Stochastic Dependence Research Articles

Towards Dependent Race Models for the Stop-Signal Paradigm

The race model for stop signal processing is based on the assumption of context independence between the go and stop process. Recent empirical evidence inconsistent with predictions of the independent race model has been interpreted as a failure of context independence. Here we demonstrate that, keeping context independence while assuming stochastic dependency between go and stop processing, one can also account for the observed violations. Several examples demonstrate how stochastically dependent race models can be derived from copulas, a rapidly developing area of statistics. The non-observability of stop signal processing time is shown to be equivalent to a well known issue in random dependent censoring.

Structured Replacement Policies for Offshore Wind Turbines

AbstractWe consider the problem of optimally maintaining an offshore wind farm in which major components progressively degrade over time due to normal usage and exposure to a randomly varying environment. The turbines exhibit both economic and stochastic dependence due to shared maintenance setup costs and their common environment. Our aim is to identify optimal replacement policies that minimize the expected total discounted setup, replacement, and lost power production costs over an infinite horizon. The problem is formulated using a Markov decision process (MDP) model from which we establish monotonicity of the cost function jointly in the degradation level and environment state and characterize the structure of the optimal replacement policy. For the special case of a two-turbine farm, we prove that the replacement threshold of one turbine depends not only on its own state of degradation but also on the state of degradation of the other turbine in the farm. This result yields a complete characterization of the replacement policy of both turbines by a monotone curve. The policies characterized herein can be used to optimally prescribe timely replacements of major components and suggest when it is most beneficial to share costly maintenance resources.

Non-periodic preventive maintenance policies for complex multi-component products sold with loss-based two-dimensional warranties

Multi-component characteristics of complex industrial equipment, such as complex structures and stochastic dependencies, complicate analyzing the failure characteristics of such products and developing effective strategies to reduce warranty costs. In addition, a substantial customer loss or service interruption owing to the shutdown of these products forces manufacturers to formulate warranty contracts while considering customer loss. From the manufacturer’s perspective, with the aim of reducing the warranty costs while restraining the costs of customer loss, we propose the following two novel types of non-periodic imperfect preventive maintenance (PM) policies: unified and customized. The proposed PM policies simultaneously take into account the effects of customer usage rate heterogeneity and product deterioration on product failure. We characterize the failure relationship between the product and corresponding components based on the reliability block diagram and the Type I failure dependency model, and further construct the decision models for the proposed PM policies. The properties of the decision models are provided for certain special cases and are further used to design an algorithm for a general case. A comparison of the results of the numerical examples reveals the following: (1) Providing PM policies is beneficial for both the warranty providers and customers. The proposed PM policies are better than traditional periodic PM policies when shutdown loss costs are considered. (2) The stochastic dependencies will increase the costs of both the warranty and shutdown loss. It is necessary to take into account the stochastic dependencies of multi-component products when analyzing the warranty costs and formulating relevant decisions. (3) Beyond formulating effective PM policies, the manufacturer can mitigate the warranty cost pressure by adjusting the warranty coverage based on market information, or improving product reliability.

Remaining useful life prediction for complex systems with multiple indicators of stochastic correlation considering random shocks

The remaining useful life (RUL) prediction in complex systems is subject to complex working conditions, such as overloads, random vibration and shocks, gradual corrosion and wearing, that cause the complex and variable performance degradation of the mechanical system. Accurate prediction of RUL requires the extraction of multiple performance indicators strongly correlated to system degradation. Accordingly, we propose an RUL prediction framework for a multi-indicator system that considers the effects of random shocks and stochastic dependence. First, considering the influence of random shocks and measurement errors, a degradation state-space model is established using the stochastic correlation of multiple performance indicators. Next, the hidden state and unknown parameters of the state-space model are jointly estimated using the expectation–maximization algorithm in conjunction with the strong tracking filter algorithm based on online monitoring data. Subsequently, the probability density function expression of the RUL is derived for a multi-indicator system with three failure modes. Finally, the accuracy of the RUL prediction model is verified for a system affected by random shocks via numerical experiments. Compared with other prediction methods, the effectiveness and adaptability of the proposed method are verified using the C-MAPSS dataset and a high-temperature furnace case.

Probabilistic load flow in distribution networks: An updated and comprehensive review with a new classification proposal

Due to the increased penetration of distributed energy resources and the presence of uncertainties in power networks, it is essential to evaluate the uncertainty of system performance. As a result, effective technologies for load flow analysis are required. The stochastic properties of power systems can be discovered via probabilistic load flow analysis. To model the uncertainties and construct the parametric tools of probabilistic power flow, several works recently utilize ensembles of probability density functions. Nevertheless, the uncertainties may not fit into any of the conventional classes of probability density functions. Thus, nonparametric tools are required. Various studies on uncertainty modeling techniques in probabilistic load flow have recently been undertaken, although there is no single best uncertainty modeling methodology to date. The load flow problem and the type of uncertain input variables determine the best strategy. There have been positive evaluations in this area, but the main focus of this research is firstly to present an overview and classification of the available load flow strategies in distribution networks from various perspectives and also, investigate the stochastic correlation or dependency of a random variable's variation relative to others. Then, based on a fresh perspective, we present a review, taxonomy, and discussion of the strengths and shortcomings of existing uncertainty modeling techniques in stochastic load flow as probability methods (parametric, semi- and non-parametric approaches) and non-probability methods. Moreover, for first time, a comprehensive comparison and assessment between these uncertainty methods based on accuracy, complexity, and simulation time presents in the uncertainties handling of the power system. The authors suggest this review to engineers, scientists and researchers who are doing their research work in this field.

Estimating and Using Block Information in the Thurstonian IRT Model

Multidimensional forced-choice (MFC) tests are increasing in popularity but their construction is complex. The Thurstonian item response model (Thurstonian IRT model) is most often used to score MFC tests that contain dominance items. Currently, in a frequentist framework, information about the latent traits in the Thurstonian IRT model is computed for binary outcomes of pairwise comparisons, but this approach neglects stochastic dependencies. In this manuscript, it is shown how to estimate Fisher information on the block level. A simulation study showed that the observed and expected standard errors based on the block information were similarly accurate. When local dependencies for block sizes >,2 were neglected, the standard errors were underestimated, except with the maximum a posteriori estimator. It is shown how the multidimensional block information can be summarized for test construction. A simulation study and an empirical application showed small differences between the block information summaries depending on the outcome considered. Thus, block information can aid the construction of reliable MFC tests.

Multi-Label Quantification

Quantification, variously called supervised prevalence estimation or learning to quantify , is the supervised learning task of generating predictors of the relative frequencies (a.k.a. prevalence values ) of the classes of interest in unlabelled data samples. While many quantification methods have been proposed in the past for binary problems and, to a lesser extent, single-label multiclass problems, the multi-label setting (i.e., the scenario in which the classes of interest are not mutually exclusive) remains by and large unexplored. A straightforward solution to the multi-label quantification problem could simply consist of recasting the problem as a set of independent binary quantification problems. Such a solution is simple but naïve, since the independence assumption upon which it rests is, in most cases, not satisfied. In these cases, knowing the relative frequency of one class could be of help in determining the prevalence of other related classes. We propose the first truly multi-label quantification methods, i.e., methods for inferring estimators of class prevalence values that strive to leverage the stochastic dependencies among the classes of interest in order to predict their relative frequencies more accurately. We show empirical evidence that natively multi-label solutions outperform the naïve approaches by a large margin. The code to reproduce all our experiments is available online.

System reliability of corroded pipelines considering spatial and stochastic dependency in irregular zones

This paper presents a probabilistic methodology for assessing the system reliability of corroded pipelines subjected to spatial and stochastic dependency, taking into account irregular zones (elbows, weld joints, and flanges). The space-variant corrosion and residual stress are considered by the mean of Karhunen-Loève expansion in order to take into account spatial variability of residual stress and soil aggressiveness over the pipe's entire length. The failure probability is evaluated by a series system combination using Monte Carlo simulations. Finally, the proposed model is applied to gas pipeline crossing several soil types in order to show the effects of the main parameters of the system, where the irregular zones have a significant influence on the pipeline system reliability and that the developed model can provide valuable information for decision-makers to improve system reliability performance.

Joint optimization of fleet-level sequential selective maintenance and repairpersons assignment for multi-state manufacturing systems

Due to limited maintenance resources, the joint optimization of fleet-level selective maintenance and repairpersons assignment aims to determine the optimal subset of maintenance actions for each repairperson to ensure that manufacturing systems in the fleet complete subsequent missions. However, related studies ignore the uncertain maintenance duration and flow dependency (a stochastic dependency caused by dynamic material flow) resulting in overestimation of system reliability and total profit. Therefore, this paper proposes a novel joint optimization model of fleet-level sequential selective maintenance and repairpersons assignment under flow dependency and uncertain maintenance duration. The model requires identifying a subset of maintenance actions, assigning the selected maintenance actions to repairpersons, and planning sequence of maintenance actions executed by each repairperson. Moreover, the degradation model of multi-state machines under flow dependency is established by analyzing dynamic characteristics of production processes. Further, the reliability of multi-state manufacturing systems considering the interaction among repairpersons, flow dependency, and uncertain maintenance duration is incorporated into the optimization model. The objective is to maximize the total profit under predetermined system reliability thresholds. Then, the optimization problem is solved by a tailored genetic algorithm with segment-based evolution strategy. Finally, numerical examples are given to verify the effectiveness of the proposed method.

Specifics of Psychoprophylaxis and Correction in Overcoming the Phenomenon of Compassion Fatigue in Volunteers

The purpose of the article is to empirically determine the features of psychoprophylaxis and correction in overcoming the phenomena of compas-sion fatigue of volunteers in the context of post­traumatic growth.research methods. Depression Anxiety Stress Scales (DASS­21) and Pro-fessional Quality of Life Scale (ProQoL) methods were used as psychodiagnostic methods in the empirical study of the phenomena of compassion fatigue to de-termine the stress resistance and professional quality of life of volunteers during the war. Mathematical and statistical methods, regression analysis, stochastic dependence between the investigated characteristics in groups, methods of psy-chological survey and comparison (Pearson’s χ2, df, ∆χ2, ∆df) were also used.research results. The internal moral conflict between the principles and challenges of reality, between universal human values and individual attitudes is attributed to the specifics of psychoprophylaxis and correction for overcoming the phenomena of compassion fatigue. Among the principles of psychohygiene and psychoprophylaxis of compassion fatigue phenomena of volunteers are such principles as the principle of complexity, the principle of systematicity, the prin-ciple of psychic development, and orientation to personal resources.conlusions. The results show that there are statistically significant differ-ences between the two groups of subjects according to the signs of compassion fatigue, among which we note the following indicators: a high level of depres-sion, professional burnout, traumatic stress and a moderate level of satisfaction with compassion. When carrying out psychological prevention of compassion fa-tigue phenomena of volunteers, at different levels (preventive, stress, resistance, exhaustion), it is necessary to focus on individual human resources and highlight psychological, biological, spiritual and social components of personality as indi-vidual parameters of human resistance.Consequently, those volunteers who directly provide assistance to victims are more prone to professional exhaustion, fatigue, psychophysical disorders and cognitive disorders than other volunteers who provide psychological interven-tions indirectly

Stochastic simulation and characteristic dependence analysis of urban short-duration rainstorms

Identifying the characteristics and risks of short-duration rainstorms and reducing the disaster caused by extreme rainstorms are important for urban sustainable development. In this study, the total rainfall (TR) and peak rainfall (PR) are generated randomly by constructing a stochastic simulation model with their dependence, and their encounter characteristics and return periods are analyzed by using the Copula function. Then, a case study is conducted in Zhengzhou City, China. The results show that: (1) the stochastic simulation model considering the contemporaneous and short-term dependencies (CSTD) is better than that considering only the contemporaneous dependence. Moreover, the simulated sequences which consider the CSTD can better maintain the characteristics of original sequences. (2) The joint probability distribution and encounter characteristics of rich (R)-poor (P) are similar between original and simulated sequences. The joint probability of TR and PR is densely distributed in the probability interval of 0.1–0.7. The probability of synchronous R-P is greater than that of asynchronous R-P, and the probability of synchronous R-P in simulated sequences is even larger, which is 73.14%. (3) The conditional probability of simulated sequences in scenario 2 is larger, and the conditional return period of rainfall events (CRPRE) is smaller. Moreover, the reference intervals of the conditional probability and CRPRE in simulated sequences are longer. Overall, the risk of extreme combination rainstorms in simulated sequences is higher than that in original sequences, and the scope of consideration and involvement is wider. These findings can provide scientific reference for the characteristics analysis and prediction of urban short-duration rainstorms.

Significant stochastic dependencies in process models

Process mining aims to artificially derive meaningful information from event logs recorded from information systems that support business processes in organisations. In many real-life processes, decisions do not only depend on the current state of the model, but also on decisions made earlier in the process. Such dependencies challenge process mining techniques: Petri nets are limited to hard dependencies (non-free-choice constructs). In this paper, we study stochastic dependencies, which model that the likelihood of decisions in a process may change dynamically based on earlier decisions. We introduce a modelling formalism that supports stochastic dependencies by extending stochastic labelled Petri nets, we study symmetries of this formalism, introduce a stochastic process discovery technique that discovers such models and we adapt two conformance checking techniques to validate the discovered models. The techniques have been implemented, and evaluated on computational feasibility and applicability. Finally, we show that the quality of our new models can compete with existing discovery techniques, and we show that stochastic dependencies are present in existing real-life logs and may lead to new types of insights.

Ruin Analysis on a New Risk Model with Stochastic Premiums and Dependence Based on Time Series for Count Random Variables

In this paper, we propose a new discrete-time risk model of an insurance portfolio with stochastic premiums, in which the temporal dependence among the premium numbers of consecutive periods is fitted by the first-order integer-valued autoregressive (INAR(1)) process and the temporal dependence among the claim numbers of consecutive periods is described by the integer-valued moving average (INMA(1)) process. To measure the risk of the model quantitatively, we study the explicit expression for a function whose solution is defined as the Lundberg adjustment coefficient and give the Lundberg approximation formula for the infinite-time ruin probability. In the case of heavy-tailed claim sizes, we establish the asymptotic formula for the finite-time ruin probability via the large deviations of the aggregate claims. Two numerical examples are provided in order to illustrate our theoretical findings.

Dynamic maintenance planning for autonomous marine systems (AMS) and operations

Compared to conventional marine systems, where the onboard crew can perform frequent and flexible maintenance, autonomous marine systems (AMS) only involve a limited (or, even no) crew during a voyage, and this challenges maintenance planning and execution. The current study identifies the relevant issues and proposes to solve these through developing a dynamic maintenance planning method for AMS. By considering economical dependencies among components, the study presents a dynamic grouping method to determine the optimum maintenance opportunities for AMS in the future. Stochastic dependencies of components are considered by using the Markov model. A multiphase Markov model is proposed for modeling stochastic dependencies between components where the limited and irregular maintenance opportunities are handled by the multiphase part of the model. A heuristic method is proposed to deal with the combinatorial challenge.To demonstrate the application of the proposed method, the maintenance planning of a cooling system of an autonomous ship is performed in a case study. To validate its performance, the proposed heuristic method is compared with existing ‘short-sighted’ methods for a selection of candidate groups for maintenance. In the validation, various scenarios with different component states and maintenance strategies are tested.

Distributed Linear Equations Over Random Networks

Distributed linear algebraic equation over networks, where nodes hold a part of problem data and cooperatively solve the equation via node-to-node communications, is a basic distributed computation task receiving an increasing research attention. Communications over a network have a stochastic nature, with both temporal and spatial dependence due to link failures, packet dropouts, or node recreation, etc. In this article, we study the convergence and convergence rate of distributed linear equation protocols over a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ast$</tex-math></inline-formula> -mixing random network, where the temporal and spatial dependencies between the node-to-node communications are allowed. When the network linear equation admits exact solutions, we prove the exponential convergence rate of the distributed projection consensus algorithm in the mean-squared sense. Motivated by the randomized Kaczmarz algorithm, we also propose a distributed randomized projection consensus algorithm, where each node randomly selects one row of local linear equations for projection per iteration, and establish an exponential rate of convergence. When the network linear equation admits no exact solution, we prove that a distributed gradient-descent-like algorithm with diminishing step-sizes can drive all nodes’ states to a least-squares solution at a sublinear rate. These results collectively illustrate that distributed computations may overcome communication correlations if the prototype algorithms enjoy certain contractive properties or are designed with suitable parameters.

The topological structures of the spaces of copulas and subcopulas

The (sub)copulas play a central role in statistics for capturing the stochastic dependence structure of random variables. A subcopula is a map from the Cartesian product of two closed subsets of the unit closed interval containing zero and one to the unit closed interval, which is grounded, 2-increasing and has uniform margins. A copula is a subcopula whose domain is the Cartesian product of the unit closed interval and itself. The uniform metric on the set of all copulas can be extended to a metric on the set of all subcopulas. In this work, we investigate topological structures of these spaces by using tools from infinite-dimensional topology. Our main result is as follows: there exists a homeomorphism from the space of subcopulas onto the Hilbert cube which sends the space of all copulas onto an end of the Hilbert cube and sends the space of exchangeable copulas onto an end of the end of the Hilbert cube. As a consequence, we obtain that the spaces of subcopulas, copulas and exchangeable copulas are homeomorphic to the Hilbert cube and hence have the fixed point property.

Availability modelling and analysis of a two-component parallel system under stochastic dependence

Availability modelling and analysis of a two-component parallel system under stochastic dependence

Формування податкової політики у країнах Європейського Союзу

The aim of the article is to generalize and systematize the provisions on the formation of tax policy in the EU countries. The dynamics of the indicator of the ratio of tax revenues to GDP in 27 EU countries during the period 2013–2022 is studied. It is found that the average value of this indicator for the EU-27 is 37.0%. A rather significant differentiation of the tax burden in the context of European countries is recorded, the lowest value observed in Ireland – 24.0%, and the maximum – in France – 47.4%. In general, a moderate level of tax burden is observed in the sample of Central European and Baltic countries. Using the method of correlation and regression analysis, it is found that for the EU countries in 2013–2022, with an increase in the tax burden by 1 percentage point, the real growth rate of the economy slows down by 0.215 percentage points, and the stochastic dependence is significant, but not too strong. In further research, it is important to pay attention to other factors influencing the growth rate of the real economy. Tax service is a key institution in the field of public revenue mobilization, in the EU-27 countries 62% of the total State revenues are collected by the tax authorities. The article pays attention to the study of the compositional tax structure both in the context of taxation of factors of production and individual taxes. Labor taxes account for the highest share in the tax structure in the EU Member States, followed by consumption taxes, and capital taxes are the least fiscally important. The determinant of the formation of the tax policy of European countries is competition in the international market to attract the main factors of production – labor and capital, which necessitates the creation of favorable conditions for their taxation. In the EU countries, there are unified taxation rules that apply to both minimum tax rates (VAT, excise duty) and control procedures, the principles of production and circulation of excisable goods, etc. In the EU member states, a standard and reduced VAT rate is used, the latter is a fiscal tool for maintaining social stability in society. The priorities of the tax authorities in the EU countries are the improvement of administration procedures, the expansion and modification of digital taxpayer services, the implementation of the institutional model of the State tax risk management and scenario modeling.

Sequence-to-Sequence Recurrent Graph Convolutional Networks for Traffic Estimation and Prediction Using Connected Probe Vehicle Data

Traffic estimation is imperative for conducting fundamental transportation engineering tasks such as transportation planning and traffic safety studies. Additionally, traffic prediction is vital for many data-driven intelligent transportation system applications. Most traffic estimation and prediction methods rely on infrastructure-based sensors to collect traffic parameters. However, infrastructure-based data collection can be costly and time consuming to set up and maintain. Additionally, the spatial distribution of the collected traffic data is limited by the location of the deployed hardware sensors. Probe vehicle data can be used to overcome these limitations. Traffic modeling for estimation and prediction is a complex task due to the stochastic nonlinear spatiotemporal dependencies exhibited by traffic parameters. In this paper, a deep learning-based sequence-to-sequence architecture called Seq2seq GCN-LSTM was proposed to estimate and predict network-wide traffic volume and speed. The proposed method utilizes short-term historical traffic data collected from a low-penetration rate probe vehicle fleet to estimate and predict traffic parameters up to 60-minutes ahead. The method utilizes Graph Convolutional Networks for spatial dependency extraction and Long Short-Term Memory networks to model temporal dependencies. The proposed method generated superior traffic results compared to the baseline models. Additionally, the model demonstrated robustness against perturbations caused by the low rate. Furthermore, the probe vehicle penetration rate was varied to test its effect on the proposed method’s modeling capability. The model was able to maintain traffic volume and speed estimation and prediction performance within a reasonable margin of error using penetration rates as low as 1.5% and 0.5%, respectively.

��²�� �� ������� ����� ���ֲ ������� � ��в�� �Ϊ����� �����

An urgent issue is to conduct systematic studies of the education role in the Ukrainian labor market formation and functioning. The study�s purpose is to identify the existing prerequisites and determine directions for the educational sector development as one of the Ukrainian labor market defining subjects. For this, several complex tasks of a comparative analysis of Ukraine�s official statistical data in peace (2021) and war (2022) years are being solved. The general methodological orientation is to identify relative proportions, taking into account the martial law impact on the labor market and the statistical information reliability. Macroeconomic indicators of the Ukraine labor market are studied by the methods of structural and diversified intersectional comparison and statistical analysis of stochastic dependencies under uncertain conditions. Theoretical generalizations of changes in macroeconomic indicators and the interpretation for the future are based on the results of the structural-dynamic analysis. Under martial law, there was a reduction in supply and demand by almost 2 times against the backdrop of a significant increase in market imbalance. According to the results of the statistical data processing, the direction and form of education activation as a catalyst for the recovery and development of the economy of Ukraine are proposed. The initial direction in the current Ukraine labor market is to use the education potential to eliminate the jobs lacking. Providing knowledge to the unemployed to fill existing vacancies remains the education prerogative. The form of implementation of these directions is the diversification of education on the basis of public-private partnerships. The public-private institutional field appropriate adjustment in the form of training and qualification complexes (primarily in the vocational education area) is a step toward the public-private partnerships introduction in other economic sectors. Further research should be focused on finding ways to activate education as the labor market subject of forming quantitative and qualitative parameters. For example, in relation to the required and available qualifications of the unemployed, working conditions, and the level of remuneration.