Stochastic Dependence Research Articles

Systemic risk: Conditional distortion risk measures

In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution (ΔCoD) measures as measures of systemic risk and analyze their properties and representations. The classes unify, and significantly extend, existing systemic risk measures such as the conditional Value-at-Risk, conditional Expected Shortfall, and risk contribution measures in terms of the VaR and ES. We provide sufficient conditions for two random vectors to be ordered by the proposed CoD-risk measures and ΔCoD-measures. These conditions are expressed using the conventional stochastic dominance, increasing convex/concave, dispersive, and excess wealth orders for the marginals and canonical positive/negative stochastic dependence notions.

Identification and Control of Multidimensional Delayed Processes in Conditions of Incomplete Information

Problems of identification and control of multidimensional discrete-continuous processes with delay in conditions of incomplete information about the object are considered. In such conditions, the form of parametric equations for various channels of the object is absent due to the lack of a priori information. Moreover, multidimensional processes have stochastic dependences of the components of the vector of output variables. Under such conditions, the mathematical description of such processes leads to a system of implicit equations. Nonparametric identification and control algorithms for multidimensional systems are proposed. The main task of modeling such processes is to determine the predicted values of the output variables from the known input. Moreover, for implicit equations, it is only known that one or another output variable can depend on other input and output variables that determine the state of a multidimensional system. In this study, a nontrivial situation arises when solving a system of implicit equations under conditions when the dependences between the components of the output variables are unknown. The application of the parametric theory of identification in this case will not lead to success. One of the possible directions is the use of the theory of nonparametric systems. The main content of the work is the solution of the identification problem in the presence of dependencies of the output variables and then the solution of the control problem for such a process. Here you should pay attention to the fact that when determining the reference actions for a multidimensional system, it is first necessary to solve the system of reference actions, since it is not possible to choose arbitrarily setting influences from the range of definition of output variables. Computational eXperiments aimed at investigating the effectiveness of the proposed identification and control algorithms are presented.

Stochastic free vibration of composite plates with temperature-dependent properties under spatially varying stochastic high thermal gradient

The uncertainty of natural frequencies of composite plates due to the uncertainty of high-temperature distribution on the plate is investigated. Mechanical properties are assumed to be uncertain linear functions of temperature with assuming a stochastic linear dependency function (SLDF). The temperature gradient is assumed to be a Gaussian stochastic field with an exponential kernel. Assuming first-order shear deformation theory, the displacement field is defined. The stochastic assumed modes (SAM) method is proposed and discretized stochastic equations of motion are derived. The probability space is studied using an intrusive polynomial chaos approach. Stochastic simulations are verified using the stochastic finite element method (SFEM) based on the Monte Carlo approach. Results show the proposed semi-analytical method is an efficient alternative to time-consuming SFEM with resulting accurate statistical moments. Uncertainty in natural frequencies is quantified for symmetric and anti-symmetric composite plates with different side to thickness ratios. The applicability of linear dependency of composite material properties to the temperature is evaluated by uncertainty propagation in SLDF. Uncertainties in SLDF and temperature distribution have significant effects on predicted natural frequencies. Based on the results, the application of linear dependency of material properties to the temperature can lead to significant errors in predicted natural frequencies.

Maintenance policy analysis of the regenerative air heater system using factored POMDPs

Maintenance optimization of multi-component systems is a difficult problem. Partially Observable Markov Decision Processes (POMDPs) are powerful tools for such problems under uncertainty in stochastic environments. In this study, the main POMDP solution approaches and solvers are surveyed. Then, based on experimental models with different complexities in the size of the system space, selected POMDP solvers using different representation patterns for modeling and different procedures for updating the value function while solving are compared. Furthermore, to show that factored representations are advantageous in modeling and solving the maintenance problem of multi-component systems where there exist also stochastic dependencies among the components, the maintenance problem of the one-line regenerative air heater system available in thermal power plants is modeled and solved with factored POMDPs. In-depth sensitivity analyses are performed on the obtained policy. The results show that factored POMDPs enable compact modeling, efficient policy generation and practical policy analysis for the tackled problem. Furthermore, they also motivate the use of factored POMDPs in the generation and analysis of maintenance policies for similar multi-component systems.

A condition-based maintenance policy for multi-component systems subject to stochastic and economic dependencies

Condition-based maintenance (CBM) optimization utilizing prognostic information and methods for complex systems has attracted increasing attention. This paper presents a bi-level approach to optimize a CBM policy for multi-component systems subject to stochastic and economic dependencies. The objective of the decision rule at the system level is to address if preventive and/or corrective maintenance actions are necessary regarding the predictive reliability of the system. At the component level, the aim is to identify the optimal group of components to be preventively maintained when maintenance is triggered due to the decision made at the system level. A maintenance efficacy indicator is introduced to prioritize components to be maintained by taking into account both the resulting reliability improvement quantity and the maintenance cost incurred. The optimal inter-inspection interval, the thresholds of system and component conditional reliability for triggering maintenance are jointly determined for minimization of the long-run average cost rate. A numerical study and sensitivity analysis on a 2oo3:G system are carried out to validate the performance of the proposed maintenance policy. Compared to another opportunistic maintenance policy without considering the system health condition, the proposed CBM policy leads to more cost gain and effectiveness in the maintenance decision-making.

Optimal allocation of distributed generation and capacitor banks using probabilistic generation models with correlations

The allocation of distributed generation and capacitor banks is critical for success in the planning of power grids. A methodology is developed for the optimal placement of distributed renewable generation (wind and photovoltaic powers) and capacitor banks is developed based on technical and economic parameters. In order to preserve the horoseasonal and stochastic dependence nature of the wind and solar power, the methodology uses a model that integrates the sequential Monte Carlo method and the diagonal band Copula model, integrating historical data of wind speed, solar radiation and feeder load from the region of study. An efficient algorithm based on Genetic Algorithms is proposed to implement the optimization. The algorithm validation demonstrates a reduction of up to 71.7% in annual losses of active power in the Bandeira feeder and 73.4% in the Recife feeder, with adequate voltage levels and a return on investment of 6–7 years.

Some properties of socio-economic systems

The purpose of the research. The main purpose of the article is to study some aspects and features of socio-economic systems within the management of their dynamic stability. Methodology. To improve the conceptual apparatus, in ("economic system", "dynamic stability", "stability") used methods such as generalization, analysis and synthesis. Results. The study found that most economic scientists do not consider this issue an integral part of the system-universal component of management of socio-economic systems and the corporate sector of the economy as signs of stability and reliability in a complex environment. It is confirmed that the stability parameters allow a certain deviation from the trend of the values of the generalized indicator as a function of time: it makes a stochastic dependence on the system parameters. Dynamic stability can be defined as a mode of system operation when it is able to achieve the target function when externally excited, when the system parameters approach the limits of stability corridors, or when the system chooses its own path when reaching the bifurcation point. It is determined that the socio-economic system is an artificially created system in which the primary elements are a person who makes decisions at his level of hierarchy. The practical significance of the study lies in the applied nature of the study, in particular, the authors highlighted the properties of systems: self-organization, communication with the environment, evolution, hierarchy, adaptability and integrity as a set of factors influencing and determining the dynamic stability of socio-economic system. Further research by the author will be devoted to this. Another area of further development will be the improvement of scientific and methodological principles of managing the dynamic stability of socio-economic systems and the formation and implementation of the appropriate type of mechanism for rapid response to threats and risks of specific functions in the context of objectification of enterprise value.

The effects of divided attention at encoding and at retrieval on multidimensional source memory.

Dividing attention (DA) between a memory task and a secondary task results in deficits in memory performance across a wide array of memory tasks, but these effects are larger when DA occurs at encoding than at retrieval. Although some research suggests the effects of DA are equal for item and associative memory, thereby suggesting that DA disrupts all components of an episode to the same extent, there have been relatively few studies directly examining the effects of DA on multiple features of the same episode. In addition, no studies have examined how DA may affect the stochastic dependency between multiple source dimensions of a given episode, which is central to theories of source memory, and episodic memory in general. Thus, in two experiments, we used a multidimensional source memory task-examining memory for items and multiple source features-and separately investigated how DA at encoding or at retrieval affects item memory, source memory, and joint source retrieval. DA was manipulated at encoding in Experiment 1 and at retrieval in Experiment 2. Whereas DA at encoding disrupted item memory, as well as source memory and source-source binding, though to a lesser extent, DA at retrieval did not affect any of these outcomes. Results are discussed in terms of levels of binding and the role of attention in encoding and retrieval of bounded episodic representations. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Assessing the "paradox" of converging evidence by modeling the joint distribution of individual differences: Comment on Davis-Stober and Regenwetter (2019).

Davis-Stober and Regenwetter (2019; D&R) showed that even when all predictions of a theory hold in separate studies, not even a single individual may be described by all predictions jointly. To illustrate this "paradox" of converging evidence, D&R derived upper and lower bounds on the proportion of individuals for whom all predictions of a theory hold. These bounds reflect extreme positive and negative stochastic dependence of individual differences across predictions. However, psychological theories often make more specific assumptions such as true individual differences being independent or positively correlated (e.g., due to a common underlying trait). Based on this psychometric perspective, I extend D&R's conceptual framework by developing a multivariate normal model of individual effects. Assuming perfect consistency (i.e., a correlation of one) of individual effects across predictions, the proportion of individuals described by all predictions of a theory is identical to D&R's upper bound. The proportion drops substantially when assuming independence of individual effects. However, irrespective of the assumed correlation structure, the multivariate normal model implies a lower bound that is strictly above D&R's lower bound if a theory makes at least three predictions. Hence, the scope of a theory can be improved by specifying whether individual effects are assumed to show a certain level of consistency across predictions (similar to a trait) or whether they are statistically independent (similar to a state). (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Random Toeplitz matrices: The condition number under high stochastic dependence

In this paper, we study the condition number of a random Toeplitz matrix. As a Toeplitz matrix is a diagonal constant matrix, its rows or columns cannot be stochastically independent. This situation does not permit us to use the classic strategies to analyze its minimum singular value when all the entries of a random matrix are stochastically independent. Using a circulant embedding as a decoupling technique, we break the stochastic dependence of the structure of the Toeplitz matrix and reduce the problem to analyze the extreme singular values of a random circulant matrix. A circulant matrix is, in fact, a particular case of a Toeplitz matrix, but with a more specific structure, where it is possible to obtain explicit formulas for its eigenvalues and also for its singular values. Among our results, we show the condition number of a non-symmetric random circulant matrix [Formula: see text] of dimension [Formula: see text] under the existence of the moment generating function of the random entries is [Formula: see text] with probability [Formula: see text] for any [Formula: see text], [Formula: see text]. Moreover, if the random entries only have the second moment, the condition number satisfies [Formula: see text] with probability [Formula: see text]. Also, we analyze the condition number of a random symmetric circulant matrix [Formula: see text]. For the condition number of a random (non-symmetric or symmetric) Toeplitz matrix [Formula: see text] we establish [Formula: see text], where [Formula: see text] is the minimum singular value of the matrix [Formula: see text]. The matrix [Formula: see text] is a random circulant matrix and [Formula: see text], where [Formula: see text] are deterministic matrices, [Formula: see text] indicates the conjugate transpose of [Formula: see text] and [Formula: see text] are random diagonal matrices. From random experiments, we conjecture that [Formula: see text] is well-conditioned if the moment generating function of the random entries of [Formula: see text] exists.

Condition-based maintenance strategies for stochastically dependent systems using Nested Lévy copulas

Nowadays, industrial systems are more and more complex and components are integrated dependently. Without consideration of dependence between components often leads to overestimate the reliability of system and high maintenance cost. In this paper, a multi-component system with hierarchical stochastic dependencies is considered. Components within subsystem are strongly correlated and dependence between subsystems is heterogeneous. Thanks to its capacity of modeling asymmetric dependence structures, the Nested Lévy copula is used in this paper. Based on the multiple sources of dependence among components and hierarchical structures, a novel condition-based maintenance policy is proposed. The inspection scheme as well as maintenance decision is dynamically planned according to the collected inspection information and the influence of stochastic dependence is investigated. The numerical results show the efficiency and robustness of proposed maintenance policy on reducing the inspection and maintenance cost.

Stochastic copula-DEA model based on the dependence structure of stochastic variables: An application to twenty bank branches

The DEA is a nonparametric method of assessing the efficiency of decision-making units using mathematical programming. The classic DEA model assumes that input and output variables are deterministic. However, there are many applications where the variables are of a stochastic nature. Based on the consideration of input and output levels as random variables, the Stochastic Data Envelopment Analysis (SDEA) was developed. Statistical distributions therefore play a major role in this regard. By considering the dependency between input and output variables, and also their simultaneous dependencies in this study, we have introduced three copula-SCCR models. We used three copulas of Gaussian, Clayton, and Gumbel to estimate the dependence between the random variables with normal distribution. We evaluated the proposed models using real data from 20 bank branches. The results showed that considering stochastic dependency between the inputs or outputs causes different results. A comparison between the Copula-SCCR models and the SCCR models revealed that the efficiency of the DMUs using the Copula-SCCR models differed from the SCCR model by a significant margin of at least 20%.

Availability of an RFID Object-Identification System in IoT Environments.

Through the latest technological and conceptual developments, the centralized cloud-computing approach has moved to structures such as edge, fog, and the Internet of Things (IoT), approaching end users. As mobile network operators (MNOs) implement the new 5G standards, enterprise computing function shifts to the edge. In parallel to interconnection topics, there is the issue of global impact over the environment. The idea is to develop IoT devices to eliminate the greenhouse effect of current applications. Radio-frequency identification (RFID) is the technology that has this potential, and it can be used in applications ranging from identifying a person to granting access in a building. Past studies have focused on how to improve RFID communication or to achieve maximal throughput. However, for many applications, system latency and availability are critical aspects. This paper examines, through stochastic Petri nets (SPNs), the availability, dependability, and latency of an object-identification system that uses RFID tags. Through the performed analysis, the optimal balance between latency and throughput was identified. Analyzing multiple communication scenarios revealed the availability of such a system when deployed at the edge layer.

616BMI and SBP impact on survival of dialytic patients: multivariate joint model approach

Abstract Background Studies on impact of routine clinical parameters on mortality of patients on peritoneal dialysis (PD), especially among elderly, are inconsistent. Although association between body mass index (BMI) and systolic blood pressure (SBP) is well known, their joint role on PD patient evolution is not clear. We aimed to model the joint impact of BMI and SBP trajectories on a cohort of incident elderly PD patients. Methods Prospective multicenter cohort study with 674 patients. Repeated measurements were modeled by random effects multivariate linear model. For the time-to-event outcome, used Cox proportional hazards model with log-Gaussian frailty. Stochastic dependence is captured by allowing random effects of the linear model to be correlated with the frailty term of the survival model, allowing for different clinical interpretations. All sub-models were adjusted for age in years. Results Isolated current values effects of increased BMI and BPS showed both as protective factors (1% and 2% risk reduction, respectively, for each unitary increase). When jointly modeled BMI changed its effect to 5% risk reduction while BPS remained the same, showing great impacts on survival depending on the combination of trajectories. Conclusions Clinical parameters association and its impact on survival is complex, and estimation of isolated effects may provide biased survival curves leading to unrealistic prognosis. A multivariate joint modeling can be seen as a valuable tool for clinical protocols on patient evolution. Key message Modern clinical epidemiology must foster use of modern statistics

Estimation of High Structural Reliability Involving Nonlinear Dependencies Based on Linear Correlations

Stochastic nonlinear dependencies have been reported extensively between different uncertain parameters or in their time or spatial variance. However, the description of dependency is commonly not provided except a linear correlation. The structural reliability incorporating nonlinear dependencies thus needs to be addressed based on the linear correlations. This paper first demonstrates the capture of nonlinear dependency by fitting various bivariate non-Gaussian copulas to limited data samples of structural material properties. The vine copula model is used to enable a flexible modeling of multiple nonlinear dependencies by mapping the linear correlations into the non-Gaussian copula parameters. A sequential search strategy is applied to achieve the estimate of numerous copula parameters, and a simplified algorithm is further designed for reliability involving stationary stochastic processes. The subset simulation is then adopted to efficiently generate random variables from the corresponding distribution for high reliability evaluation. Two examples including a frame structure with different stochastic material properties and a cantilever beam with spatially variable stochastic modulus are investigated to discuss the possible effects of nonlinear dependency on structural reliability. Since the dependency can be determined qualitatively from limited data, the proposed method provides a feasible way for reliability evaluation with prescriptions on correlated stochastic parameters.

СТОХАСТИЧЕСКИЙ АНАЛИЗ И ОПТИМАЛЬНОЕ УПРАВЛЕНИЕ СТИМУЛИРОВАНИЕМ ПЕРСОНАЛА КОММЕРЧЕСКОЙ ОРГАНИЗАЦИИ

The article discusses the issues of research and assessment of the impact of quantitative parameters of material and social incentives for personnel on the financial results of the activities of commercial organizations, as well as issues of optimal management of these parameters. Stimulation of personnel acts as a tool that guides employees of the organization to achieve specific productive indicators of its activity that have value for the organization by strengthening the desired motives and reinforcing the required motivational structure in the team. Studying the influence of individual incentives on the motivation and performance of an organization is an important management task that provides information necessary for making decisions on improving the incentive system. Therefore, the paper substantiates the methodological tools for stochastic analysis, forecasting and programming the dependence of financial results of work on the quantitative values of individual stimulating factors based on the methods of regression and economic analysis, the index forecasting method. Also, a methodological toolkit for mathematical modeling and optimal decision-making on the prospective structure of quantitative parameters of the organization's personnel incentive system was developed on the basis of the obtained stochastic dependencies and linear programming methods. The article presents an example of mathematical formalization, practical implementation and economic interpretation of tools for stochastic analysis and optimal management of staff incentives based on the proceedings of an agricultural organization. The methods and tools for managing staff incentives described in the work can be used by business entities of various industries and spheres of activity when justifying the directions of restructuring the systems of motivation and incentives for personnel

Group maintenance strategy of CNC machine tools considering three kinds of maintenance dependence and its optimization

Unreasonable maintenance strategy will increase maintenance cost and reduce the efficiency of CNC (Computer Numerical Control) machine tools. Therefore, not only the degradation state of components but also their coupling effect should be considered to obtain a scientific and reasonable system-level maintenance strategy because of the dependence among different components of CNC machine tools. This study proposes a group maintenance strategy of CNC machine tools considering economic dependence, structural dependence, and stochastic dependence among critical components and optimizes the group maintenance strategy. The model of group maintenance of CNC machine tools is composed of four sub-models: sub-model of component degression, sub-model of group maintenance decision, sub-model of imperfect maintenance, sub-model of maintenance cost. Utilizing the model of group maintenance of CNC machine tools, the time, objectives, and measure of maintenance can be decided according to the degression state and failures of components. And then, the cost of each maintenance can be calculated. In the group maintenance model, economic dependence and structural dependence among components are quantified by cost, while stochastic dependence is quantified by failure intensity. On that basis, the Monte Carlo method is used to simulate the machine tool operation process, and the long-term maintenance cost of CNC machine tools corresponding to a certain failure intensity threshold is calculated. Finally, genetic algorithm is used to optimize the failure intensity thresholds of preventive maintenance and group maintenance. A numerical example verifies the effectiveness of the proposed optimization method for the group maintenance strategy.

A numerical study of Markov decision process algorithms for multi-component replacement problems

We present a unified modeling framework for Time-Based Maintenance (TBM) and Condition-Based Maintenance (CBM) for optimization of replacements in multi-component systems. The considered system has a K-out-of-N reliability structure, and components deteriorate according to a multivariate gamma process with Lévy copula dependence. The TBM and CBM models are formulated as Markov Decision Processes (MDPs), and optimal policies are found using dynamic programming. Solving the CBM model requires that the continuous deterioration process is discretized. We therefore investigate the discretization level required for obtaining a near-optimal policy. Our results indicate that a coarser discretization level than previously suggested in the literature is adequate, indicating that dynamic programming is a feasible approach for optimization in multi-component systems. We further demonstrate this through empirical results for the size limit of the MDP models when solved with an optimized implementation of modified policy iteration. The TBM model can generally be solved with more components than the CBM model, since the former has a sparser state transition structure. In the special case of independent component deterioration, transition probabilities can be calculated efficiently at runtime. This reduces the memory requirements substantially. For this case, we also achieved a tenfold speedup when using ten processors in a parallel implementation of algorithm. Altogether, our results show that the computational requirements for systems with independent component deterioration increase at a slower rate than for systems with stochastic dependence.

Lack-of-partial-memory and aging properties of multivariate generalized Marshall-Olkin distributions

This article finds that multivariate generalized Marshall-Olkin distributions are of the lack-of-partial-memory property in the sense of residual lifetimes of elder components being independent of those younger ones’ ages. Also, we further investigate aging behavior and stochastic dependence of the multivariate residual lifetime of this family of random vectors.

Extreme eigenvalues of nonlinear correlation matrices with applications to additive models

The maximum correlation of functions of a pair of random variables is an important measure of stochastic dependence. It is known that this maximum nonlinear correlation is identical to the absolute value of the Pearson correlation for a pair of Gaussian random variables or a pair of finite sums of iid random variables. This paper extends these results to pairwise Gaussian vectors and processes, nested sums of iid random variables, and permutation symmetric functions of sub-groups of iid random variables. It also discusses applications to additive regression models.