Miracle-dz/UniFAR-FTUs huggingface dataset:
A Bayesian hierarchical model for comparative evaluation of teaching quality indicators in higher education

The problem motivating the paper is the quantification of students' preferences regarding teaching/coursework quality, under certain numerical restrictions, in order to build a model for identifying, assessing and monitoring the major components of the overall teaching quality. We propose a Bayesian hierarchical beta regression model, with a Dirichlet prior on the model coefficients. The coefficients of the model can then be interpreted as weights and thus they measure the relative importance that students give to the different attributes. This approach not only allows for the incorporation of informative prior when it is available but also provides user-friendly interfaces and direct probability interpretations for all quantities. Furthermore, it is a natural way to implement the usual constraints for the model coefficients. This model is applied to data collected in 2009 and 2013 from undergraduate students in the Panteion University, Athens, Greece and besides the construction of an instrument for the assessment and monitoring of teaching quality, it gave some input for a preliminary discussion on the association of the differences in students' preferences between the two time-periods with the current Greek socioeconomic transformation. Results from the proposed approach are compared with the ones obtained by two alternative statistical techniques.
A Framework for Monte Carlo based Multiple Testing

We are concerned with a situation in which we would like to test multiple hypotheses with tests whose p‐values cannot be computed explicitly but can be approximated using Monte Carlo simulation. This scenario occurs widely in practice. We are interested in obtaining the same rejections and non‐rejections as the ones obtained if the p‐values for all hypotheses had been available. The present article introduces a framework for this scenario by providing a generic algorithm for a general multiple testing procedure. We establish conditions that guarantee that the rejections and non‐rejections obtained through Monte Carlo simulations are identical to the ones obtained with the p‐values. Our framework is applicable to a general class of step‐up and step‐down procedures, which includes many established multiple testing corrections such as the ones of Bonferroni, Holm, Sidak, Hochberg or Benjamini–Hochberg. Moreover, we show how to use our framework to improve algorithms available in the literature in such a way as to yield theoretical guarantees on their results. These modifications can easily be implemented in practice and lead to a particular way of reporting multiple testing results as three sets together with an error bound on their correctness, demonstrated exemplarily using a real biological dataset.
Estimation of Causal Invertible VARMA Models

We present a re-parameterization of vector autoregressive moving average (VARMA) models that allows estimation of parameters under the constraints of causality and invertibility. The parameter constraints associated with a causal invertible VARMA model are highly complex. Currently there are no procedures that can maintain the constraints in the estimated VARMA process, except in the special case of a vector autoregression (VAR), where some moment based causal estimators are available. Even in the VAR case, the available likelihood based estimators are not causal. The maximum likelihood estimator based on the full likelihood that does not condition on the initial observations by definition satisfies the causal invertible constraints but optimization of the likelihood under the complex constraints is an intractable problem. The commonly used Bayesian procedure for VAR often has posterior mass outside the causal set because the priors are not constrained to the causal set of parameters. We provide an exact mathematical solution to this problem. An $m$-variate VARMA$(p, q)$ process contains $(p+ q) m^2 + \binom{m+1}{2}$ parameters, which must be constrained to a subset of Euclidean space in order to guarantee causality and invertibility. This space is implicitly described in this paper, through the device of parameterizing the entire space of block Toeplitz matrices in terms of positive definite matrices and orthogonal matrices. The parameterization has connection to Schur- stability of polynomials and the associated Stein transformation that are often used in dynamical systems literature. As an important by-product of our investigation, we generalize a classical result in dynamical systems to provide a characterization of Schur stable matrix polynomials.
Population counts along elliptical habitat contours: hierarchical modelling using Poisson-lognormal mixtures with nonstationary spatial structure

Ecologists often interpret variation in the spatial distribution of populations in terms of responses to environmental features, but disentangling the effects of individual variables can be difficult if latent effects and spatial and temporal correlations are not accounted for properly. Here, we use hierarchical models based on a Poisson log-normal mixture to understand the spatial variation in relative abundance (counts per standardized unit of effort) of yellow perch, Perca flavescens, the most abundant fish species in Lake Saint Pierre, Quebec, Canada. The mixture incorporates spatially varying environmental covariates that represent local habitat characteristics, and random temporal and spatial effects that capture the effects of unobserved ecological processes. The sampling design covers the margins but not the central region of the lake. We fit spatial generalized linear mixed models based on three different prior covariance structures for the local latent effects: a single Gaussian process (GP) over the lake, a GP over a circle, and independent GP for each shore. The models allow for independence, isotropy, or nonstationary spatial effects. Nonstationarity is dealt with using two different approaches, geometric anisotropy, and the inclusion of covariates in the correlation structure of the latent spatial process. The proposed approaches for specification of spatial domain and choice of Gaussian process priors may prove useful in other applications that involve spatial correlation along an irregular contour or in discontinous spatial domains.
Rates of contraction for posterior distributions in Lr-metrics, 1 ≤ r ≤ ∞

The frequentist behavior of nonparametric Bayes estimates, more specifically, rates of contraction of the posterior distributions to shrinking $L^r$-norm neighborhoods, $1\le r\le\infty$, of the unknown parameter, are studied. A theorem for nonparametric density estimation is proved under general approximation-theoretic assumptions on the prior. The result is applied to a variety of common examples, including Gaussian process, wavelet series, normal mixture and histogram priors. The rates of contraction are minimax-optimal for $1\le r\le2$, but deteriorate as $r$ increases beyond 2. In the case of Gaussian nonparametric regression a Gaussian prior is devised for which the posterior contracts at the optimal rate in all $L^r$-norms, $1\le r\le\infty$.
The P\'olya sum kernel and Bayes estimation

We consider a particular Cox process from a Bayesian viewpoint and show that the Bayes estimator of the intensity measure is the so-called P\'olya sum kernel, which occurred recently in the context of the construction of the so-called Papangelou processes. More precisely, if the prior, the directing measure of the Cox process, is a Poisson-Gamma random measure, then the posterior is again a Poisson-Gamma random measure and the Bayes estimator of the intensity is the P\'olya sum kernel. Moreover, we extend this result to doubly stochastic Poisson-Gamma priors and give conditions under which one can identify the Bayes estimator for the intensity.
Accuracy of empirical projections of high-dimensional Gaussian matrices

Let $X=C+\mathrm{E}$ with a deterministic matrix $C\in\R^{M\times M}$ and $\mathrm{E}$ some centered Gaussian $M\times M$-matrix whose entries are independent with variance $\sigma^2$. In the present work, the accuracy of reduced-rank projections of $X$ is studied. Non-asymptotic universal upper and lower bounds are derived, and favorable and unfavorable prototypes of matrices $C$ in terms of the accuracy of approximation are characterized. The approach does not involve analytic perturbation theory of linear operators and allows for multiplicities in the singular value spectrum. Our main result is some general non-asymptotic upper bound on the accuracy of approximation which involves explicitly the singular values of $C$, and which is shown to be sharp in various regimes of $C$. The results are accompanied by lower bounds under diverse assumptions. Consequences on statistical estimation problems, in particular in the recent area of low-rank matrix recovery, are discussed.
Simulation based sequential Monte Carlo methods for discretely observed Markov processes

Parameter estimation for discretely observed Markov processes is a challenging problem. However, simulation of Markov processes is straightforward using the Gillespie algorithm. We exploit this ease of simulation to develop an effective sequential Monte Carlo (SMC) algorithm for obtaining samples from the posterior distribution of the parameters. In particular, we introduce two key innovations, coupled simulations, which allow us to study multiple parameter values on the basis of a single simulation, and a simple, yet effective, importance sampling scheme for steering simulations towards the observed data. These innovations substantially improve the efficiency of the SMC algorithm with minimal effect on the speed of the simulation process. The SMC algorithm is successfully applied to two examples, a Lotka-Volterra model and a Repressilator model.
The inverse Lindley distribution: a stress-strength reliability model with application to head and neck cancer data

In this article, we proposed one parameter, inverse Lindley distribution, with its fundamental properties such as quantiles, mode, stochastic ordering, entropy, and stress–strength reliability. The proposed distribution has upside-down bathtub shape for its failure rate function. The estimation of stress–strength reliability has been approached by both classical and Bayesian methods. Under Bayesian set-up, both non-informative (Jeffrey) and informative (gamma) priors are considered under symmetric (squared error) and asymmetric (entropy) loss functions. The Lindley’s approximation method is used for Bayesian computation. The performances of the estimators have been compared in terms of their mean squared errors using simulated samples. Two real data-sets, representing the survival times of head and neck cancer patients, are considered for demonstrating the applicability of the proposed model.
High-dimensional genome-wide association study and misspecified mixed model analysis

We study behavior of the restricted maximum likelihood (REML) estimator under a misspecified linear mixed model (LMM) that has received much attention in recent gnome-wide association studies. The asymptotic analysis establishes consistency of the REML estimator of the variance of the errors in the LMM, and convergence in probability of the REML estimator of the variance of the random effects in the LMM to a certain limit, which is equal to the true variance of the random effects multiplied by the limiting proportion of the nonzero random effects present in the LMM. The aymptotic results also establish convergence rate (in probability) of the REML estimators as well as a result regarding convergence of the asymptotic conditional variance of the REML estimator. The asymptotic results are fully supported by the results of empirical studies, which include extensive simulation studies that compare the performance of the REML estimator (under the misspecified LMM) with other existing methods.
Sparse and Low-Rank Covariance Matrices Estimation

This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and nuclear norm to favor the low-rank property. For the proposed estimator, we then prove that with large probability, the Frobenious norm of the estimation rate can be of order $O(\sqrt{s(\log{r})/n})$ under a mild case, where $s$ and $r$ denote the number of sparse entries and the rank of the population covariance respectively, $n$ notes the sample capacity. Finally an efficient alternating direction method of multipliers with global convergence is proposed to tackle this problem, and meantime merits of the approach are also illustrated by practicing numerical simulations.
High-Dimensional Inference: Confidence Intervals, $p$-Values and R-Software hdi

We present a (selective) review of recent frequentist highdimensional inference methods for constructing p-values and confidence intervals in linear and generalized linear models. We include a broad, comparative empirical study which complements the viewpoint from statistical methodology and theory. Furthermore, we introduce and illustrate the Rpackage hdi which easily allows the use of different methods and supports reproducibility.
Multi-colour random fields with polygonal realisations

We introduce a class of random fields that can be understood as discrete versions of multi-colour polygonal fields built on regular linear tessellations. We focus fir st on consistent polygonal fields, for which we show Markovianity and solvability by means of a dynamic representation. This representation forms the basis for new sampling techniques for Gibbsian modifications of such fields, a class which cove rs lattice based random fields. A flux based modification is applied to the extracti on of the field tracks network from a SAR image of a rural area.
Comment on "Bayesian astrostatistics: a backward look to the future" by Tom Loredo, arXiv:1208.3036

This short note points out two of the incongruences that I find in the Loredo (2012) comments on Andreon (2012), i.e. on my chapter written for the book "Astrostatistical Challenges for the New Astronomy". First, I find illogic the Loredo decision of putting my chapter among those presenting simple models, because one of the models illustrated in my chapter is qualified by him as "impressing for his complexity". Second, Loredo criticizes my chapter at one location confusing it with another paper by another author, because my chapter do not touch the subject mentioned by Loredo (2012) critics, the comparison between Bayesian and frequentist fitting models.
Density Level Sets: Asymptotics, Inference, and Visualization

ABSTRACT We study the plug-in estimator for density level sets under Hausdorff loss. We derive asymptotic theory for this estimator, and based on this theory, we develop two bootstrap confidence regions for level sets. We introduce a new technique for visualizing density level sets, even in multidimensions, which is easy to interpret and efficient to compute. Supplementary materials for this article are available online.
The Final Solutions of Monty Hall Problem and Three Prisoners Problem

Recently we proposed the linguistic interpretation of quantum mechanics (called quantum and classical measurement theory, or quantum language), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy). And we believe that this quantum language is the most powerful language to describe science. The purpose of this paper is to describe the Monty-Hall problem and the three prisoners problem in quantum language. We of course believe that our proposal is the final solutions of the two problems. Thus in this paper, we can answer the question: "Why have philosophers continued to stick to these problems? " And the readers will find that these problems are never elementary, and they can not be solved without the deep understanding of "probability" and "dualism". KEY WORDS: Philosophy of probability, Fisher Maximum Likelihood Method, Bayes' Method,The Principle of Equal (a priori) Probabilities
Jointly Sparse Global SIMPLS Regression

Partial least squares (PLS) regression combines dimensionality reduction and prediction using a latent variable model. Since partial least squares regression (PLS-R) does not require matrix inversion or diagonalization, it can be applied to problems with large numbers of variables. As predictor dimension increases, variable selection becomes essential to avoid over-fitting, to provide more accurate predictors and to yield more interpretable parameters. We propose a global variable selection approach that penalizes the total number of variables across all PLS components. Put another way, the proposed global penalty encourages the selected variables to be shared among the PLS components. We formulate PLS-R with joint sparsity as a variational optimization problem with objective function equal to a novel global SIMPLS criterion plus a mixed norm sparsity penalty on the weight matrix. The mixed norm sparsity penalty is the $\ell_1$ norm of the $\ell_2$ norm on the weights corresponding to the same variable used over all the PLS components. A novel augmented Lagrangian method is proposed to solve the optimization problem and soft thresholding for sparsity occurs naturally as part of the iterative solution. Experiments show that the modified PLS-R attains better or as good performance with many fewer selected predictor variables.
Path Following and Empirical Bayes Model Selection for Sparse Regression

In recent years, a rich variety of regularization procedures have been proposed for high dimensional regression problems. However, tuning parameter choice and computational efficiency in ultra-high dimensional problems remain vexing issues. The routine use of $\ell_1$ regularization is largely attributable to the computational efficiency of the LARS algorithm, but similar efficiency for better behaved penalties has remained elusive. In this article, we propose a highly efficient path following procedure for combination of any convex loss function and a broad class of penalties. From a Bayesian perspective, this algorithm rapidly yields maximum a posteriori estimates at different hyper-parameter values. To bypass the inefficiency and potential instability of cross validation, we propose an empirical Bayes procedure for rapidly choosing the optimal model and corresponding hyper-parameter value. This approach applies to any penalty that corresponds to a proper prior distribution on the regression coefficients. While we mainly focus on sparse estimation of generalized linear models, the method extends to more general regularizations such as polynomial trend filtering after reparameterization. The proposed algorithm scales efficiently to large $p$ and/or $n$. Solution paths of 10,000 dimensional examples are computed within one minute on a laptop for various generalized linear models (GLM). Operating characteristics are assessed through simulation studies and the methods are applied to several real data sets.
Generalised matricvariate $T$-distribution

Assuming Kotz-Riesz type I and II distributions and their corresponding independent Riesz distributions the associated generalised matricvariate T distributions, termed matricvariate T-Riesz distributions for real normed division algebras are obtained with respect to the Lebesgue measure. In addition some of their properties are also studied.
Probabilistic Network Metrics: Variational Bayesian Network Centrality

Network metrics form a fundamental part of the network analysis toolbox. Used to quantitatively measure different aspects of the network, these metrics can give insights into the underlying network structure and function. In this work, we connect network metrics to modern probabilistic machine learning. We focus on the centrality metric, which is used a wide variety of applications from web search to gene-analysis. First, we formulate an eigenvector-based Bayesian centrality model for determining node importance. Compared to existing methods, our probabilistic model allows for the assimilation of multiple edge weight observations, the inclusion of priors and the extraction of uncertainties. To enable tractable inference, we develop a variational lower bound (VBC) that is demonstrated to be effective on a variety of networks (two synthetic and five real-world graphs). We then bridge this model to sparse Gaussian processes. The sparse variational Bayesian centrality Gaussian process (VBC-GP) learns a mapping between node attributes to latent centrality and hence, is capable of predicting centralities from node features and can potentially represent a large number of nodes using only a limited number of inducing inputs. Experiments show that the VBC-GP learns high-quality mappings and compares favorably to a two-step baseline, i.e., a full GP trained on the node attributes and pre-computed centralities. Finally, we present two case-studies using the VBC-GP: first, to ascertain relevant features in a taxi transport network and second, to distribute a limited number of vaccines to mitigate the severity of a viral outbreak.
Equivalence of Kernel Machine Regression and Kernel Distance Covariance for Multidimensional Trait Association Studies

Associating genetic markers with a multidimensional phenotype is an important yet challenging problem. In this work, we establish the equivalence between two popular methods: kernel-machine regression (KMR), and kernel distance covariance (KDC). KMR is a semiparametric regression frameworks that models the covariate effects parametrically, while the genetic markers are considered non-parametrically. KDC represents a class of methods that includes distance covariance (DC) and Hilbert-Schmidt Independence Criterion (HSIC), which are nonparametric tests of independence. We show the equivalence between the score test of KMR and the KDC statistic under certain conditions. This result leads to a novel generalization of the KDC test that incorporates the covariates. Our contributions are three-fold: (1) establishing the equivalence between KMR and KDC; (2) showing that the principles of kernel machine regression can be applied to the interpretation of KDC; (3) the development of a broader class of KDC statistics, that the members are the quantities of different kernels. We demonstrate the proposals using simulation studies. Data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) is used to explore the association between the genetic variants on gene \emph{FLJ16124} and phenotypes represented in 3D structural brain MR images adjusting for age and gender. The results suggest that SNPs of \emph{FLJ16124} exhibit strong pairwise interaction effects that are correlated to the changes of brain region volumes.