Are You Normal? The Problem of Confounded Residual Structures in Hierarchical Linear Models

We encounter hierarchical data structures in a wide range of applications. Regular linear models are extended by random effects to address correlation between observations in the same group. Inference for random effects is sensitive to distributional misspecifications of the model, making checks for (distributional) assumptions particularly important. The investigation of residual structures is complicated by the presence of different levels and corresponding dependencies. Ignoring these dependencies leads to erroneous conclusions using our familiar tools, such as Q–Q plots or normal tests. We first show the extent of the problem, then we introduce the fraction of confounding as a measure of the level of confounding in a model and finally introduce rotated random effects as a solution to assessing distributional model assumptions. This article has supplementary materials online.     

Dealing with external actions in belief causal networks

Graphical models are efficient and simple ways to represent dependencies between variables. We introduce in this paper the so-called belief causal networks where dependencies are uncertain causal links and where the uncertainty is represented by belief masses. Through these networks, we propose to represent the results of passively observing the spontaneous behavior of the system and also evaluate the effects of external actions. Interventions are very useful for representing causal relations, we propose to compute their effects using a generalization of the “do” operator. Even if the belief chain rule is different from the Bayesian chain rule, we show that the joint distributions of the altered structures to graphically describe interventions are equivalent. This paper also addresses new issues that are arisen when handling interventions: we argue that in real world applications, external manipulations may be imprecise and show that they have a natural encoding under the belief function framework.     

Non-deterministic ideal operators: An adequate tool for formalization in Data Bases

In this paper, we propose the application of formal methods to Software Engineering. The most used data model is the relational model and we present, within the general framework of lattice theory, this analysis of functional dependencies. For this reason, we characterize the concept of f-family by means of a new concept which we call non-deterministic ideal operator (nd.ideal-o). The study of nd.ideal-o.s allows us to obtain results about functional dependencies as trivial particularizations, to clarify the semantics of the functional dependencies and to progress in their efficient use, and to extend the concept of schema. Moreover, the algebraic characterization of the concept of Key of a schema allows us to propose new formal definitions in the lattice framework for classical normal forms in relation schemata. We give a formal definition of the normal forms for functional dependencies more frequently used in the bibliography: the second normal form (2FN), the third normal form(3FN) and Boyce-Codd's normal form (FNBC).     

Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso

The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that data are drawn identically from a generating distribution. Introducing sparsity and sparse-difference inducing priors, we relax these assumptions and propose a novel regularized M-estimator to jointly estimate both the graph and changepoint structure. The resulting estimator possesses the ability to therefore favor sparse dependency structures and/or smoothly evolving graph structures, as required. Moreover, our approach extends current methods to allow estimation of changepoints that are grouped across multiple dependencies in a system. An efficient algorithm for estimating structure is proposed. We study the empirical recovery properties in a synthetic setting. The qualitative effect of grouped changepoint estimation is then demonstrated by applying the method on a genetic time-course dataset. Supplementary material for this article is available online.     

Modeling Dependencies in Operational Risk with Hybrid Bayesian Networks

This paper addresses the problem of quantifying and modeling financial institutions’ operational risk in accordance with the Advanced Measurement Approach put forth in the Basel II Accord. We argue that standard approaches focusing on modeling stochastic dependencies are not sufficient to adequately assess operational risk. In addition to stochastic dependencies, causal topological dependencies between the risk classes are typically encountered. These dependencies arise when risk units have common information- and/or work-flows and when failure of upstream processes imply risk for downstream processes. In this paper, we present a modeling strategy that explicitly captures both topological and stochastic dependencies between risk classes. We represent the operational-risk taxonomy in the framework of a hybrid Bayesian network (BN) and provide an intuitively compelling approach for handling causal relationships and external influences. We demonstrate the use of hybrid BNs as a tool for mapping causal dependencies between frequencies and severities of risk events and for modeling common shocks. Monte-Carlo simulations illustrate that the impact of topological dependencies on triggering overall system breakdowns can be substantial.     

Modelling of extreme wave heights and periods through copulas

Optimal design of coastal or offshore structures requires the estimation of extreme quantiles of oceanographic data such as wave heights and wave periods. Since there are strong correlations between oceanographic variables, it is necessary to use multivariate models in order to capture its dependencies. To achieve this, an approach based on copulas is proposed and is compared to a model based on the physical behaviour of waves.     

Multimaterial Lattice Structures With Thermally Programmable Mechanical Behaviors北大核心CSCD

传统的点阵结构一旦制备完成,其力学性能通常在使用寿命内保持不变。设计和制造具有环境适应特性的智能点阵结构,可编程地感知和响应外界变化(例如光强、压强、溶液、温度、电磁场、电化学激励),并在时间和空间上进行形状重构、模式转换和性能调控,仍然是人造材料研究领域重要的科学挑战。该文采用具有不同玻璃化转变温度和温度依赖性的多种聚合物材料,通过合理设计材料空间分布,提出了一类具有热可编程力学响应能力的多材料点阵结构。结合理论分析和有限元模拟,研究了组分材料相对刚度对多材料点阵结构的Poisson比、变形模式以及结构稳定性的影响。通过温度变化实现了对多材料点阵结构弹性常数、压溃响应和结构稳定性的调控,使多材料点阵结构表现出极大的热变形、超弹性和形状记忆效应。为设计和制造自适应保护装备、生物医学设备、航空航天领域的变形结构、柔性电子设备、自组装结构和可变形软体机器人等开辟了新途径。     

A new analytical approximation for European puts with stochastic volatility

In this paper, we apply singular perturbation techniques to price European puts with a stochastic volatility model, and derive a simple and elegant analytical formula as an approximation for the value of European put options. In contrast to the existing Heston’s semi-analytical formula, this approximation has the following unique feature: the latter only involves the standard normal distribution function, which is as fast and easy to implement as the Black–Scholes formula; whereas the former requires the evaluation of a logarithm with a complex argument during the involved Fourier inverse transform, which may sometimes result in numerical instability. Various numerical experiments suggest that our new formula can achieve a high order of accuracy for a large class of option derivatives with relatively short tenor.     

Automated prover for attribute dependencies in data with grades

We present a new axiomatization of logic for dependencies in data with grades, which includes ordinal data and data over domains with similarity relations, and an efficient reasoning method that is based on the axiomatization. The logic has its ordinary-style completeness characterizing the ordinary, bivalent entailment as well as the graded-style completeness characterizing the general, possibly intermediate degrees of entailment. A core of the method is a new inference rule, called the rule of simplification, from which we derive convenient equivalences that allow us to simplify sets of dependencies while retaining semantic closure. The method makes it possible to compute a closure of a given collection of attributes with respect to a collection of dependencies, decide whether a given dependency is entailed by a given collection of dependencies, and more generally, compute the degree to which the dependency is entailed by a collection of dependencies. We also present an experimental evaluation of the presented method.     

Inferring null join dependencies in relational databases

The inference problem for data dependencies in relational databases is the problem of deciding whether a set of data dependencies logically implies another data dependency. For join dependencies (JDs), the inference problem has been extensively studied by utilising the well-known chase procedure. We generalise JDs to null join dependencies (NJDs) that hold in relations which may contain null values. In our model for incomplete information we allow only a single unmarked null value denoted bynull. This allows us to solve the inference problem for NJDs by extending the chase procedure to the or-chase procedure. In order to define the or-chase procedure we generalise relations with nulls to or-relations which contain a limited form of disjunctive information. The main result of the paper shows that the inference problem for NJDs, including embedded NJDs (which are a special case of NJDs), is decidable; this is realised via the or-chase procedure.     

Tractability frontiers in probabilistic team semantics and existential second-order logic over the reals

Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus is on the axiomatizability, complexity, and expressivity of probabilistic inclusion logic and its extensions. We identify a natural fragment of existential second-order logic with additive real arithmetic that captures exactly the expressivity of probabilistic inclusion logic. We furthermore relate these formalisms to linear programming, and doing so obtain PTIME data complexity for the logics. Moreover, on finite structures, we show that the full existential second-order logic with additive real arithmetic can only express NP properties. Lastly, we present a sound and complete axiomatization for probabilistic inclusion logic at the atomic level.     

Some generalized type functional dependencies formalized as equality set on matrices

In this paper we deal with functional (f) dependencies and their generalizations, the dual, strong (d, s) and weak (w) dependencies. We give new axioms instead of Armstrong's and Czédli's and axiomatize the full w-families. Our axioms are based on a characterization of equality-sets of matrices. We demonstrate an essential difference between the weak dependency and the rest. We give an estimation for the number of rows which is needed for some antichain of an n-element set to represent it as the set of candidate keys in a relation. Finally, we give a combinatorial characterization of the generating sets with minimal cardinality of full f-families.     

Epitaxial growth and electrical transport properties of La0.5Sr0.5Co03 thin films prepared by pulsed laser deposition

Epitaxial growth of the La_0.5Sr_{0.5 3}(LO) thin films has been realized on Lin3, SrTiC₃ and MgO substrates by pulsed laser deposition. The epitaxial growth behavior and the electrical transport properties of these films were studied systematically. The temperature dependencies of the resistivity of the film have been determined. Studies indicate that close dependencies exist between the crystal structures and the electrical transport properties of the epitaxial LSCO films, and that the epitaxial thin films are of low resistivity and metallic conductive features. The epitaxial films deposited on the LaA10₃ substrates at about 700 °C possess the optimal properties compared with the others. Discussions of the dependencies and the mechanisms of the epitaxial structures on the electrical transport properties of the LSCO films have been made. Project supported by the National Natural Science Foundation of China (Grant No. 19574003 and No. 19674001).     

Multivariate Gaussian criteria in SMAA

We consider stochastic multicriteria decision-making problems with multiple decision makers. In such problems, the uncertainty or inaccuracy of the criteria measurements and the partial or missing preference information can be represented through probability distributions. In many real-life problems the uncertainties of criteria measurements may be dependent. However, it is often difficult to quantify these dependencies. Also, most of the existing methods are unable to handle such dependency information.In this paper, we develop a method for handling dependent uncertainties in stochastic multicriteria group decision-making problems. We measure the criteria, their uncertainties and dependencies using a stochastic simulation model. The model is based on decision variables and stochastic parameters with given distributions. Based on the simulation results, we determine for the criteria measurements a joint probability distribution that quantifies the uncertainties and their dependencies. We then use the SMAA-2 stochastic multicriteria acceptability analysis method for comparing the alternatives based on the criteria distributions. We demonstrate the use of the method in the context of a strategic decision support model for a retailer operating in the liberated European electricity market.     

Modeling the process of human body iron homeostasis using a variant of timed Petri nets

The body iron homeostasis is one of the most important processes in the human body. This complex process is not fully understood and until recently only some parts of it have been described in the literature. In our recent papers the main part of the process has been described and a model based on Petri net theory has been proposed. However, in this model any time dependencies occurring in the biochemical process have not been taken into account. In the present paper the model is enriched in the way that durations of biochemical reactions composing this process have been included into the model. A variant of Petri net where with each place a time interval is associated has been used in order to describe these dependencies. The time interval associated with a place corresponds to a time lag of biochemical conditions which must be fulfilled in order to enable a biochemical reaction to start.     

Multiway Dependence in Exponential Family Conditional Distributions

Conditionally specified statistical models are frequently constructed from one-parameter exponential family conditional distributions. One way to formulate such a model is to specify the dependence structure among random variables through the use of a Markov random field (MRF). A common assumption on the Gibbsian form of the MRF model is that dependence is expressed only through pairs of random variables, which we refer to as the “pairwise-only dependence” assumption. Based on this assumption, J. Besag (1974, J. Roy. Statist. Soc. Ser. B36, 192–225) formulated exponential family “auto-models” and showed the form that one-parameter exponential family conditional densities must take in such models. We extend these results by relaxing the pairwise-only dependence assumption, and we give a necessary form that one-parameter exponential family conditional densities must take under more general conditions of multiway dependence. Data on the spatial distribution of the European corn borer larvae are fitted using a model with Bernoulli conditional distributions and several dependence structures, including pairwise-only, three-way, and four-way dependencies.     

The state-dependent <Emphasis Type="Italic">M</Emphasis> / <Emphasis Type="Italic">G</Emphasis> / 1 queue with orbit

We consider a state-dependent single-server queue with orbit. This is a versatile model for the study of service systems, where the server needs a non-negligible time to retrieve waiting customers every time he completes a service. This situation arises typically when the customers are not physically present at a system, but they have a remote access to it, as in a call center station, a communication node, etc. We introduce a probabilistic approach for the performance evaluation of this queueing system, that we refer to as the queueing and Markov chain decomposition approach. Moreover, we discuss the applicability of this approach for the performance evaluation of other non-Markovian service systems with state dependencies.     

Extremality Results for Discontinuous Sturm‐Liouville Boundary Value Problems

In this paper we derive extremalit and comparison results for explicit and implicit boundary value problems of Sturm‐Liouville differential equations. Differential equations and boundary conditions ma involve discontinuous and functional dependencies.     

Heavy-tailed longitudinal data modeling using copulas

In this paper, we consider “heavy-tailed” data, that is, data where extreme values are likely to occur. Heavy-tailed data have been analyzed using flexible distributions such as the generalized beta of the second kind, the generalized gamma and the Burr. These distributions allow us to handle data with either positive or negative skewness, as well as heavy tails. Moreover, it has been shown that they can also accommodate cross-sectional regression models by allowing functions of explanatory variables to serve as distribution parameters.The objective of this paper is to extend this literature to accommodate longitudinal data, where one observes repeated observations of cross-sectional data. Specifically, we use copulas to model the dependencies over time, and heavy-tailed regression models to represent the marginal distributions. We also introduce model exploration techniques to help us with the initial choice of the copula and a goodness-of-fit test of elliptical copulas for model validation. In a longitudinal data context, we argue that elliptical copulas will be typically preferred to the Archimedean copulas. To illustrate our methods, Wisconsin nursing homes utilization data from 1995 to 2001 are analyzed. These data exhibit long tails and negative skewness and so help us to motivate the need for our new techniques. We find that time and the nursing home facility size as measured through the number of beds and square footage are important predictors of future utilization. Moreover, using our parametric model, we provide not only point predictions but also an entire predictive distribution.