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At least 703 records · Page 39Linked to original sources
arXiv2021

The case for balanced hypothesis tests and equal-tailed confidence intervals

Introduction: there is an ongoing debate about directional inference of two-sided hypothesis tests for which some authors argue that rejecting $θ= θ_0$ does not allow to conclude that $θ> θ_0$ or $θ< θ_0$ but only that $θ\neq θ_0$, while others argue that this is a minor error without practical consequence. Discussion: new elements are brought to the debate. It is shown that the directional interpretation of some non-directional hypothesis tests about Receiver Operating Characteristic (ROC) and survival curves may lead to inflated type III error rates with a probability of concluding that a difference exists in the opposite side of the actual difference that can reach 50% in the worst case. Some of the issues of directional tests also apply to two-sided confidence intervals (CIs). It is shown that equal-tailed CIs should be preferred to shortest CIs. New assessment criteria of two-sided CIs and hypothesis tests are proposed to provide a reliable directional interpretation: partial left-sided and right-sided $α$ error rates for hypothesis tests, probabilities of overestimation and underestimation $α_L$ and $α_U$ and interval half-widths for two-sided CIs. Conclusion: two-sided CIs and two-sided tests are interpreted directionally. This implies that directional interpretation be taken in account in the development and evaluation of confidence intervals and tests.

stat.OT↗
arXiv2022

Conditions and Assumptions for Constraint-based Causal Structure Learning

We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that output graphs that are Markov equivalent to the causal graph. Under the faithfulness assumption, this natural family contains all exact structure-learning algorithms. We also provide a set of assumptions, under which any natural structure-learning algorithm outputs Markov equivalent graphs to the causal graph. These assumptions can be thought of as a relaxation of faithfulness, and most of them can be directly tested from (the underlying distribution) of the data, particularly when one focuses on structural causal models. We specialize the definitions and results for structural causal models.

math.ST↗
arXiv2021

Inference in the stochastic Cox-Ingersol-Ross diffusion process with continuous sampling: Computational aspects and simulation

In this paper, we consider a stochastic model based on the Cox- Ingersoll- Ross model (CIR). The stochastic model is parameterized analytically by applying Itô's calculus and the trend functions of the proposed process is calculated. The parameter estimators are then derived by means of two procedures: the first is used to estimate the parameters in the drift coefficient by the maximum likelihood (ML) method, based on continuous sampling, and the second procedure approximates the diffusion coefficient by two methods. Finally, a simulation of the process is presented. Thus, a typical simulated trajectory of the process and its estimators is obtained.

stat.ME↗
arXiv2021

Are Multilevel functional models the next step in sports biomechanics and wearable technology? A case study of Knee Biomechanics patterns in typical training sessions of recreational runners

This paper illustrates how multilevel functional models can detect and characterize biomechanical changes along different sport training sessions. Our analysis focuses on the relevant cases to identify differences in knee biomechanics in recreational runners during low and high-intensity exercise sessions with the same energy expenditure by recording $20$ steps. To do so, we review the existing literature of multilevel models, and then, we propose a new hypothesis test to look at the changes between different levels of the multilevel model as low and high-intensity training sessions. We also evaluate the reliability of measures recorded in three-dimension knee angles from the functional intra-class correlation coefficient (ICC) obtained from the decomposition performed with the multilevel funcional model taking into account $20$ measures recorded in each test. The results show that there are no statistically significant differences between the two modes of exercise. However, we have to be careful with the conclusions since, as we have shown, human gait-patterns are very individual and heterogeneous between groups of athletes, and other alternatives to the p-value may be more appropriate to detect statistical differences in biomechanical changes in this context.

stat.AP↗
arXiv2021

A Review of Containerization for Interactive and Reproducible Analysis

In recent decades the analysis of data has become increasingly computational. Correspondingly, this has changed how scientific and statistical work is shared. For example, it is now commonplace for underlying analysis code and data to be proffered alongside journal publications and conference talks. Unfortunately, sharing code faces several challenges. First, it is often difficult to take code from one computer and run it on another. Code configuration, version, and dependency issues often make this challenging. Secondly, even if the code runs, it is often hard to understand or interact with the analysis. This makes it difficult to assess the code and its findings, for example, in a peer review process. In this review we describe the combination of two computing technologies that help make analyses shareable, interactive, and completely reproducible. These technologies are (1) analysis containerization, which leverages virtualization to fully encapsulate analysis, data, code and dependencies into an interactive and shareable format, and (2) code notebooks, a literate programming format for interacting with analyses. The fusion of these two technologies offers significant advantages over using either individually. This review surveys how the combination enhances the accessibility and reproducibility of code, analyses, and ideas.

stat.OT↗
arXiv2021

Impact of climate change on West Nile virus distribution in South America

West Nile virus (WNV) is a vector-borne pathogen of global relevance and is currently the most widely distributed flavivirus of encephalitis worldwide. This virus infects birds, humans, horses, and other mammals, and its transmission cycle occurs in urban and rural areas. Climate conditions have direct and indirect impacts on vector abundance and virus dynamics within the mosquito. The significance of environmental variables as drivers in WNV epidemiology is increasing under the current climate change scenario. In this study, we used a machine learning algorithm to model WNV distributions in South America. Our model evaluated eight environmental variables (type of biome, annual temperature, seasonality of temperature, daytime temperature variation, thermal amplitude, seasonality of precipitation, annual rainfall, and elevation) for their contribution to the occurrence of WNV since its introduction in South America (2004). Our results showed that environmental variables can directly alter the occurrence of WNV, with lower precipitation and higher temperatures associated with increased virus incidence. High-risk areas may be modified in the coming years, becoming more evident with high greenhouse gas emission levels. Countries such as Bolivia and Paraguay will be greatly affected, drastically changing their current WNV distribution. Several Brazilian areas will also increase the likelihood of presenting WNV, mainly in the Northeast and Midwest regions and the Pantanal biome. The Galapagos Islands will also probably increase their geographic range suitable for WNV occurrence. It is necessary to develop preventive policies to minimize potential WNV infection in humans and enhance active epidemiological surveillance in birds, humans, and other mammals before it becomes a more significant public health problem in South America.

q-bio.PE↗
arXiv2021

Geodesic B-Score for Improved Assessment of Knee Osteoarthritis

Three-dimensional medical imaging enables detailed understanding of osteoarthritis structural status. However, there remains a vast need for automatic, thus, reader-independent measures that provide reliable assessment of subject-specific clinical outcomes. To this end, we derive a consistent generalization of the recently proposed B-score to Riemannian shape spaces. We further present an algorithmic treatment yielding simple, yet efficient computations allowing for analysis of large shape populations with several thousand samples. Our intrinsic formulation exhibits improved discrimination ability over its Euclidean counterpart, which we demonstrate for predictive validity on assessing risks of total knee replacement. This result highlights the potential of the geodesic B-score to enable improved personalized assessment and stratification for interventions.

cs.CV↗
arXiv2021

The general conformable fractional grey system model and its applications

Grey system theory is an important mathematical tool for describing uncertain information in the real world. It has been used to solve the uncertainty problems specially caused by lack of information. As a novel theory, the theory can deal with various fields and plays an important role in modeling the small sample problems. But many modeling mechanisms of grey system need to be answered, such as why grey accumulation can be successfully applied to grey prediction model? What is the key role of grey accumulation? Some scholars have already given answers to a certain extent. In this paper, we explain the role from the perspective of complex networks. Further, we propose generalized conformable accumulation and difference, and clarify its physical meaning in the grey model. We use our newly proposed fractional accumulation and difference to our generalized conformable fractional grey model, or GCFGM(1,1), and employ practical cases to verify that GCFGM(1,1) has higher accuracy compared to traditional models.

stat.OT↗
arXiv2022

Distributional data analysis of accelerometer data from the NHANES database using nonparametric survey regression models

Accelerometers enable an objective measurement of physical activity levels among groups of individuals in free-living environments, providing high-resolution detail about physical activity changes at different time scales. Current approaches used in the literature for analyzing such data typically employ summary measures such as total inactivity time or compositional metrics. However, at the conceptual level, these methods have the potential disadvantage of discarding important information from recorded data when calculating these summaries and metrics since these typically depend on cut-offs related to exercise intensity zones chosen subjectively or even arbitrarily. Furthermore, much of the data collected in these studies follow complex survey designs. Then, using specific estimation strategies adapted to a particular sampling mechanism is mandatory. The aim of this paper is two-fold. First, a new functional representation of a distributional nature accelerometer data is introduced to build a complete individualized profile of each subject's physical activity levels. Second, we extend two nonparametric functional regression models, kernel smoothing and kernel ridge regression, to handle survey data and obtain reliable conclusions about the influence of physical activity in the different analyses performed in the complex sampling design NHANES cohort and so, show representation advantages.

stat.ME↗
arXiv2021

Deepest Voting: a new way of electing

This article aims to present a unified framework for grading-based voting processes. The idea is to represent the grades of each voter on d candidates as a point in R^d and to define the winner of the vote using the deepest point of the scatter plot. The deepest point is obtained by the maximization of a depth function. Universality, unanimity, and neutrality properties are proved to be satisfied. Monotonicity and Independence to Irrelevant Alternatives are also studied. It is shown that usual voting processes correspond to specific choices of depth functions. Finally, some basic paradoxes are explored for these voting processes.

stat.OT↗
arXiv2021

Interpreting the outcomes of research assessments: a geometrical approach

Research evaluations and comparison of the assessments of academic institutions (scientific areas, departments, universities etc.) are among the major issues in recent years in higher education systems. One method, followed by some national evaluation agencies, is to assess the research quality by the evaluation of a limited number of publications in a way that each publication is rated among $n$ classes. This method produces, for each institution, a distribution of the publications in the $n$ classes. In this paper we introduce a natural geometric way to compare these assessments by introducing an ad hoc distance from the performance of an institution to the best possible achievable assessment. Moreover, to avoid the methodological error of comparing non-homogeneous institutions, we introduce a {\em geometric score} based on such a distance. The latter represents the probability that an ideal institution, with the same configuration as the one under evaluation, performs worst. We apply our method, based on the geometric score, to rank, in two specific scientific areas, the Italian universities using the results of the evaluation exercise VQR 2011-2014.

cs.DL↗
arXiv2021

Bisecting for selecting: using a Laplacian eigenmaps clustering approach to create the new European football Super League

We use European football performance data to select teams to form the proposed European football Super League, using only unsupervised techniques. We first used random forest regression to select important variables predicting goal difference, which we used to calculate the Euclidian distances between teams. Creating a Laplacian eigenmap, we bisected the Fielder vector to identify the five major European football leagues' natural clusters. Our results showed how an unsupervised approach could successfully identify four clusters based on five basic performance metrics: shots, shots on target, shots conceded, possession, and pass success. The top two clusters identify those teams who dominate their respective leagues and are the best candidates to create the most competitive elite super league.

stat.AP↗
arXiv2026

Transitional Conditional Independence

Statistical models contain variables that are not random: parameters, treatments, environments, design points. Ordinary conditional independence cannot express relations involving such variables. To apply it one must first put a distribution on them, and that changes the meaning of the statement. This paper introduces transitional conditional independence. It relates three variables on a Markov kernel $K(W|T)$ with non-stochastic input $T$, and is defined by a single factorization: \[ X\perp\!\!\perp_{K(W|T)} Y |Z \quad :\iff \quad \exists\, Q(X|Z):\; K(X,Y,Z|T) = Q(X|Z)\otimes K(Y,Z|T).\] The relation asserts a Markov kernel $Q(X|Z)$ that is the same for every input $t$. It therefore yields a factorization rather than an almost-sure identity between conditional expectations, and it needs no distribution on the input space. The relation is asymmetric. We show that the asymmetry is essential: symmetrizing it destroys the statements it was built to make. We prove left and right versions of all separoid rules except Symmetry. Ten of them hold on arbitrary measurable spaces, the remaining ones under one condition on the spaces involved, and we give criteria for when Symmetry itself holds. We axiomatize the resulting structure and show that it arises from any symmetric separoid by a shift. We give several applications. Ancillarity, sufficiency and adequacy become factorizations that hold pointwise in the parameter, without a prior and without null sets; the theorems of Fisher--Neyman and of Basu take this form. The invariance hypothesis of invariant prediction, $Y \perp\!\!\perp E | X_S$, receives its intended meaning: one kernel predicts $Y$ from $X_S$ in every environment $E$. And Bayesian networks with non-stochastic input nodes satisfy a directed global Markov property whose graphical id-separation criterion returns a factorization of Markov kernels, on arbitrary input spaces.

math.ST↗
arXiv2021

Contraction of a quasi-Bayesian model with shrinkage priors in precision matrix estimation

Currently several Bayesian approaches are available to estimate large sparse precision matrices, including Bayesian graphical Lasso (Wang, 2012), Bayesian structure learning (Banerjee and Ghosal, 2015), and graphical horseshoe (Li et al., 2019). Although these methods have exhibited nice empirical performances, in general they are computationally expensive. Moreover, we have limited knowledge about the theoretical properties, e.g., posterior contraction rate, of graphical Bayesian Lasso and graphical horseshoe. In this paper, we propose a new method that integrates some commonly used continuous shrinkage priors into a quasi-Bayesian framework featured by a pseudo-likelihood. Under mild conditions, we establish an optimal posterior contraction rate for the proposed method. Compared to existing approaches, our method has two main advantages. First, our method is computationally more efficient while achieving similar error rate; second, our framework is more amenable to theoretical analysis. Extensive simulation experiments and the analysis on a real data set are supportive of our theoretical results.

stat.ME↗
arXiv2021

Changepoint detection in random coefficient autoregressive models

We propose a family of CUSUM-based statistics to detect the presence of changepoints in the deterministic part of the autoregressive parameter in a Random Coefficient AutoRegressive (RCA) sequence. In order to ensure the ability to detect breaks at sample endpoints, we thoroughly study weighted CUSUM statistics, analysing the asymptotics for virtually all possible weighing schemes, including the standardised CUSUM process (for which we derive a Darling-Erdos theorem) and even heavier weights (studying the so-called Rényi statistics). Our results are valid irrespective of whether the sequence is stationary or not, and no prior knowledge of stationarity or lack thereof is required. Technically, our results require strong approximations which, in the nonstationary case, are entirely new. Similarly, we allow for heteroskedasticity of unknown form in both the error term and in the stochastic part of the autoregressive coefficient, proposing a family of test statistics which are robust to heteroskedasticity, without requiring any prior knowledge as to the presence or type thereof. Simulations show that our procedures work very well in finite samples. We complement our theory with applications to financial, economic and epidemiological time series.

math.ST↗