Search

The high velocity, variety and volume of data generation by today's systems have necessitated Big Data (BD) analytic techniques. This has penetrated a wide range of industries; BD as a notion has various types and characteristics, and therefore a variety of analytic techniques would be required. The traditional analysis methods are typically unable to analyse spatial-temporal BD. Interpolation is required to approximate the values between the already existing data points, yet since there exist both location and time dimensions, only a multivariate interpolation would be appropriate. Nevertheless, existing software are unable to perform such complex interpolations. To overcome this challenge, this paper presents a layer by layer interpolation approach for spatial-temporal BD. Developing this layered structure provides the opportunity for working with much smaller linear system of equations. Consequently, this structure increases the accuracy and stability of numerical structure of the considered BD interpolation. To construct this layer by layer interpolation, we have used the good properties of Radial Basis Functions (RBFs). The proposed new approach is applied to numerical examples in spatial-temporal big data and the obtained results confirm the high accuracy and low computational cost. Finally, our approach is applied to explore one of the air pollution indices, i.e. daily P M 2.5 concentration, based on different stations in the contiguous United States, and it is evaluated by leave-one-out cross validation.

Meshfree methods based on radial basis functions (RBFs) are popular tools for the numerical solution of stochastic partial differential equations (SPDEs) due to their nice properties. However, the RBF collocation methods in global view have some disadvantages for the numerical solution of time-dependent SPDEs. Calculation of matrix condition number in the resulting dense linear systems indicates that the meshless method using global RBFs may be unstable at each realization to solve SPDEs. In order to avoid numerical instabilities in global RBF methods, we are interested in the use of RBF methods in local view for the numerical solution of time-dependent SPDEs. In this paper, the RBF partition of unity collocation method based on a finite difference scheme for the Gaussian random field (RBF-PU-FD) as a localized RBF approximation presented to deal with these issues. For this purpose, we simulate the Gaussian field with spatial covariance structure at a finite collection of predetermined collocation points. The matrices formed during the RBF-PU-FD method will be sparse and, hence, will not suffer from ill-conditioning and high computational cost. We will show that the method is viable through analyzing its numerical accuracy, CPU time, stability and sparsity structure. For the test problems, we perform 1000 realizations and statistical criterions such as mean, standard deviation, lower bound and upper bound of prediction are computed and evaluated using the Monte-Carlo method.

In this article we examine the functional central limit theorem for the first passage time of reward processes defined over a finite state space semi-Markov process. In order to apply this process ...

Background: Within the UK, COVID-19 has contributed towards over 103,000 deaths. Although multiple risk factors for COVID-19 have been identified, using this data to improve clinical care has proven challenging. The main aim of this study is to develop a reliable, multivariable predictive model for COVID-19 in-patient outcomes, thus enabling risk-stratification and earlier clinical decision-making. Methods: Anonymised data consisting of 44 independent predictor variables from 355 adults diagnosed with COVID-19, at a UK hospital, was manually extracted from electronic patient records for retrospective, case–control analysis. Primary outcomes included inpatient mortality, required ventilatory support, and duration of inpatient treatment. Pulmonary embolism sequala was the only secondary outcome. After balancing data, key variables were feature selected for each outcome using random forests. Predictive models were then learned and constructed using Bayesian networks. Results: The proposed probabilistic models were able to predict, using feature selected risk factors, the probability of the mentioned outcomes. Overall, our findings demonstrate reliable, multivariable, quantitative predictive models for four outcomes, which utilise readily available clinical information for COVID-19 adult inpatients. Further research is required to externally validate our models and demonstrate their utility as risk stratification and clinical decision-making tools.

IntroductionWithin the UK, COVID-19 has contributed towards over 103,000 deaths. Multiple risk factors for COVID-19 have been identified including various demographics, co-morbidities, biochemical parameters, and physical assessment findings. However, using this vast data to improve clinical care has proven challenging.Aimsto develop a reliable, multivariable predictive model for COVID-19 in-patient outcomes, to aid risk-stratification and earlier clinical decision-making.MethodsAnonymized data regarding 44 independent predictor variables of 355 adults diagnosed with COVID-19, at a UK hospital, was manually extracted from electronic patient records for retrospective, case-controlled analysis. Primary outcomes included inpatient mortality, level of ventilatory support and oxygen therapy required, and duration of inpatient treatment. Secondary pulmonary embolism was the only secondary outcome. After balancing data, key variables were feature selected for each outcome using random forests. Predictive models were created using Bayesian Networks, and cross-validated.ResultsOur multivariable models were able to predict, using feature selected risk factors, the probability of inpatient mortality (F1 score 83.7%, PPV 82%, NPV 67.9%); level of ventilatory support required (F1 score varies from 55.8% “High-flow Oxygen level” to 71.5% “ITU-Admission level”); duration of inpatient treatment (varies from 46.7% for “≥ 2 days but < 3 days” to 69.8% “≤ 1 day”); and risk of pulmonary embolism sequelae (F1 score 85.8%, PPV of 83.7%, and NPV of 80.9%).ConclusionOverall, our findings demonstrate reliable, multivariable predictive models for 4 outcomes, that utilize readily available clinical information for COVID-19 adult inpatients. Further research is required to externally validate our models and demonstrate their utility as clinical decision-making tools.HighlightsUsing COVID-19 risk-factor data to assist clinical decision making is a challengeAnonymous data from 355 COVID-19 inpatients was collected & balancedKey independent variables were feature selected for 4 different outcomesAccurate, multi-variable predictive models were computed, using Bayesian NetworksFuture research should externally validate our models & demonstrate clinical utility

Frost, particularly during the spring, is one of the most damaging weather phenomena for vineyards, causing significant economic losses to vineyards around the world each year. The risk of tardive frost damage in vineyards due to changing climate is considered as an important threat to the sustainable production of grapes. Therefore, the cold monitoring strategies is one of the criteria with significant impacts on the yields and prosperity of horticulture and raisin factories. Frost events can be characterized by duration and severity. This paper investigates the risk and impacts of frost phenomenon in the vineyards by modeling the joint distribution of duration and severity factors and analyzing the influential parameter’s dependency structure using capabilities of copula functions. A novel mathematical framework is developed within this study to understand the risk and uncertainties associate with frost events and the impacts on yields of vineyards by analyzing the non-linear dependency structure using copula functions as an efficient tool. The developed model was successfully validated for the case study of vineyard in Malayer city of Iran. The copula model developed in this study was shown to be a robust tool for predicting the return period of the frost events.

Many biological and biomedical research areas such as drug design require analyzing the Gene Regulatory Networks (GRNs) to provide clear insight and understanding of the cellular processes in live cells. Under normality assumption for the genes, GRNs can be constructed by assessing the nonzero elements of the inverse covariance matrix. Nevertheless, such techniques are unable to deal with non-normality, multi-modality and heavy tailedness that are commonly seen in current massive genetic data. To relax this limitative constraint, one can apply copula function which is a multivariate cumulative distribution function with uniform marginal distribution. However, since the dependency structures of different pairs of genes in a multivariate problem are very different, the regular multivariate copula will not allow for the construction of an appropriate model. The solution to this problem is using Pair-Copula Constructions (PCCs) which are decompositions of a multivariate density into a cascade of bivariate copula, and therefore, assign different bivariate copula function for each local term. In fact, in this paper, we have constructed inverse covariance matrix based on the use of PCCs when the normality assumption can be moderately or severely violated for capturing a wide range of distributional features and complex dependency structure. To learn the non-Gaussian model for the considered GRN with non-Gaussian genomic data, we apply modified version of copula-based PC algorithm in which normality assumption of marginal densities is dropped. This paper also considers the Dynamic Time Warping (DTW) algorithm to determine the existence of a time delay relation between two genes. Breast cancer is one of the most common diseases in the world where GRN analysis of its subtypes is considerably important; Since by revealing the differences in the GRNs of these subtypes, new therapies and drugs can be found. The findings of our research are used to construct GRNs with high performance, for various subtypes of breast cancer rather than simply using previous models.

This study assesses the succession of insects on rabbit carcass. The study was conducted in sunny and shaded sites in the west of Iran during four seasons in 2016 and 2017. Based on the results of this study, various factors such as body size, carcass location, and carcass injury could affect the pattern of insect succession on carcass. In this study, we estimated the elapsed time since death (R2 > 0.98, P = 0.00) based on carcass weight loss during the stages of decomposition and the cubic method. Jaccard analysis was performed to determine the similarity of insect taxa during decomposition of rabbit carrion in two different sites during a period of four seasons. Succession pattern analysis for necrophagous insects in both habitats showed a similarity between bloat and decay stages for each habitat. On the other hand, pairwise similarities in taxa were low at the fresh and dry stages, however increased at bloat and decay stages of decomposition. This study shows that succession has some limitations in determining the elapsed time of death. Therefore, the use of source of information such as a weight loss model seems to be essential.

In this paper, we propose a new lifetime model as a discrete version of the continuous weighted exponential distribution which is called discrete weighted exponential distribution (DWED). This model is a generalization of the discrete exponential distribution which is originally introduced by Chakraborty (2015). We present various statistical indices/properties of this distribution including reliability indices, moment generating function, probability generating function, survival and hazard rate functions, index of dispersion, and stress-strength parameter. We first present a numerical method to compute the maximum likelihood estimations (MLEs) of the models parameters, and then conduct a simulation study to further analyze these estimations. The advantages of the DWED are shown in practice by applying it on two real world applications and compare it with some other well-known lifetime distributions.

Sometimes healthcare perspectives in communications technologies require data mining, especially classification as a supervised learning. Support vector machines (SVMs) are considered as efficient supervised learning approaches for classification due to their robustness against several types of model misspecifications and outliers. Kernel-based SVMs are known to be more flexible tools for a wide range of supervised learning tasks and can efficiently handle non-linear relationship between input variables and outputs (or labels). They are more robust with respect to the aforementioned model misspecifications, and also more accurate in the sense that the root-mean-square error computed by fitting the kernel-based SVMs is considerably smaller than the one computed by fitting the standard/linear SVMs. However, the choice of kernel type and particularity kernel’s parameters could have significant impact on the classification accuracy and other supervised learning tasks required in network security, Internet of things, cybersecurity, etc. One of the findings of this study is that larger kernel parameter(s) would encourage SVMs with more localities and vice versa. This chapter provides some results on the effect of the kernel parameter on the kernel-based SVM classification. We thus first examine the effect of these parameters on the classification results using the kernel-based SVM, and then specify the optimal value of these parameters using cross-validation (CV) technique.

The problem of estimating lifetime distribution parameters under progressively Type-II censoring originated in the context of reliability. But traditionally it is assumed that the available data from this censoring scheme are performed in exact numbers. However, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. Thus, it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers. This paper deals with the estimation of lifetime distribution parameters under progressively Type-II censoring scheme when the lifetime observations are reported by means of fuzzy numbers. A new method is proposed to determine the maximum likelihood estimates of the parameters of interest. The methodology is illustrated with two popular models in lifetime analysis, the Rayleigh and Lognormal lifetime distributions.

Since the global financial crash, one of the main trends in the financial engineering discipline has been to enhance the efficiency and flexibility of financial probabilistic risk assessments. Creditors could immensely benefit from such improvements in analysis hoping to minimise potential monetary losses. Analysis of real world financial scenarios require modeling of multiple uncertain quantities with a view to present more accurate, near future probabilistic predictions. Such predictions are essential for an informed decision making. In this article, the authors extend Bayesian Networks Pair-Copula Construction (BN-PCC) further using the minimum information vine model which results in a more flexible and efficient approach in modeling multivariate dependencies of heavy-tailed distribution and tail dependence as observed in the financial data. The authors demonstrate that the extended model based on minimum information Pair-Copula Construction (PCC) can approximate any non-Gaussian BN to any degree of approximation. The proposed method has been applied to the portfolio data derived from a Brazilian case study. The results show that the fitting of the multivariate distribution approximated using the proposed model has been improved compared to other previously published approaches.

In this paper, a novel method for copula density estimation using Legendre multiwavelet is proposed. In general, copula density estimation methods based on the multiwavelet benefit from some useful properties, including they are symmetric, orthogonal and have compact support. In particular, the Legendre multiwavelet as a more general and vector-valued polynomial type of wavelets would results a more flexible and accurate approximation for the given copula density. In addition to high ability and nice properties of Legendre multiwavelet in approximation, its support is defined on unit interval, [0,1], as copulas that are normalized to have the support on the unit square and uniform marginal. We further make this approximation method more accurate by using multiresolution techniques. The comparative study reveals that the approximation proposed in this paper is more accurate than a scalar wavelet bases approximation. We eventually apply presented method to approximate multivariate distribution using pair-copula as a flexible multivariate copula to model a dataset of Norwegian financial data.

Many financial modeling applications require to jointly model multiple uncertain quantities to present more accurate, near future probabilistic predictions. Informed decision making would certainly benefit from such predictions. Bayesian Networks (BNs) and copulas are widely used for modeling numerous uncertain scenarios. Copulas, in particular, have attracted more interest due to their nice property of approximating the probability distribution of the data with heavy tail. Heavy tail data is frequently observed in financial applications. The standard multivariate copula suffer from serious limitations which made them unsuitable for modeling the financial data. An alternative copula model called the Pair-Copula Construction (PCC) model is more flexible and efficient for modeling the complex dependence of financial data. The only restriction of PCC model is the challenge of selecting the best model structure. This issue can be tackled by capturing conditional independence using the Bayesian Network PCC (BN-PCC). The flexible structure of this model can be derived from conditional independences statements learned from data. Additionally, the difficulty of computing conditional distributions in graphical models for non-Gaussian distributions can be eased using pair-copulas. In this paper, we extend this approach further using the minimum information vine model which results in a more flexible and efficient approach in understanding the complex dependence between multiple variables with heavy tail dependence and asymmetric features which appear widely in the financial applications.

Cybercriminology as a subject area has numerous dimensions. Some studies in the field primarily focus on a corrective action to reduce the impact of an already committed crime. However, there are existing computational techniques which can assist in predicting and therefore preventing cyber-crimes. These quantitative techniques are capable of providing valuable holistic and strategic insights for law enforcement units and police forces to prevent the crimes from happening. Moreover, these techniques can be used to analyse crime patterns to provide a better understanding of the world of cyber-criminals. The main beneficiaries of such research works, are not only the law enforcement units, as in the era of Internet-connectivity, many business would also benefit from cyber attacks and crimes being committed in the cyber environment. This chapter provides an all-embracing overview of machine learning techniques for crime analysis followed by a detailed critical discussion of data mining and predictive analysis techniques within the context of cybercriminology.

A consecutive linear (circular) [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: F system consists of [Formula: see text] linear (circular)-ordered components such that the system fails if and only if there exists a set of [Formula: see text] consecutive linear (circular) component that contains at least [Formula: see text] failed components. Consecutive linear (circular) [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: F systems attract tremendous attention for researchers of reliability analysis. Recent efforts in this area have focused on simple situations or approximation bands for their reliability but closed form and exact amount not gained. In this paper, we designed an innovative algorithm and an innovative program to obtain the exact reliability for an extensive class of consecutive circular [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]: F system with particular emphasis for equal and unequal component probabilities. Finally, we reviewed an applied example and applied comparative and numerical results and calculated the exact reliability of this strategic system.

In the life-cycle management of systems under continuous deterioration, studying the sensitivity analysis of the optimised preventive maintenance decisions with respect to the changes in the model parameters is of a great importance. Since the calculations of the mean cost rates considered in the preventive maintenance policies are not sufficiently robust, the corresponding maintenance model can generate outcomes that are not robust and this would subsequently require interventions that are costly. This chapter presents a computationally efficient decision-theoretic sensitivity analysis for a maintenance optimisation problem for systems/structures/assets subject to measurable deterioration using the Partial Expected Value of Perfect Information (PEVPI) concept. Furthermore, this sensitivity analysis approach provides a framework to quantify the benefits of the proposed maintenance/replacement strategies or inspection schedules in terms of their expected costs and in light of accumulated information about the model parameters and aspects of the system, such as the ageing process. In this paper, we consider random variable model and stochastic Gamma process model as two well-known probabilistic models to present the uncertainty associated with the asset deterioration. We illustrate the use of PEVPI to perform sensitivity analysis on a maintenance optimisation problem by using two standard preventive maintenance policies, namely age-based and condition-based maintenance policies. The optimal strategy of the former policy is the time of replacement or repair and the optimal strategies of the later policy are the inspection time and the preventive maintenance ratio. These optimal strategies are determined by minimising the corresponding expected cost rates for the given deterioration models’ parameters, total cost and replacement or repair cost. The robust optimised strategies to the changes of the models’ parameters can be determined by evaluating PEVPI’s which involves the computation of multi-dimensional integrals and is often computationally demanding, and conventional numerical integration or Monte Carlo simulation techniques would not be helpful. To overcome this computational difficulty, we approximate the PEVPI using Gaussian process emulators.

The multivariate distribution of five main indices of Tehran stock exchange is approximated using a pair-copula model. A vine graphical model is used to produce an n-dimensional copula. This is accomplished using a flexible copula called a minimum information (MI) copula as a part of pair-copula construction. Obtained results show that the achieved model has a good level of approximation.

In this paper, we concentrate on new methodologies for copulas introduced and developed by Joe, Cooke, Bedford, Kurowica, Daneshkhah and others on the new class of graphical models called vines as a way of constructing higher dimensional distributions. We develop the approximation method presented by Bedford et al (2012) at which they show that any $n$-dimensional copula density can be approximated arbitrarily well pointwise using a finite parameter set of 2-dimensional copulas in a vine or pair-copula construction. Our constructive approach involves the use of minimum information copulas that can be specified to any required degree of precision based on the available data or experts' judgements. By using this method, we are able to use a fixed finite dimensional family of copulas to be employed in a vine construction, with the promise of a uniform level of approximation. The basic idea behind this method is to use a two-dimensional ordinary polynomial series to approximate any log-density of a bivariate copula function by truncating the series at an appropriate point. We present an alternative approximation of the multivariate distribution of interest by considering orthonormal polynomial and Legendre multiwavelets as the basis functions. We show the derived approximations are more precise and computationally faster with better properties than the one proposed by Bedford et al. (2012). We then apply our method to modelling a dataset of Norwegian financial data that was previously analysed in the series of papers, and finally compare our results by them., 31 pages, 7 figures. arXiv admin note: text overlap with arXiv:1206.2700 by other authors