Miracle-dz/UniFAR-FTUs huggingface dataset:
Around the goal: examining the effect of the first goal on the second goal in soccer using survival analysis methods

Abstract In this paper we apply survival techniques to soccer data, treating a goal scoring as the event of interest. It specifically concerns the relationship between the time of the first goal in the game and the time of the second goal. In order to do so, the relevant survival analysis concepts are readjusted to fit the problem and a Cox model is developed for the hazard function. Time dependent covariates and a frailty term are also considered. We also use a reliable propensity score to summarize the pre-game covariates. The conclusions derived from the results are that a first goal occurrence could either expedite or impede the next goal scoring, depending on the time it was scored. Moreover, once a goal is scored, another goal scoring becomes more and more likely as the game progresses. Furthermore, the first goal effect is the same whether the goal was scored or conceded.
Qualitative robustness of statistical functionals under strong mixing

A new concept of (asymptotic) qualitative robustness for plug-in estimators based on identically distributed possibly dependent observations is introduced, and it is shown that Hampel’s theorem for general metrics d still holds. Since Hampel’s theorem assumes the UGC property w.r. t. d, i.e. convergence in probability of the empirical probability measure to the true marginal distribution w.r. t. d uniformly in the class of all admissible laws on the sample path space, this property is shown for a large class of strongly mixing laws for three different metrics d. For realvalued observations the UGC property is established for both the Kolomogorov φ-metric and the Lévy ψ-metric, and for observations in a general locally compact and second countable Hausdorff space the UGC property is established for a certain metric generating the ψ-weak topology. The key is a new uniform weak LLN for strongly mixing random variables. The latter is of independent interest and relies on Rio’s maximal inequality.
A Remark on the Assumptions of Bayes' Theorem

We formulate simple equivalent conditions for the validity of Bayes' formula for conditional densities. We show that for any random variables X and Y (with values in arbitrary measurable spaces), the following are equivalent: 1. X and Y have a joint density w.r. t. a product measure \mu x \nu, 2. P_{X,Y} << P_X x P_Y, (here P_{.} denotes the distribution of {.}) 3. X has a conditional density p(x | y) w.r. t. a sigma-finite measure \mu, 4. X has a conditional distribution P_{X|Y} such that P_{X|y} << P_X for all y, 5. X has a conditional distribution P_{X|Y} and a marginal density p(x) w.r. t. a measure \mu such that P_{X|y} << \mu for all y. Furthermore, given random variables X and Y with a conditional density p(y | x) w.r. t. \nu and a marginal density p(x) w.r. t. \mu, we show that Bayes' formula p(x | y) = p(y | x)p(x) / \int p(y | x)p(x)d\mu(x) yields a conditional density p(x | y) w.r. t. \mu if and only if X and Y satisfy the above conditions. Counterexamples illustrating the nontriviality of the results are given, and implications for sequential adaptive estimation are considered.
Properties and numerical evaluation of the Rosenblatt distribution

This paper studies various distributional properties of the Rosenblatt distribution. We begin by describing a technique for computing the cumulants. We then study the expansion of the Rosenblatt distribution in terms of shifted chi-squared distributions. We derive the coefficients of this expansion and use these to obtain the L\'{e}vy-Khintchine formula and derive asymptotic properties of the L\'{e}vy measure. This allows us to compute the cumulants, moments, coefficients in the chi-square expansion and the density and cumulative distribution functions of the Rosenblatt distribution with a high degree of precision. Tables are provided and software written to implement the methods described here is freely available by request from the authors.
Information Geometry and Sequential Monte Carlo

This paper explores the application of methods from information geometry to the sequential Monte Carlo (SMC) sampler. In particular the Riemannian manifold Metropolis-adjusted Langevin algorithm (mMALA) is adapted for the transition kernels in SMC. Similar to its function in Markov chain Monte Carlo methods, the mMALA is a fully adaptable kernel which allows for efficient sampling of high-dimensional and highly correlated parameter spaces. We set up the theoretical framework for its use in SMC with a focus on the application to the problem of sequential Bayesian inference for dynamical systems as modelled by sets of ordinary differential equations. In addition, we argue that defining the sequence of distributions on geodesics optimises the effective sample sizes in the SMC run. We illustrate the application of the methodology by inferring the parameters of simulated Lotka-Volterra and Fitzhugh-Nagumo models. In particular we demonstrate that compared to employing a standard adaptive random walk kernel, the SMC sampler with an information geometric kernel design attains a higher level of statistical robustness in the inferred parameters of the dynamical systems.
Identification of Finite Dimensional L\'evy Systems in Financial Mathematics

L\'evy processes are widely used in financial mathematics to model return data. Price processes are then defined as a corresponding geometric L\'evy process, implying the fact that returns are independent. In this paper we propose an alternative class of models allowing to describe dependence between return data. Technically such an alternative model class is obtained by considering finite dimensional linear stochastic SISO systems driven by a L\'evy process. In this paper we consider a discrete-time version of this model, focusing on the problem of identifying the dynamics and the noise characteristics of such a so-called L\'evy system. The special feature of this problem is that the characteristic function (c.f.) of the driving noise is explicitly known, possibly up to a few unknown parameters. We develop and analyze a variety of novel identification methods by adapting the so-called empirical characteristic function method (ECF) originally devised for estimating parameters of c.f. -s from i.i. d. samples. Precise characterization of the errors of these estimators will be given, and their asymptotic covariance matrices will be obtained. Their potential to outperform the prediction error method in estimating the system parameters will also be demonstrated.
Projection-based nonparametric goodness-of-fit testing with functional covariates

This paper studies the problem of nonparametric testing for the effect of a random functional covariate on a real-valued error term. The covariate takes values in L 2 [0,1], the Hilbert space of the square-integrable real-valued functions on the unit interval. The error term could be directly observed as a response or estimated from a functional parametric model, like for instance the functional linear regression. Our test is based on the remark that checking the no-effect of the functional covariate is equivalent to checking the nullity of the conditional expectation of the error term given a sufficiently rich set of projections of the covariate.Such projections could be on elements of norm 1 from finite-dimension subspaces of L 2 [0,1]. Next, the idea is to search a finite-dimension element of norm 1 that is, in some sense, the least favorable for the null hypothesis. Finally, it remains to perform a nonparametric check of the nullity of the conditional expectation of the error term given the scalar product between the covariate and the selected least favorable direction. For such finite-dimension search and nonparametric check we use a kernel-based approach. As a result, our test statistic is a quadratic form based on univariate kernel smoothing and the asymptotic critical values are given by the standard normal law. The test is able to detect nonparametric alternatives, including the polynomial ones. The error term could present heteroscedasticity of unknown form. We do no require the law of the covariate X to be known. The test could be implemented quite easily and performs well in simulations and real data applications. We illustrate the performance of our test for checking the functional linear regression model.
Adaptive estimation of the density matrix in quantum homodyne tomography with noisy data

In the framework of noisy quantum homodyne tomography with efficiency parameter 1/2 < η ⩽ 1, we propose a novel estimator of a quantum state whose density matrix elements ρm, n decrease like Ce−B(m+n)r/2? >, for fixed C ⩾ 1, B > 0 and 0 < r ⩽ 2. In contrast to previous works, we focus on the case where r, C and B are unknown. The procedure estimates the matrix coefficients by a projection method on the pattern functions, and then by soft-thresholding the estimated coefficients. We prove that under the L2? >-loss our procedure is adaptive rate-optimal, in the sense that it achieves the same rate of convergence as the best possible procedure relying on the knowledge of (r, B, C). Finite sample behaviour of our adaptive procedure is explored through numerical experiments.
Uncertainty Quantification in Complex Simulation Models Using Ensemble Copula Coupling

Critical decisions frequently rely on high-dimensional output from complex computer simulation models that show intricate cross-variable, spatial and temporal dependence structures, with weather and climate predictions being key examples. There is a strongly increasing recognition of the need for uncertainty quantification in such settings, for which we propose and review a general multi-stage procedure called ensemble copula coupling (ECC), proceeding as follows: 1. Generate a raw ensemble, consisting of multiple runs of the computer model that differ in the inputs or model parameters in suitable ways. 2. Apply statistical postprocessing techniques, such as Bayesian model averaging or nonhomogeneous regression, to correct for systematic errors in the raw ensemble, to obtain calibrated and sharp predictive distributions for each univariate output variable individually. 3. Draw a sample from each postprocessed predictive distribution. 4. Rearrange the sampled values in the rank order structure of the raw ensemble to obtain the ECC postprocessed ensemble. The use of ensembles and statistical postprocessing have become routine in weather forecasting over the past decade. We show that seemingly unrelated, recent advances can be interpreted, fused and consolidated within the framework of ECC, the common thread being the adoption of the empirical copula of the raw ensemble. Depending on the use of Quantiles, Random draws or Transformations at the sampling stage, we distinguish the ECC-Q, ECC-R and ECC-T variants, respectively. We also describe relations to the Schaake shuffle and extant copula-based techniques. In a case study, the ECC approach is applied to predictions of temperature, pressure, precipitation and wind over Germany, based on the 50-member European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble.
Discussion: Latent variable graphical model selection via convex optimization

Since recently, there have been an increasing interest in the problem of estimating a high-dimensional matrix K that can be decomposed in a sum of a sparse matrix S (i.e., a matrix having only a small number of nonzero entries) and a low rank matrix L . This is motivated by applications in computer vision, video segmentation, computational biology, semantic indexing etc. The main contribution and novelty of Chandrasekaran, Parrilo and Willsky paper (CPW in what follows) is to propose and study a method of inference about such decomposable matrices for a particular setting where K is the precision (concentration) matrix of a partially observed sparse Gaussian graphical model (GGM). In this case, K is the inverse of the covariance matrix of a Gaussian vector XO extracted from a larger Gaussian vector (XO,XH) with sparse inverse covariance matrix. Then it is easy to see that K can be represented as a sum of a sparse precision matrix S corresponding to the observed variables XO and a matrix L with rank at most h, where h is the dimension of the latent variables XH. If h is small, which is a typical situation in practice, then L has low rank. The GGM with latent variables is of major interest for applications in biology or in social networks where one often does not observe all the variables relevant for depicting sparsely the conditional dependencies. Note that formally this is just one possible motivation and mathematically the problem is dealt with in more generality, namely, postulating that the precision matrix satisfies
Kernel density estimation via diffusion and the complex exponentials approximation problem

A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when the complex exponentials approximation problem is considered in Gaussian noise. Several moments problems can be formulated in this framework and the estimation of the condensed density above is the main critical step for their solution. It is shown that the condensed density satisfies approximately a diffusion equation, which allows to estimate an optimal bandwidth. It is proved by simulation that good results can be obtained even when the signal-to-noise ratio is so small that other methods fail.
Composite likelihood estimation of sparse Gaussian graphical models with symmetry

In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be computational intensive. The composite likelihood offers an alternative formulation of the objective function and yields consistent estimators. When a sparse model is considered, the penalized composite likelihood estimation can yield estimates satisfying both the symmetry and sparsity constraints and possess ORACLE property. Application of the proposed method is demonstrated through simulation studies and a network analysis of a biological data set.
Distributions on symmetric cones II: Beta-Riesz distribution

This article derives several properties of the Riesz distributions, such as their corresponding Bartlett decompositions, the inverse Riesz distributions and the distribution of the generalised variance for real normed division algebras. In addition, introduce a kind of generalised beta distribution termed beta-Riesz distribution for real normed division algebras. Two versions of this distributions are proposed and some properties are studied.
Conjugate distributions in hierarchical Bayesian ANOVA for computational efficiency and assessments of both practical and statistical significance

Assessing variability according to distinct factors in data is a fundamental technique of statistics. The method commonly regarded to as analysis of variance (ANOVA) is, however, typically confined to the case where all levels of a factor are present in the data (i.e. the population of factor levels has been exhausted). Random and mixed effects models are used for more elaborate cases, but require distinct nomenclature, concepts and theory, as well as distinct inferential procedures. Following a hierarchical Bayesian approach, a comprehensive ANOVA framework is shown, which unifies the above statistical models, emphasizes practical rather than statistical significance, addresses issues of parameter identifiability for random effects, and provides straightforward computational procedures for inferential steps. Although this is done in a rigorous manner the contents herein can be seen as ideological in supporting a shift in the approach taken towards analysis of variance.
Marginals of multivariate Gibbs distributions with applications in Bayesian species sampling

Gibbs partition models are the largest class of infinite exchangeable partitions of the positive integers generalizing the product form of the probability function of the two-parameter Poisson-Dirichlet family. Recently those models have been investigated in a Bayesian nonparametric approach to species sampling problems as alternatives to the Dirichlet and the Pitman-Yor process priors. Here we derive marginals of conditional and unconditional multivariate distributions arising from exchangeable Gibbs partitions to obtain explicit formulas for joint falling factorial moments of corresponding conditional and unconditional Gibbs sampling formulas. Our proofs rely on a known result on factorial moments of sum of non independent indicators. We provide an application to a Bayesian nonparametric estimation of the predictive probability to observe a species already observed a certain number of times.
On Dependence Structure of Copula-based Markov chains

We consider dependence coefficients for stationary Markov chains. We emphasize on some equivalencies for reversible Markov chains. We improve some known results and provide a necessary condition for Markov chains based on Archimedean copulas to be exponential $\rho$-mixing. We analyze the example of the Mardia and Frechet copula families using small sets.
CONSTRUCTION OF A CALIBRATED PROBABILISTIC CLASSIFICATION CATALOG: APPLICATION TO 50k VARIABLE SOURCES IN THE ALL-SKY AUTOMATED SURVEY

With growing data volumes from synoptic surveys, astronomers necessarily must become more abstracted from the discovery and introspection processes. Given the scarcity of follow-up resources, there is a particularly sharp onus on the frameworks that replace these human roles to provide accurate and well-calibrated probabilistic classification catalogs. Such catalogs inform the subsequent follow-up, allowing consumers to optimize the selection of specific sources for further study and permitting rigorous treatment of classification purities and efficiencies for population studies. Here, we describe a process to produce a probabilistic classification catalog of variability with machine learning from a multi-epoch photometric survey. In addition to producing accurate classifications, we show how to estimate calibrated class probabilities and motivate the importance of probability calibration. We also introduce a methodology for feature-based anomaly detection, which allows discovery of objects in the survey that do not fit within the predefined class taxonomy. Finally, we apply these methods to sources observed by the All-Sky Automated Survey (ASAS), and release the Machine-learned ASAS Classification Catalog (MACC), a 28 class probabilistic classification catalog of 50,124 ASAS sources in the ASAS Catalog of Variable Stars. We estimate that MACC achieves a sub-20% classification error rate and demonstrate that the class posterior probabilities are reasonably calibrated. MACC classifications compare favorably to the classifications of several previous domain-specific ASAS papers and to the ASAS Catalog of Variable Stars, which had classified only 24% of those sources into one of 12 science classes.
Spatially adaptive post‐processing of ensemble forecasts for temperature

We propose a statistical post‐processing method that yields locally calibrated probabilistic forecasts of temperature, based on the output of an ensemble prediction system. It represents the mean of the predictive distributions as a sum of short‐term averages of local temperatures and ensemble prediction system driven terms. For the spatial interpolation of temperature averages and local forecast uncertainty parameters we use an intrinsic Gaussian random‐field model with a location‐dependent nugget effect that accounts for small‐scale variability. Applied to the COSMO‐DE ensemble, our method yields locally calibrated and sharp probabilistic forecasts and compares favourably with other approaches.
Nonconcave Penalized Spline

Regression spline is a useful tool in nonparametric regression. However, finding the optimal knot locations is a known difficult problem. In this article, we introduce the Non-concave Penalized Regression Spline. This proposal method not only produces smoothing spline with optimal convergence rate, but also can adaptively select optimal knots simultaneously. It is insensitive to the number of origin knots. The method's performance in a simulation has been studied to compare the other methods. The problem of how to choose smoothing parameters, i.e. penalty parameters in the non-concave regression spline is addressed.
A SARIMAX coupled modelling applied to individual load curves intraday forecasting

A dynamic coupled modelling is investigated to take temperature into account in the individual energy consumption forecasting. The objective is both to avoid the inherent complexity of exhaustive SARIMAX models and to take advantage of the usual linear relation between energy consumption and temperature for thermosensitive customers. We first recall some issues related to individual load curves forecasting. Then, we propose and study the properties of a dynamic coupled modelling taking temperature into account as an exogenous contribution and its application to the intraday prediction of energy consumption. Finally, these theoretical results are illustrated on a real individual load curve. The authors discuss the relevance of such an approach and anticipate that it could form a substantial alternative to the commonly used methods for energy consumption forecasting of individual customers.
Dirichlet Posterior Sampling with Truncated Multinomial Likelihoods

We consider the problem of drawing samples from posterior distributions formed under a Dirichlet prior and a truncated multinomial likelihood, by which we mean a Multinomial likelihood function where we condition on one or more counts being zero a priori. Sampling this posterior distribution is of interest in inference algorithms for hierarchical Bayesian models based on the Dirichlet distribution or the Dirichlet process, particularly Gibbs sampling algorithms for the Hierarchical Dirichlet Process Hidden Semi-Markov Model. We provide a data augmentation sampling algorithm that is easy to implement, fast both to mix and to execute, and easily scalable to many dimensions. We demonstrate the algorithm's advantages over a generic Metropolis-Hastings sampling algorithm in several numerical experiments.
A sufficient criterion for control of generalised error rates in multiple testing

Based on the work of Romano and Shaikh (2006a,b); Lehmann and Romano (2005) we give a sufficient criterion for controlling generalised error rates for arbitrarily dependent p-values. This criterion is formulated in terms of matrices associated with the corresponding error rates and thus it is possible to view the corresponding critical constants as solutions of sets of certain linear inequalities. This property can in some cases be used to improve the power of existing procedures by finding optimal solutions to an associated linear programming problem.