Statistics

We analyze the results of the German Team Handball Bundesliga for ten seasons in a model-free statistical time series approach. We will show that the home advantage is nearly negligible compared to the total sum of goals. Specific interest has been spent on the time evolution of the team fitness expressed in terms of the goal difference. In contrast to soccer, our results indicate a decay of the team fitness values over a season while the long time correlation behavior over years is nearly comparable. We are able to explain the dominance of a few teams by the large value for the total number of goals in a match. A method for the prediction of match winners is presented in good accuracy with the real results. We analyze the properties of promoted teams and indicate drastic level changes between the Bundesliga and the second league. Our findings reflect in good agreement recent discussions on modern successful attack strategies.

Sensitivity analysis is an important concept to analyze the influences of parameters in a system, an equation or a collection of data. The methods used for sensitivity analysis are divided into deterministic and statistical techniques. Generally, deterministic techniques analyze fixed points of a model whilst stochastic techniques analyze a range of values. Deterministic methods fail in analyze the entire range of input values and stochastic methods generate outcomes with random errors. In this manuscript, we are interested in stochastic methods, mainly in variance-based techniques such as Variance and Sobol indices, since this class of techniques is largely used on literature. The objective of this manuscript is to present an analytical solution for variance based sensitive analysis. As a result of this research, two small programs were developed in Javascript named as AVaN Pack (Analysis of Variance through Numerical solution). These programs allow users to find the contribution of each individual parameter in any function by means of a mathematical solution, instead of sampling-based ones.

Statistical analysis is often used to evaluate the evidence for or against scientific hypotheses, and various statistics (e.g., p-values, likelihood ratios, Bayes factors) are interpreted as measures of evidence strength. Here I consider evidence measurement from the point of view of representational measurement theory, and argue that familiar evidence statistics do not conform to any legitimate measurement scale type. I then consider the notion of an absolute scale for evidence measurement, in a sense to be defined, focusing particularly on the notion of absolute 0 evidence, which turns out to be something other than what one might have expected.

In this paper, we explore how we should aggregate the degrees of belief of of a group of agents to give a single coherent set of degrees of belief, when at least some of those agents might be probabilistically incoherent. There are a number of way of aggregating degrees of belief, and there are a number of ways of fixing incoherent degrees of belief. When we have picked one of each, should we aggregate first and then fix, or fix first and then aggregate? Or should we try to do both at once? And when do these different procedures agree with one another? In this paper, we focus particularly on the final question.

In the context of industrial engineering, cold-standby redundancies allocation strategy is usually adopted to improve the reliability of coherent systems. This paper investigates optimal allocation strategies of cold standbys for series and parallel systems comprised of dependent components with left/right tail weakly stochastic arrangement increasing lifetimes. For the case of heterogeneous and independent matched cold standbys, it is proved that better redundancies should be put in the nodes having weaker [better] components for series [parallel] systems. For the case of homogeneous and independent cold standbys, it is shown that more redundancies should be put in standby with weaker [better] components to enhance the reliability of series [parallel] systems. The results developed here generalize and extend those corresponding ones in the literature to the case of series and parallel systems with dependent components. Numerical examples are also presented to provide guidance for the practical use of our theoretical findings.

In this paper we give an outline on the Bayesian Decision Theory.

We describe how we both use and extend the PrarieLearn framework by taking advantage of its built-in support for external auto-graders. By using a custom Docker container, we can match our course requirements perfectly. Moreover, by relying on the flexibility of the interface we can customize our Docker container. A specific extension for unit testing is described which creates context-dependent difference between student answers and reference solution providing a more comprehensive response at test time.

Surrogates in lieu of expensive-to-evaluate performance functions can accelerate the reliability analysis greatly. This paper proposes a new two-stage framework for surrogate-aided reliability analysis named Surrogates for Importance Sampling (S4IS). In the first stage, a coarse surrogate is built to gain the information about failure regions; the second stage zooms into the important regions and improves the accuracy of the failure probability estimator by adaptively selecting support points therein. The learning functions are proposed to guide the selection of support points such that the exploration and exploitation can be dynamically balanced. As a generic framework, S4IS has the potential to incorporate different types of surrogates (Gaussian Processes, Support Vector Machines, Neural Network, etc.). The effectiveness and efficiency of S4IS is validated by five illustrative examples, which involve system reliability, highly nonlinear limit-state function, small failure probability and moderately high dimensionality. The implementation of S4IS is made available to download at this https URL.

A concrete, stylized example illustrates that inferences may be degraded, rather than improved, by incorporating supplementary data via a joint likelihood. In the example, the likelihood is assumed to be correctly specified, as is the prior over the parameter of interest; all that is necessary for the joint modeling approach to suffer is misspecification of the prior over a nuisance parameter.

The realistic modeling intended to quantify precisely some biological mechanisms is a task requiering a lot of a priori knowledge and generally leading to heavy mathematical models. On the other hand, the structure of the classical Machine Learning algorithms, such as Neural Networks, limits their flexibility and the possibility to take into account the existence of complex underlying phenomena, such as delay, saturation and accumulation. The aim of this paper is to reach a compromise between precision, parsimony and flexibility to design an efficient biomimetic predictive tool extracting knowledge from livestock data. To achieve this, we build a Mathematical Model based on Partial Differential Equations (PDE) embarking the mathematical expression of biological determinants. We made the hypothesis that all the physico-chemical phenomena occurring in animal body can be summarized by the evolution of a global information. Therefore the developed PDE system describes the evolution and the action of an information circulating in an Avatar of the Real Animal. This Avatar outlines the dynamics of the biological reactions of animal body in the framework of a specific problem. Each PDE contains parameters corresponding to biological-like factors which can be learnt from data by the developed Statistical Learning Tool.