon of positive ageing classes and also helpful to guide the practitioners when there are crossing hazard rates and/or crossing mean residual lives. We study some characterizations of these orderings. Inter-relations among these orderings have also been discussed.
Power-Expected-Posterior Priors for Generalized Linear Models

The power-expected-posterior (PEP) prior provides an objective, automatic, consistent and parsimonious model selection procedure. At the same time it resolves the conceptual and computational problems due to the use of imaginary data. Namely, (i) it dispenses with the need to select and average across all possible minimal imaginary samples, and (ii) it diminishes the effect that the imaginary data have upon the posterior distribution. These attributes allow for large sample approximations, when needed, in order to reduce the computational burden under more complex models. In this work we generalize the applicability of the PEP methodology, focusing on the framework of generalized linear models (GLMs), by introducing two new PEP definitions which are in effect applicable to any general model setting. Hyper-prior extensions for the power parameter that regulates the contribution of the imaginary data are introduced. We further study the validity of the predictive matching and of the model selection consistency, providing analytical proofs for the former and empirical evidence supporting the latter. For estimation of posterior model and inclusion probabilities we introduce a tuning-free Gibbs-based variable selection sampler. Several simulation scenarios and one real life example are considered in order to evaluate the performance of the proposed methods compared to other commonly used approaches based on mixtures of g-priors. Results indicate that the GLM-PEP priors are more effective in the identification of sparse and parsimonious model formulations.
Mixture models applied to heterogeneous populations

Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular, when the number of subpopulations is considered unknown, more sophisticated methods are required to perform Bayesian analysis. The Reversible Jump Markov Chain Monte Carlo is an alternative method for computing the posterior distribution by simulation in this case. Some problems associated with the Bayesian analysis of these class of models are frequent, such as the so-called "label-switching" problem. However, as the level of heterogeneity in the population increases, these problems are expected to become less frequent and the model's performance to improve. Thus, the aim of this work is to evaluate the normal mixture model fit using simulated data under different settings of heterogeneity and prior information about the mixture proportions. A simulation study is also presented to evaluate the model's performance considering the number of components known and estimating it. Finally, the model is applied to a censored real dataset containing antibody levels of Cytomegalovirus in individuals.
A Gibbs Sampler for Multivariate Linear Regression

Kelly (2007, hereafter K07) described an efficient algorithm, using Gibbs sampling, for performing linear regression in the fairly general case where non-zero measurement errors exist for both the covariates and response variables, where these measurements may be correlated (for the same data point), where the response variable is affected by intrinsic scatter in addition to measurement error, and where the prior distribution of covariates is modeled by a flexible mixture of Gaussians rather than assumed to be uniform. Here I extend the K07 algorithm in two ways. First, the procedure is generalized to the case of multiple response variables. Second, I describe how to model the prior distribution of covariates using a Dirichlet process, which can be thought of as a Gaussian mixture where the number of mixture components is learned from the data. I present an example of multivariate regression using the extended algorithm, namely fitting scaling relations of the gas mass, temperature, and luminosity of dynamically relaxed galaxy clusters as a function of their mass and redshift. An implementation of the Gibbs sampler in the r language, called lrgs, is provided.
Regression‐based covariance functions for nonstationary spatial modeling

In many environmental applications involving spatially‐referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of models for continuously‐indexed spatial data is the covariance function, which is traditionally assumed to belong to a parametric class of stationary models. However, stationarity is rarely a realistic assumption. Alternative methods that more appropriately model the nonstationarity present in environmental processes often involve high‐dimensional parameter spaces, which lead to difficulties in model fitting and interpretability. To overcome this issue, we build on the growing literature of covariate‐driven nonstationary spatial modeling. Using process convolution techniques, we propose a Bayesian model for continuously‐indexed spatial data based on a flexible parametric covariance regression structure for a convolution‐kernel covariance matrix. The resulting model is a parsimonious representation of the kernel process, and we explore properties of the implied model, including a description of the resulting nonstationary covariance function and the interpretational benefits in the kernel parameters. Furthermore, we demonstrate that our model provides a practical compromise between stationary and highly parameterized nonstationary spatial covariance functions that do not perform well in practice. We illustrate our approach through an analysis of annual precipitation data. Copyright © 2015 John Wiley & Sons, Ltd.
Graphical structure of conditional independencies in determinantal point processes

Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional independence. We describe some conditional independencies through the conditions on the kernel of a determinantal point process, and show many can be obtained using the graph induced by a kernel of the $L$-ensemble.
INTERPRETING THE DISTANCE CORRELATION RESULTS FOR THE COMBO-17 SURVEY

The accurate classification of galaxies in large-sample astrophysical databases of galaxy clusters depends sensitively on the ability to distinguish between morphological types, especially at higher redshifts. This capability can be enhanced through a new statistical measure of association and correlation, called the distance correlation coefficient, which has more statistical power to detect associations than does the classical Pearson measure of linear relationships between two variables. The distance correlation measure offers a more precise alternative to the classical measure since it is capable of detecting nonlinear relationships that may appear in astrophysical applications. We showed recently that the comparison between the distance and Pearson correlation coefficients can be used effectively to isolate potential outliers in various galaxy data sets, and this comparison has the ability to confirm the level of accuracy associated with the data. In this work, we elucidate the advantages of distance correlation when applied to large databases. We illustrate how the distance correlation measure can be used effectively as a tool to confirm nonlinear relationships between various variables in the COMBO-17 database, including the lengths of the major and minor axes, and the alternative redshift distribution. For these outlier pairs, the distance correlation coefficient is routinely higher than the Pearson coefficient since it is easier to detect nonlinear relationships with distance correlation. The V-shaped scatter plots of Pearson versus distance correlation coefficients also reveal the patterns with increasing redshift and the contributions of different galaxy types within each redshift range.
A comparative review of variable selection techniques for covariate dependent Dirichlet process mixture models

Dirichlet Process Mixture (DPM) models have been increasingly employed to specify random partition models that take into account possible patterns within covariates. Furthermore with large numbers of covariates methods for selecting the most important covariates have been proposed. Commonly the covariates are chosen either for their importance in determining the clustering of the observations or for their effect on the level of a response variable (when a regression model is specified). Typically both strategies involve the specification of latent indicators that regulate the inclusion of the covariates in the model. Common examples involve the use of spike and slab prior distributions. In this work we review the most relevant DPM models that include covariate information in the induced partition of the observations and we focus on available variable selection techniques for these models. We highlight the main features of each model and demonstrate them using simulations and a real data application. The Canadian Journal of Statistics 45: 254–273; 2017 © 2017 Statistical Society of Canada
Entropic representation and estimation of diversity indices

This paper serves a twofold purpose. First, a unified perspective on diversity indices is introduced based on an entropic basis. It is shown that the class of all linear combinations of the entropic basis, referred to as the class of linear diversity indices, covers a wide range of diversity indices used in the literature. Second, a class of estimators for linear diversity indices is proposed and it is shown that these estimators have rapidly decaying biases and asymptotic normality.
Confidence intervals for high-dimensional inverse covariance estimation

We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian limiting distribution. Asymptotic properties of the novel estimator are analyzed for the case of sub-Gaussian observations under a sparsity assumption on the entries of the true precision matrix and regularity conditions. Thresholding the de-sparsified estimator gives guarantees for edge selection in the associated graphical model. Performance of the proposed method is illustrated in a simulation study.
Adaptive elastic net and Separate Selection from Least Squares for ultra-high dimensional regression models

This paper studies the asymptotic properties of the adaptive elastic net in ultra-high dimensional sparse linear regression models and proposes a new method called SSLS (Separate Selection from Least Squares) to improve prediction accuracy. Besides, we prove that SSLS has the superior performance both in the theoretical part and empirical part. In this paper, we prove that the probability of adaptive elastic net selecting wrong variables can decays at an exponential rate with very few conditions. Irrepresentable Condition or similar constraint isn't necessary in our proof. We derive accurate bounds of bias and mean squared error (MSE) which both depend on the choice of parameters, and also show that there exists a bias of asymptotic normality of the adaptive elastic net. Furthermore, simulations and empirical part both show that the prediction accuracy of the penalized least squares requires more improvement. Therefore, we propose SSLS to improve the prediction. It selects variable first, reducing high dimension to low dimension by using the adaptive elastic net in this paper. In the second step, the coefficients are constructed based on the OLS estimation. We show that the bias of SSLS can decays at an exponential rate. Also, MSE decays to zero. Finally, we prove that the variable selection consistency of SSLS implies the asymptotic normality of SSLS. Simulations given in this paper illustrate the performance of the SSLS, adaptive elastic net and other penalized least squares. The index tracking problem in stock market is studied in the empirical part with other methods.
High-dimensional Ising model selection with Bayesian information criteria

We consider the use of Bayesian information criteria for selection of the graph underlying an Ising model. In an Ising model, the full conditional distributions of each variable form logistic regression models, and variable selection techniques for regression allow one to identify the neighborhood of each node and, thus, the entire graph. We prove high-dimensional consistency results for this pseudo-likelihood approach to graph selection when using Bayesian information criteria for the variable selection problems in the logistic regressions. The results pertain to scenarios of sparsity and following related prior work the information criteria we consider incorporate an explicit prior that encourages sparsity.
Spawning Models for the CPHD Filter

In its classical form, the Cardinalized Probability Hypothesis Density (CPHD) filter does not model the appearance of new targets through spawning, yet there are applications for which spawning models more appropriately account for newborn objects when compared to spontaneous birth models. In this paper, we propose a principled derivation of the CPHD filter with spawning from the Finite Set Statistics framework. A Gaussian Mixture implementation of the CPHD filter with spawning is then presented, illustrated with three applicable spawning models on a simulated scenario involving two parent targets spawning a total of five objects. Results show that filter implementations with spawn models provide more accurate results when compared to a birth model implementation.
Testing the maximal rank of the volatility process for continuous diffusions observed with noise

In this paper, we present a test for the maximal rank of the volatility process in continuous diffusion models observed with noise. Such models are typically applied in mathematical finance, where latent price processes are corrupted by microstructure noise at ultra high frequencies. Using high frequency observations we construct a test statistic for the maximal rank of the time varying stochastic volatility process. Our methodology is based upon a combination of a matrix perturbation approach and pre-averaging. We will show the asymptotic mixed normality of the test statistic and obtain a consistent testing procedure.
Model Selection in Overlapping Stochastic Block Models

Networks are a commonly used mathematical model to describe the rich set of interactions between objects of interest. Many clustering methods have been developed in order to partition such structures, among which several rely on underlying probabilistic models, typically mixture models. The relevant hidden structure may however show overlapping groups in several applications. The Overlapping Stochastic Block Model (2011) has been developed to take this phenomenon into account. Nevertheless, the problem of the choice of the number of classes in the inference step is still open. To tackle this issue, we consider the proposed model in a Bayesian framework and develop a new criterion based on a non asymptotic approximation of the marginal log-likelihood. We describe how the criterion can be computed through a variational Bayes EM algorithm, and demonstrate its efficiency by running it on both simulated and real data.
Generalized Functional Additive Mixed Models

We propose a comprehensive framework for additive regression models for non-Gaussian functional responses, allowing for multiple (partially) nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data as well as linear and nonlinear effects of functional and scalar covariates that may vary smoothly over the index of the functional response. Our implementation handles functional responses from any exponential family distribution as well as many others like Beta- or scaled non-central $t$-distributions. Development is motivated by and evaluated on an application to large-scale longitudinal feeding records of pigs. Results in extensive simulation studies as well as replications of two previously published simulation studies for generalized functional mixed models demonstrate the good performance of our proposal. The approach is implemented in well-documented open source software in the "pffr()" function in R-package "refund".
Bayesian spatio-temporal epidemic models with applications to sheep pox

Epidemic data often possess certain characteristics, such as the presence of many zeros, the spatial nature of the disease spread mechanism or environmental noise. This paper addresses these issues via suitable Bayesian modelling. In doing so we utilise stochastic regression models appropriate for spatio-temporal count data with an excess number of zeros. The developed regression framework can incorporate serial correlation and time varying covariates through an Ornstein Uhlenbeck process formulation. In addition, we explore the effect of different priors, including default options and techniques based upon variations of mixtures of $g$-priors. The effect of different distance kernels for the epidemic model component is investigated. We proceed by developing branching process-based methods for testing scenarios for disease control, thus linking traditional spatio-temporal models with epidemic processes, useful in policy-focused decision making. The approach is illustrated with an application to a sheep pox dataset from the Evros region, Greece.
Signal extraction and breakpoint identification for array CGH data using robust state space model

Array comparative genomic hybridization(CGH) is a high resolution technique to assess DNA copy number variation. Identifying breakpoints where copy number changes will enhance the understanding of the pathogenesis of human diseases, such as cancers. However, the biological variation and experimental errors contained in array CGH data may lead to false positive identification of breakpoints. We propose a robust state space model for array CGH data analysis. The model consists of two equations: an observation equation and a state equation, in which both the measurement error and evolution error are specified to follow t-distributions with small degrees of freedom. The completely unspecified CGH profiles are estimated by a Markov Chain Monte Carlo(MCMC) algorithm. Breakpoints and outliers are identified by a novel backward selection procedure based on posterior draws of the CGH profiles. Compared to three other popular methods, our method demonstrates several desired features, including false positive rate control, robustness against outliers, and superior power of breakpoint detection. All these properties are illustrated using simulated and real datasets.
Asymptotics of Selective Inference

In this paper, we seek to establish asymptotic results for selective inference procedures removing the assumption of Gaussianity. The class of selection procedures we consider are determined by affine inequalities, which we refer to as affine selection procedures. Examples of affine selection procedures include selective inference along the solution path of the least absolute shrinkage and selection operator (LASSO), as well as selective inference after fitting the least absolute shrinkage and selection operator at a fixed value of the regularization parameter. We also consider some tests in penalized generalized linear models. Our result proves asymptotic convergence in the high‐dimensional setting where n