Miracle-dz/UniFAR-FTUs huggingface dataset:
On wavelet to select the parametric form of a regression model

Abstract We consider the problem of estimating the relationship between a response variable and a set of explanatory variates. We suppose a set of parametric forms as candidates for the aforementioned regression. Wavelet regression is used as auxiliary for the choice of the most appropriate parametric form of the model, particularly for the cases of nonlinear and generalized linear models. The use of a wavelet method for the choice of the most appropriate parametric relationship is interesting in practice for four main reasons. The first is that it provides a statistically sound method to choose the ’best’ parametric model for a data set, given that no pre-determined regression form nor probability distribution are assumed to be known. On the other hand, the parametric models are easier to interpret and more convenient for prediction purposes than non-parametric ones. Moreover, since wavelet methods possess a natural data-driven shrinkage paradigm, we can ascertain that overfitting is not expected. For instance, the results show that few non-null coefficients remain after thresholding. Finally, fast wavelet methods are widely available which makes this a feasible procedure for researchers as well as data analysts. We evaluate the performance of the proposed wavelet procedure based on the correct classification rates of the underlying parametric form on a range of candidate models, taking into account a wide range of scenarios. The method is also illustrated by real data analyses. Computer codes are available as supplementary material.
Adaptive Tuning Of Hamiltonian Monte Carlo Within Sequential Monte Carlo

Sequential Monte Carlo (SMC) samplers form an attractive alternative to MCMC for Bayesian computation. However, their performance depends strongly on the Markov kernels used to re- juvenate particles. We discuss how to calibrate automatically (using the current particles) Hamiltonian Monte Carlo kernels within SMC. To do so, we build upon the adaptive SMC ap- proach of Fearnhead and Taylor (2013), and we also suggest alternative methods. We illustrate the advantages of using HMC kernels within an SMC sampler via an extensive numerical study.
A General Framework for Vecchia Approximations of Gaussian Processes

Gaussian processes (GPs) are commonly used as models for functions, time series, and spatial fields, but they are computationally infeasible for large datasets. Focusing on the typical setting of modeling data as a GP plus an additive noise term, we propose a generalization of the Vecchia (1988) approach as a framework for GP approximations. We show that our general Vecchia approach contains many popular existing GP approximations as special cases, allowing for comparisons among the different methods within a unified framework. Representing the models by directed acyclic graphs, we determine the sparsity of the matrices necessary for inference, which leads to new insights regarding the computational properties. Based on these results, we propose a novel sparse general Vecchia approximation, which ensures computational feasibility for large spatial datasets but can lead to considerable improvements in approximation accuracy over Vecchia's original approach. We provide several theoretical results and conduct numerical comparisons. We conclude with guidelines for the use of Vecchia approximations in spatial statistics.
On Optimal Allocation of Treatment/Condition Variance in Principal Component Analysis

The allocation of a (treatment) condition-effect on the wrong principal component (misallocation of variance) in principal component analysis (PCA) has been addressed in research on event-related potentials of the electroencephalogram. However, the correct allocation of condition-effects on PCA components might be relevant in several domains of research. The present paper investigates whether different loading patterns at each condition-level are a basis for an optimal allocation of between-condition variance on principal components. It turns out that a similar loading shape at each condition-level is a necessary condition for an optimal allocation of between-condition variance, whereas a similar loading magnitude is not necessary.
A survey of blockchain frameworks and applications

The applications of the blockchain technology are still being discovered. When a new potential disruptive technology emerges, there is a tendency to try to solve every problem with that technology. However, it is still necessary to determine what approach is the best for each type of application. To find how distributed ledgers solve existing problems, this study looks for blockchain frameworks in the academic world. Identifying the existing frameworks can demonstrate where the interest in the technology exists and where it can be missing. This study encountered several blockchain frameworks in development. However, there are few references to operational needs, testing, and deploy of the technology. With the widespread use of the technology, either integrating with pre-existing solutions, replacing legacy systems, or new implementations, the need for testing, deploying, exploration, and maintenance is expected to intensify.
Asymptotic of Approximate Least Squares Estimators of Parameters Two-Dimensional Chirp Signal.

In this paper, we address the problem of parameter estimation of a 2-D chirp model under the assumption that the errors are stationary. We extend the 2-D periodogram method for the sinusoidal model, to find initial values to use in any iterative procedure to compute the least squares estimators (LSEs) of the unknown parameters, to the 2-D chirp model. Next we propose an estimator, known as the approximate least squares estimator (ALSE), that is obtained by maximising a periodogram-type function and is observed to be asymptotically equivalent to the LSE. Moreover the asymptotic properties of these estimators are obtained under slightly mild conditions than those required for the LSEs. For the multiple component 2-D chirp model, we propose a sequential method of estimation of the ALSEs, that significantly reduces the computational difficulty involved in reckoning the LSEs and the ALSEs. We perform some simulation studies to see how the proposed method works and a data set has been analysed for illustrative purposes.
Fundamental limits of detection in the spiked Wigner model

We study the fundamental limits of detecting the presence of an additive rank-one perturbation, or spike, to a Wigner matrix. When the spike comes from a prior that is i.i. d. across coordinates, we prove that the log-likelihood ratio of the spiked model against the non-spiked one is asymptotically normal below a certain reconstruction threshold which is not necessarily of a "spectral" nature, and that it is degenerate above. This establishes the maximal region of contiguity between the planted and null models. It is known that this threshold also marks a phase transition for estimating the spike: the latter task is possible above the threshold and impossible below. Therefore, both estimation and detection undergo the same transition in this random matrix model. We also provide further information about the performance of the optimal test. Our proofs are based on Gaussian interpolation methods and a rigorous incarnation of the cavity method, as devised by Guerra and Talagrand in their study of the Sherrington--Kirkpatrick spin-glass model.
Randomized Predictive P-values: A Versatile Model Diagnostic Tool with Unified Reference Distribution

Examining residuals such as Pearson and deviance residuals, is a standard tool for assessing normal regression. However, for discrete response, these residuals cluster on lines corresponding to distinct response values. Their distributions are far from normality; graphical and quantitative inspection of these residuals provides little information for model diagnosis. Marshall and Spiegelhalter (2003) defined a cross-validatory predictive p-value for identifying outliers. Predictive p-values are uniformly distributed for continuous response but not for discrete response. We propose to use randomized predictive p-values (RPP) for diagnosing models with discrete responses. RPPs can be transformed to "residuals" with normal distribution, called NRPPs by us. NRPPs can be used to diagnose all regression models with scalar response using the same way for diagnosing normal regression. The NRPPs are nearly the same as the randomized quantile residuals (RQR), which are previously proposed by Dunn and Smyth (1996) but remain little known by statisticians. This paper provides an exposition of RQR using the RPP perspective. The contributions of this exposition include: (1) we give a rigorous proof of uniformity of RPP and illustrative examples to explain the uniformity under the true model; (2) we conduct extensive simulation studies to demonstrate the normality of NRPPs under the true model; (3) our simulation studies also show that the NRPP method is a versatile diagnostic tool for detecting many kinds of model inadequacies due to lack of complexity. The effectiveness of NRPP is further demonstrated with a health utilization dataset.
An Explicit Mean-Covariance Parameterization for Multivariate Response Linear Regression

Abstract We develop a new method to fit the multivariate response linear regression model that exploits a parametric link between the regression coefficient matrix and the error covariance matrix. Specifically, we assume that the correlations between entries in the multivariate error random vector are proportional to the cosines of the angles between their corresponding regression coefficient matrix columns, so as the angle between two regression coefficient matrix columns decreases, the correlation between the corresponding errors increases. We highlight two models under which this parameterization arises: a latent variable reduced-rank regression model and the errors-in-variables regression model. We propose a novel nonconvex weighted residual sum of squares criterion which exploits this parameterization and admits a new class of penalized estimators. The optimization is solved with an accelerated proximal gradient descent algorithm. Our method is used to study the association between microRNA expression and cancer drug activity measured on the NCI-60 cell lines. An R package implementing our method, MCMVR, is available online.
The M33 Synoptic Stellar Survey. II. Mira Variables

We present the discovery of 1847 Mira candidates in the Local Group galaxy M33 using a novel semi-parametric periodogram technique coupled with a random forest classifier. The algorithms were applied to ∼2.4 × 105 I-band light curves previously obtained by the M33 Synoptic Stellar Survey. We derive preliminary period–luminosity relations at optical, near-infrared, and mid-infrared wavelengths and compare them to the corresponding relations in the Large Magellanic Cloud.
Predictive Inference Based on Markov Chain Monte Carlo Output

In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate probabilistic forecasts from such simulation output. Based on proper scoring rules, we develop a notion of consistency that allows to assess the adequacy of methods for estimating the stationary distribution underlying the simulation output. We then provide asymptotic results that account for the salient features of Bayesian posterior simulators and derive conditions under which choices from the literature satisfy our notion of consistency. Importantly, these conditions depend on the scoring rule being used, such that the choices of approximation method and scoring rule are intertwined. While the logarithmic rule requires fairly stringent conditions, the continuous ranked probability score yields consistent approximations under minimal assumptions. These results are illustrated in a simulation study and an economic data example. Overall, mixture‐of‐parameters approximations that exploit the parametric structure of Bayesian models perform particularly well. Under the continuous ranked probability score, the empirical distribution function is a simple and appealing alternative option.
An Interactive Greedy Approach to Group Sparsity in High Dimensions

Abstract Sparsity learning with known grouping structure has received considerable attention due to wide modern applications in high-dimensional data analysis. Although advantages of using group information have been well-studied by shrinkage-based approaches, benefits of group sparsity have not been well-documented for greedy-type methods, which much limits our understanding and use of this important class of methods. In this paper, generalizing from a popular forward-backward greedy approach, we propose a new interactive greedy algorithm for group sparsity learning and prove that the proposed greedy-type algorithm attains the desired benefits of group sparsity under high dimensional settings. An estimation error bound refining other existing methods and a guarantee for group support recovery are also established simultaneously. In addition, we incorporate a general M-estimation framework and introduce an interactive feature to allow extra algorithm flexibility without compromise in theoretical properties. The promising use of our proposal is demonstrated through numerical evaluations including a real industrial application in human activity recognition at home. Supplementary materials for this article are available online.
Bivariate Exponentiated Generalized Linear Exponential Distribution with Applications in Reliability Analysis

The aim of this paper, is to define a bivariate exponentiated generalized linear exponential distribution based on Marshall-Olkin shock model. Statistical and reliability properties of this distribution are discussed. This includes quantiles, moments, stress-strength reliability, joint reliability function, joint reversed (hazard) rates functions and joint mean waiting time function. Moreover, the hazard rate, the availability and the mean residual lifetime functions for a parallel system, are established. One data set is analyzed, and it is observed that, the proposed distribution provides a better fit than Marshall-Olkin bivariate exponential, bivariate generalized exponential and bivariate generalized linear failure rate distributions. Simulation studies are presented to estimate both the relative absolute bias, and the relative mean square error for the distribution parameters based on complete data.
Reducing training time by efficient localized kernel regression

We study generalization properties of kernel regularized least squares regression based on a partitioning approach. We show that optimal rates of convergence are preserved if the number of local sets grows sufficiently slowly with the sample size. Moreover, the partitioning approach can be efficiently combined with local Nyström subsampling, improving computational cost twofold.
Auxiliary Variables for Multi-Dirichlet Priors

Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over Dirichlet parameters complicate the joint distribution of model parameters. This paper shows a novel auxiliary variable scheme which helps to simplify the inference for models involving hierarchical MDs and MDPs. Using this scheme, it is easy to derive fully collapsed inference schemes which allow for an efficient inference.
Economic variable selection

Regression plays a central role in the discipline of statistics and is the primary analytic technique in many research areas. Variable selection is a classical and major problem for regression. This article emphasizes the economic aspect of variable selection. The problem is formulated in terms of the cost of predictors to be purchased for future use: only the subset of covariates used in the model will need to be purchased. This leads to a decision‐theoretic formulation of the variable selection problems, which includes the cost of predictors as well as their effect. We adopt a Bayesian perspective and propose two approaches to address uncertainty about the model and model parameters. These approaches, termed the restricted and extended approaches, lead us to rethink model averaging. From an objective or robust Bayes point of view, the former is preferred. The proposed method is applied to three popular datasets for illustration.
Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap

To identify the estimand in missing data problems and observational studies, it is common to base the statistical estimation on the ‘missingness at random’ and ‘no unmeasured confounder’ assumptions. However, these assumptions are unverifiable by using empirical data and pose serious threats to the validity of the qualitative conclusions of statistical inference. A sensitivity analysis asks how the conclusions may change if the unverifiable assumptions are violated to a certain degree. We consider a marginal sensitivity model which is a natural extension of Rosenbaum's sensitivity model that is widely used for matched observational studies. We aim to construct confidence intervals based on inverse probability weighting estimators, such that asymptotically the intervals have at least nominal coverage of the estimand whenever the data‐generating distribution is in the collection of marginal sensitivity models. We use a percentile bootstrap and a generalized minimax–maximin inequality to transform this intractable problem into a linear fractional programming problem, which can be solved very efficiently. We illustrate our method by using a real data set to estimate the causal effect of fish consumption on blood mercury level.
Inference after black box selection.

We consider the problem of inference for parameters selected to report only after some algorithm, the canonical example being inference for model parameters after a model selection procedure. The conditional correction for selection requires knowledge of how the selection is affected by changes in the underlying data, and current research explicitly describes this selection. In this work, we assume 1) we have in silico access to the selection algorithm and 2) for parameters of interest, the data input into the algorithm satisfies (pre-selection) a central limit theorem jointly with an estimator of our parameter of interest. Under these assumptions, we recast the problem into a statistical learning problem which can be fit with off-the-shelf models for binary regression. The feature points in this problem are set by the user, opening up the possibility of active learning methods for computationally expensive selection algorithms. We consider two examples previously out of reach of this conditional approach: stability selection and multiple cross-validation.
Note on the geodesic Monte Carlo

Geodesic Monte Carlo (gMC) is a powerful algorithm for Bayesian inference on non-Euclidean manifolds. The original gMC algorithm was cleverly derived in terms of its progenitor, the Riemannian manifold Hamiltonian Monte Carlo (RMHMC). Here, it is shown that alternative and theoretically simpler derivations are available in which the original algorithm is a special case of two general classes of algorithms characterized by non-trivial mass matrices. The proposed derivations work entirely in embedding coordinates and thus clarify the original algorithm as applied to manifolds embedded in Euclidean space.
Estimation of large block covariance matrices: Application to the analysis of gene expression data

Motivated by an application in molecular biology, we propose a novel, efficient and fully data-driven approach for estimating large block structured sparse covariance matrices in the case where the number of variables is much larger than the number of samples without limiting ourselves to block diagonal matrices. Our approach consists in approximating such a covariance matrix by the sum of a low-rank sparse matrix and a diagonal matrix. Our methodology can also deal with matrices for which the block structure only appears if the columns and rows are permuted according to an unknown permutation. Our technique is implemented in the R package \texttt{BlockCov} which is available from the Comprehensive R Archive Network and from GitHub. In order to illustrate the statistical and numerical performance of our package some numerical experiments are provided as well as a thorough comparison with alternative methods. Finally, our approach is applied to gene expression data in order to better understand the toxicity of acetaminophen on the liver of rats.
Possible unitarity of black hole evaporation.

In the framework of finite-dimensional Fock space models, for a fixed given mean number of particles \bar{n}_{k}, blackbody-like or another, it is shown that there are, in the space S of all pure states, a multi-dimensional subspace s_{\bar{n}_{k}} of initial pure states and a corresponding multi-dimensional subspace S_{\bar{n}_{k}} of final pure states yielding \bar{n}_{k}, which are mutually related by a unitary transformation. In consequence it follows that the blackbody form of the Hawking spectrum does not contradict unitarity of black hole evaporation.
Estimating the distribution and thinning parameters of a homogeneous multimode Poisson process

In this paper we propose estimators of the distribution of events of different kinds in a multimode Poisson process. We give the explicit solution for the maximum likelihood estimator, and derive its strong consistency and asymptotic normality. We also provide an order restricted estimator and derive its consistency and asymptotic distribution. We discuss the application of the estimator to the detection of neutrons in a novel detector being developed at the European Spallation Source in Lund, Sweden. The inference problem gives rise to Sylvester-Ramanujan system of equations.
The origin of stellar populations in the Galactic bulge from chemical abundances

In this work, we study the formation and chemical evolution of the Galactic bulge with particular focus on the abundance pattern ([Mg/Fe] versus [Fe/H]), metallicity, and age distribution functions. We consider detailed chemical evolution models for the Galactic bulge and inner disc, with the aim of shedding light on the connection between these components and the origin of bulge stars. In particular, we first present a model assuming a fast and intense star formation, with the majority of bulge stars forming on a time-scale less than 1 Gyr. Then we analyse the possibility of two distinct stellar populations in the bulge, as suggested by Gaia-ESO and APOGEE data. These two populations, one metal poor and the other metal rich, can have had two different origins: (i) the metal rich formed after a stop of ∼250 Myr in the star formation rate of the bulge or (ii) the metal-rich population is made of stars formed in the inner disc and brought into the bulge by the early secular evolution of the bar. We also examine the case of multiple starbursts in the bulge with consequent formation of multiple populations, as suggested by studies of microlensed stars. After comparing model results and observations, we suggest that the most likely scenario is that there are two main stellar populations, both made mainly by old stars (>10 Gyr), with the metal-rich and younger one formed from inner thin disc stars, in agreement with kinematical arguments. However, on the basis of dynamical simulations, we cannot completely exclude that the second population formed after a stop in the star formation during the bulge evolution, so that all the stars formed in situ.