Assumption Of Dependence Research Articles

Comparative diagnostic accuracy studies with an imperfect reference standard \u2013 a comparison of correction methods

BackgroundStaquet et al. and Brenner both developed correction methods to estimate the sensitivity and specificity of a binary-response index test when the reference standard is imperfect and its sensitivity and specificity are known. However, to our knowledge, no study has compared the statistical properties of these methods, despite their long application in diagnostic accuracy studies.AimTo compare the correction methods developed by Staquet et al. and Brenner.MethodsSimulations techniques were employed to compare the methods under assumptions that the new test and the reference standard are conditionally independent or dependent given the true disease status of an individual. Three clinical datasets were analysed to understand the impact of using each method to inform clinical decision-making.ResultsUnder the assumption of conditional independence, the Staquet et al. correction method outperforms the Brenner correction method irrespective of the prevalence of disease and whether the performance of the reference standard is better or worse than the index test. However, when the prevalence of the disease is high (> 0.9) or low (< 0.1), the Staquet et al. correction method can produce illogical results (i.e. results outside [0,1]). Under the assumption of conditional dependence; both methods failed to estimate the sensitivity and specificity of the index test especially when the covariance terms between the index test and the reference standard is not close to zero.ConclusionWhen the new test and the imperfect reference standard are conditionally independent, and the sensitivity and specificity of the imperfect reference standard are known, the Staquet et al. correction method outperforms the Brenner method. However, where the prevalence of the target condition is very high or low or the two tests are conditionally dependent, other statistical methods such as latent class approaches should be considered.

A Model for Aedes aegypti Infestation According to Meteorological Variables: case of Caratinga (Minas Gerais - Brazil)

Aedes aegypti mosquitoes are the vector of diseases such as dengue, zika, chikungunya, and yellow fever among others. All the stages of development, eggs, larvae, pupa, and the adult of the species have its population modulated by meteorological variables, such as precipitation and temperature through affecting the productivity of breeding sites, metabolic processes, and others. Since adult females are responsible for transmitting the virus, the population of females becomes a direct indicator of the risk of infection. For this reason, some ongoing vector surveillance programs are based on adult female capture. In turn, all the stages of development have its population modulated by meteorological variables, such as precipitation and temperature, through productivity of breeding sites, metabolic processes and others. In this work, field data of capture of females was used to evaluate if a population dynamics model of Aedes aegypti under the effect of weather would be able to forecast field population. The nonlinear dynamic system model comprises: (1) four equations for the populations of the stages of development of the mosquito, designed for the ongoing surveillance program; (2) parametric dependencies of the rates of development on mean temperature and weekly accumulated precipitation. The dependencies on temperature and precipitation are modelled with aim of simplicity with the fewer number of parameters as possible. Temperature dependence is modelled based on values of the related literature under the assumption of existence of a optimum temperature for the rates, getting worse for extreme temperatures. The dependence on precipitation which is barely treated in experiments is modelled under the assumption of a monotonic dependence described by a power law with values estimated in orders of magnitude from data in the literature. By comparison with field data of an entomological indicator based on the number of Ae. aegypti females captured by a public health program in the city of Caratinga (Minas Gerais, Brazil), the model showed a significant correlation (R = 0.75). The result shows that the approach, if refined, can provide forecasting for of the population size.

Causal Mechanism Transfer Network for Time Series Domain Adaptation in Mechanical Systems

Data-driven models are becoming essential parts in modern mechanical systems, commonly used to capture the behavior of various equipment and varying environmental characteristics. Despite the advantages of these data-driven models on excellent adaptivity to high dynamics and aging equipment, they are usually hungry for massive labels, mostly contributed by human engineers at a high cost. Fortunately, domain adaptation enhances the model generalization by utilizing the labeled source data and the unlabeled target data. However, the mainstream domain adaptation methods cannot achieve ideal performance on time series data, since they assume that the conditional distributions are equal. This assumption works well in the static data but is inapplicable for the time series data. Even the first-order Markov dependence assumption requires the dependence between any two consecutive time steps. In this article, we assume that the causal mechanism is invariant and present our Causal Mechanism Transfer Network (CMTN) for time series domain adaptation. By capturing causal mechanisms of time series data, CMTN allows the data-driven models to exploit existing data and labels from similar systems, such that the resulting model on a new system is highly reliable even with limited data. We report our empirical results and lessons learned from two real-world case studies, on chiller plant energy optimization and boiler fault detection, which outperform the existing state-of-the-art method.

Direct Effect and Spillover Effect of ICT on Electricity Consumption in China: Evidence from a Spatial Panel Analysis

The extensive use of information and communication technologies (ICT) has facilitated people’s lives and promoted the improvement of productivity. In the meantime, ICT has a profound effect on the efficiency of electricity utilization and the demand for electricity. The existing studies consider the direct effect of ICT on electricity consumption (EC) but neglect the spillover effect of ICT on EC and their action channels. Under the assumption of cross-section dependence, this paper introduces spatial modeling techniques to confirm the positive direct effect and negative spillover effect of ICT on EC. The positive direct effects and negative spillover effects of information technology on EC are similar to those of the communication technology, and the absolute value of the former is also greater than the latter. Additionally, the results of meditation effect modeling also confirm that there exists an incomplete mediating effect in the process of the ICT affecting EC through the channels of economic growth and the adjustment of the industrial structure. This study provides freshly empirical evidence for people to better understand the role of ICT in EC and opens fresh insights for policymakers to make corresponding policy adjustments.

Copula-Based Bayesian Reliability Analysis of a Product of a Probability and a Frequency Model for Parallel Systems When Components Are Dependent

While the dependence assumption among the components is naturally important in evaluating the reliability of a system, studies investigating the issues of aggregation errors in Bayesian reliability analyses have been focused mainly on systems with independent components. This study developed a copula-based Bayesian reliability model to formulate dependency between components of a parallel system and to estimate the failure rate of the system. In particular, we integrated Monte Carlo simulation and classification tree learning to identify key factors that affect the magnitude of errors in the estimation of posterior means of system reliability (for different Bayesian analysis approaches—aggregate analysis, disaggregate analysis, and simplified disaggregate analysis) to provide important guidelines for choosing the most appropriate approach for analyzing a model of products of a probability and a frequency for parallel systems with dependent components.

H\xf6lder estimates for magnetic Schr\xf6dinger semigroups in {mathbb {R}}^{d} from mirror coupling

We use the mirror coupling of Brownian motion to show that under a beta in (0,1)-dependent Kato-type assumption on the possibly nonsmooth electromagnetic potential, the corresponding magnetic Schrödinger semigroup in {mathbb {R}}^d has a global L^{p}-to-C^{0,beta } Hölder smoothing property for all pin [1,infty ]; in particular, his all eigenfunctions are uniformly beta -Hölder continuous. This result shows that the eigenfunctions of the Hamilton operator of a molecule in a magnetic field are uniformly beta -Hölder continuous under weak L^q-assumptions on the magnetic potential.

A reliable ensemble based approach to semi-supervised learning

Semi-supervised learning (SSL) methods attempt to achieve better classification of unseen data through the use of unlabeled data than can be achieved by learning from the available labeled data alone. Most SSL methods require the user to familiarize themselves with novel, complex concepts and to ensure the underlying assumptions made by these methods match the problem structure, or they risk a decrease in predictive performance. In this paper, we present the reliable semi-supervised ensemble learning (RESSEL) method, which exploits unlabeled data by using it to generate diverse classifiers through self-training and combines these classifiers into an ensemble for prediction. Our method functions as a wrapper around a supervised base classifier and refrains from introducing additional problem dependent assumptions. We conduct experiments on a number of commonly used data sets to prove its merit. The results show RESSEL improves significantly upon the supervised alternatives, provided that the base classifier which is used is able to produce adequate probability-based rankings. It is shown that RESSEL is reliable in that it delivers results comparable to supervised learning methods if this requirement is not met, while the method also broadens the range of good parameter values. Furthermore, RESSEL is demonstrated to outperform existing self-labeled wrapper approaches.

Probabilistic definition of the clinical target volume—implications for tumor control probability modeling and optimization

Evidence has been presented that moving beyond the binary definition of clinical target volume (CTV) towards a probabilistic CTV can result in better treatment plans. The probabilistic CTV takes the likelihood of disease spread outside of the gross tumor into account. An open question is: how to optimize tumor control probability (TCP) based on the probabilistic CTV. We derive expressions for TCP under the assumptions of voxel independence and dependence. For the dependent case, we make the assumption that tumors grow outward from the gross tumor volume. We maximize the (non-convex) TCP under convex dose constraints for all models. For small numbers of voxels, and when a dose-influence matrix is not used, we use exhaustive search or Lagrange multiplier theory to compute optimal dose distributions. For larger cases we present (1) a multi-start strategy using linear programming with a random cost vector to provide random feasible starting solutions, followed by a local search, and (2) a heuristic strategy that greedily selects which subvolumes to dose, and then for each subvolume assignment runs a convex approximation of the optimization problem. The optimal dose distributions are in general different for the independent and dependent models even though the probabilities of each voxel being tumorous are set to the same in both cases. We observe phase transitions, where a subvolume is either dosed to a high level, or it gets ‘sacrificed’ by not dosing it at all. The greedy strategy often yields solutions indistinguishable from the multi-start solutions, but for the 2D case involving organs-at-risk and the dependent TCP model, discrepancies of around 5% (absolute) for TCP are observed. For realistic geometries, although correlated voxels is a more reasonable assumption, the correlation function is in general unknown. We demonstrate a tractable heuristic that works very well for the independent models and reasonably well for the dependent models. All data are provided.

Relationship Between Outward Foreign Direct Investment and Domestic Investment: Evidence from GCC Countries

This paper examines the relationship between outward foreign direct investment and domestic investment, which is regarded with increased interest as a driver of growth in domestic markets for Gulf Cooperation Council (GCC) economies. Mean group (MG), pooled mean group (PMG) and dynamic fixed effect (DFE) approaches have been applied to measure short-run and long-run effects of domestic investment (DI) on outward foreign direct investment (OFDI) by relaxing the assumption of cross-sectional dependence (CD). This research shows that ignoring cross-sectional dependency among the countries which are parallel in economic structure may result in biased economic estimations. The findings of the dynamic fixed effect estimators show that domestic investment has negative and significant effects on FDI outflows in the long run in GCC countries. Furthermore, some of macroeconomic variables (trade and inflation) have insignificant effects on OFDI, whereas human capital has positive and significant effects on FDI outflows in the long run. The findings of this research remain important for policy makers to determine the practical efficacy of market reforms steered towards boosting domestic investment and growth. Furthermore, the policies related to the development of human capital can also take guidance from this study.

Voltage Dependence of the Reference System in Medium- and High-Voltage Current Transformer Calibrations

A sampling current ratio measurement system has been developed to calibrate the voltage dependence of ratio error and phase displacement of current transformers (CTs) used for medium-voltage (MV) and high-voltage (HV) applications. The influence of voltage-induced leakage current on the apparent ratio error and phase displacement of the reference circuit was unambiguously demonstrated using a novel measurement method. Measurement results for voltages up to 24 kV show that the observed leakage current is purely capacitive and caused by the shielded cable capacitance of the HV cable used to feed the current. The maximum ratio error and phase displacement were found to be about 100 parts in 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> and 100 μrad for the smallest current of 100 A used for these investigations. Since these values scale linearly with the applied voltage and inversely proportional with current, the assumption of negligible voltage dependence used in other reference systems presented in literature is questionable. Using the corrected reference circuit, a commercial class 0.2S MV CT with 2500-A nominal current was calibrated at voltage levels up to 24 kV. The voltage dependence of ratio error and phase displacement for primary currents up to 500 A was demonstrated to be capacitive as well, with a maximum impact on the current ratio of almost 0.9% for a primary current of 100 A (corresponding to 3.6% at 1% of nominal current). This value is beyond the limits of in-force standards, which emphasizes the necessity of implementing voltage dependence testing in those standards.

Complex-Valued Imaging with Total Variation Regularization: An Application to Full-Waveform Inversion in Visco-acoustic Media

Full waveform inversion (FWI) is a nonlinear PDE constrained optimization problem, which seeks to estimate constitutive parameters of a medium such as phase velocity, density, and anisotropy, by fitting waveforms. Attenuation is an additional parameter that needs to be taken into account in viscous media to exploit the full potential of FWI. Attenuation is more easily implemented in the frequency domain by using complex-valued velocities in the time-harmonic wave equation. These complex velocities are frequency-dependent to guarantee causality and account for dispersion. Since estimating a complex frequency-dependent velocity at each grid point in space is not realistic, the optimization is generally performed in the real domain by processing the phase velocity (or slowness) at a reference frequency and attenuation (or quality factor) as separate real parameters. This real parametrization requires an a priori empirical relation (such as the nonlinear Kolsky-Futterman (KF) or standard linear solid (SLS) attenuation models) between the complex velocity and the two real quantities, which is prone to generate modeling errors if it does not represent accurately the attenuation behavior of the subsurface. Moreover, it leads to a multivariate inverse problem, which is twice larger than the actual size of the medium and ill-posed due to the cross-talk between the two classes of real parameters. To alleviate these issues, we present a mono-variate algorithm that solves directly the optimization problem in the complex domain by processing in sequence narrow bands of frequencies under the assumption of band-wise frequency dependence of the sought complex velocities.

Modeling the Extreme Rainfall Data of Several Sites in Sabah using Sandwich Estimator

ABSTRACT When the extreme data were obtained from several sites in a region, spatial extreme analysis is always been considered. In this paper, we model the annual maximum rainfall data by using generalized extreme value distribution. We fit the model independently for each site to prevent extreme value complex modeling. However, it also cause the statistical assumption of dependency between sites been violated. Therefore, we applied the sandwich estimator to correct the variance of the model. We also consider an analysis of small sample sizes of the observed data. The method of penalized maximum likelihood estimation was carried out to improve the inference of the model. In the end, the return levels of the annual maximum rainfall data were computed by using the corrected model.

Ecology through the eyes of a non-ecologist

Ecology is a branch of biology that deals with the life of plants and animals in their environment. Nature protection are practical actions where ecology is applied. Ecology is the most biological branch of biology because it deals with individuals in their living environment, and individuals "exist" only in biology. The most important issue being considered in ecology is biodiversity: its changes and its persistence. In their research, ecologists focus on the functioning of ecological systems. In classical terms, they assume that the most important mechanism is density dependence. Mathematical models traditionally applied in ecology include ordinary difference and differential equations, which fits well with the assumption of density dependence, but this results in ecology being dominated by considerations of the stability of ecological systems. Evolutionary biology and ecology have separate areas of interest. Evolutionary biology explains the formation of optimal characteristics of individuals. Ecology also takes into account those individuals who have lost in the process of natural selection. The mathematical methods used in classical ecology were developed for the use of physics. The question arises whether they give a precise picture of the dynamics of ecological systems. Recently, a view has emerged stating that in order to see the importance of full-scale biodiversity, we should refer to individuals (rather than population density) as basic "atoms" that make up ecological systems. In ecology, we call this an individual-based approach. However, it gives a very complex picture of how ecological systems work. In ecology, however, there is an alternative way to describe the dynamics of ecological systems, i.e. through the circulation of matter in them and the flow of energy through them. It allows the use of traditional difference and differential equations in the formulation of mathematical models, which has proven itself in practical applications many times.

Warmer, Wetter Climates Accelerate Mechanical Weathering in Field Data, Independent of Stress‐Loading

AbstractWeathering is a foundational process in most Earth systems, but there has been a lack of data directly quantifying what influences mechanical weathering. Here we use multiple years of in situ field data, “listening” to acoustic emissions of naturally cracking rocks, to test a hypothesized link between climate and subcritical crack‐tip processes (i.e., the bond‐breaking mechanism thought to embody most mechanical weathering). Our results challenge the assumption of a singular dependence of mechanical weathering on stresses. We find that mechanical weathering rates exponentially increase as functions of atmospheric vapor pressure (VP), temperature, and relative humidity, even when controlling for stress‐loading. VP exerts the most pronounced influence on the observed mechanical weathering rates. Put in the context of global climate change, our results underscore the potential for climate‐dependent subcritical crack‐tip processes to influence all weathering‐allied problems including the long‐term stabilization of the climate by weathering‐carbon‐cycle feedbacks.

Modeling risk dependence and portfolio VaR forecast through vine copula for cryptocurrencies.

Risk in finance may come from (negative) asset returns whilst payment loss is a typical risk in insurance. It is often that we encounter several risks, in practice, instead of single risk. In this paper, we construct a dependence modeling for financial risks and form a portfolio risk of cryptocurrencies. The marginal risk model is assumed to follow a heteroscedastic process of GARCH(1,1) model. The dependence structure is presented through vine copula. We carry out numerical analysis of cryptocurrencies returns and compute Value-at-Risk (VaR) forecast along with its accuracy assessed through different backtesting methods. It is found that the VaR forecast of returns, by considering vine copula-based dependence among different returns, has higher forecast accuracy than that of returns under prefect dependence assumption as benchmark. In addition, through vine copula, the aggregate VaR forecast has not only lower value but also higher accuracy than the simple sum of individual VaR forecasts. This shows that vine copula-based forecasting procedure not only performs better but also provides a well-diversified portfolio.

Ordering results for elliptical distributions with applications to risk bounds

A classical result of Slepian (1962) for the normal distribution and extended by Das Guptas et al. (1972) for elliptical distributions gives one-sided (lower orthant) comparison criteria for the distributions with respect to the (generalized) correlations. Müller and Scarsini (2000) established that the ordering conditions even characterize the stronger supermodular ordering in the normal case. In the present paper, we extend this result to elliptical distributions. We also derive a similar comparison result for the directionally convex ordering of elliptical distributions. As application, we obtain several results on risk bounds in elliptical classes of risk models under restrictions on the correlations or on the partial correlations. Furthermore, we obtain extensions and strengthening of recent results on risk bounds for various classes of partially specified risk factor models with elliptical dependence structure of the individual risks and the common risk factor. The moderate dependence assumptions on this type of models allow flexible applications and, in consequence, are relevant for improved risk bounds in comparison to the marginal based standard bounds.

Probabilistic Modeling for Frequency Vectors Using a Flexible Shifted-Scaled Dirichlet Distribution Prior

Burstiness and overdispersion phenomena of count vectors pose significant challenges in modeling such data accurately. While the dependency assumption of the multinomial distribution causes its failure to model frequency vectors in several machine learning and data mining applications, researchers found that by extending the multinomial distribution to the Dirichlet Compound multinomial (DCM), both phenomena modeling can be addressed. However, Dirichlet distribution is not the best choice, as a prior, given its negative-correlation and equal-confidence requirements. Thus, we propose to use a flexible generalization of the Dirichlet distribution, namely, the shifted-scaled Dirichlet, as a prior to the multinomial, which grants the model a capability to better fit real data, and we call the new model the Multinomial Shifted-Scaled Dirichlet (MSSD). Given that the likelihood function plays a key role in statistical inference, e.g., in maximum likelihood estimation and Fisher information matrix investigation, we propose to improve the efficiency of computing the MSSD log-likelihood by approximating its function based on Bernoulli polynomials where the log-likelihood function is computed using the proposed mesh algorithm. Moreover, given the sparsity and high-dimensionality nature of count vectors, we propose to improve its computation efficiency by approximating the novel MSSD as a member of the exponential family of distribution, which we call EMSSD. The clustering is based on mixture models, and for learning a model, selection approach is seamlessly integrated with the estimation of the parameters. The merits of the proposed approach are validated via challenging real-world applications such as hate speech detection in Twitter, real-time recognition of criminal action, and anomaly detection in crowded scenes. Results reveal that the proposed clustering frameworks offer a good compromise between other state-of-the-art techniques and outperform other approaches previously used for frequency vectors modeling. Besides, comparing to the MSSD, the approximation EMSSD has reduced the computational complexity in high-dimensional feature spaces.

An investigation of weighting schemes suitable for incorporating large ensembles into multi-model ensembles

Abstract. Multi-model ensembles can be used to estimate uncertainty in projections of regional climate, but this uncertainty often depends on the constituents of the ensemble. The dependence of uncertainty on ensemble composition is clear when single-model initial condition large ensembles (SMILEs) are included within a multi-model ensemble. SMILEs allow for the quantification of internal variability, a non-negligible component of uncertainty on regional scales, but may also serve to inappropriately narrow uncertainty by giving a single model many additional votes. In advance of the mixed multi-model, the SMILE Coupled Model Intercomparison version 6 (CMIP6) ensemble, we investigate weighting approaches to incorporate 50 members of the Community Earth System Model (CESM1.2.2-LE), 50 members of the Canadian Earth System Model (CanESM2-LE), and 100 members of the MPI Grand Ensemble (MPI-GE) into an 88-member Coupled Model Intercomparison Project Phase 5 (CMIP5) ensemble. The weights assigned are based on ability to reproduce observed climate (performance) and scaled by a measure of redundancy (dependence). Surface air temperature (SAT) and sea level pressure (SLP) predictors are used to determine the weights, and relationships between present and future predictor behavior are discussed. The estimated residual thermodynamic trend is proposed as an alternative predictor to replace 50-year regional SAT trends, which are more susceptible to internal variability. Uncertainty in estimates of northern European winter and Mediterranean summer end-of-century warming is assessed in a CMIP5 and a combined SMILE–CMIP5 multi-model ensemble. Five different weighting strategies to account for the mix of initial condition (IC) ensemble members and individually represented models within the multi-model ensemble are considered. Allowing all multi-model ensemble members to receive either equal weight or solely a performance weight (based on the root mean square error (RMSE) between members and observations over nine predictors) is shown to lead to uncertainty estimates that are dominated by the presence of SMILEs. A more suitable approach includes a dependence assumption, scaling either by 1∕N, the number of constituents representing a “model”, or by the same RMSE distance metric used to define model performance. SMILE contributions to the weighted ensemble are smallest (&lt;10 %) when a model is defined as an IC ensemble and increase slightly (&lt;20 %) when the definition of a model expands to include members from the same institution and/or development stream. SMILE contributions increase further when dependence is defined by RMSE (over nine predictors) amongst members because RMSEs between SMILE members can be as large as RMSEs between SMILE members and other models. We find that an alternative RMSE distance metric, derived from global SAT and hemispheric SLP climatology, is able to better identify IC members in general and SMILE members in particular as members of the same model. Further, more subtle dependencies associated with resolution differences and component similarities are also identified by the global predictor set.

Inflation and Stock Returns in 18 OECD Countries: Some Robust Panel Integration and Cointegration Tests

Applying Im, Pesaran and Shin (2003) and Pesaran (2007) approach, we examine the presence of unit roots in inflation rates and stock returns of 18 OECD countries. Under the assumption of cross sectional dependence, results support unit roots in our sample. Application of Johansen (1991) test fails to detect cointegration in some cases. Larsson, Lyhagen and Löthgren (2001) panel test provides strong evidence of cointegration for all the countries in the sample. We fail to support the presence of a uniformly positive relationship between inflation and stock returns, thus casting some doubt over equities as effective long run inflation hedges.

Testing financial time series for autocorrelation: Robust Tests

Two modified Portmanteau statistics are studied under dependence assumptions common in financial applications which can be used for testing that heteroskedastic time series are serially uncorrelated without assuming independence or Normality. Their asymptotic distribution is found to be null and their small sample properties are examined via Monte Carlo. The power of the tests is studied under the MA and GARCH-in-mean alternatives. The tests exhibit an appropriate empirical size and are seen to be more powerful than a robust Box-Pierce to the selected alternatives. Real data on daily stock returns and exchange rates is used to illustrate the tests.