Multivariate Process Model Research Articles

An extended class of multivariate counting processes and its main properties

Abstract In this paper, a new multivariate counting process model (called Multivariate Poisson Generalized Gamma Process) is developed and its main properties are studied. Some basic stochastic properties of the number of events in the new multivariate counting process are initially derived. It is shown that this new multivariate counting process model includes the multivariate generalized Pólya process as a special case. The dependence structure of the multivariate counting process model is discussed. Some results on multivariate stochastic comparisons are also obtained.

A new multivariate gamma process model for degradation analysis

AbstractIn reliability engineering, it is frequently encountered that multiple performance characteristics (PCs) deteriorate simultaneously. The associated degradation processes are usually dependent and exhibit some heterogeneity from unit to unit, which makes the multivariate degradation modeling and reliability evaluation more challenging. To this end, we propose a new multivariate gamma process model. This model introduces a multivariate random vector, whose joint distribution is constructed by marginal gamma distributions and a copula function, to describe the unit‐to‐unit variability and the dependence among PCs. Meanwhile, it does not require all PCs to be inspected at the same time points in contrast to the traditional copula‐based degradation models. In addition, two reliability evaluation methods are developed. Model parameters are estimated by the stochastic expectation maximization algorithm, and a three‐step procedure is provided to initialize this algorithm. Subsequently, numerical simulations are implemented to verify the proposed methods. Finally, two examples are provided for illustration, and it is shown that the proposed model and methods scale well to the degradation data with different numbers of PCs. What is more, comparisons with several benchmark models are performed, and the superiority of the proposed model is well demonstrated.

A multivariate student-t process model for dependent tail-weighted degradation data

Traditionally, the Gaussian assumption, implied by the Wiener process, is widely admitted for modeling degradation processes. However, when degradation data exhibit heavy tails, this assumption is not suitable. To overcome this limitation, this article proposes a novel class of tail-weighted multivariate degradation model, which is built upon Student-t process. The model is able to account for both between-unit variability and process dependency, while allowing the adjustment of tail heaviness through tuning the parameter of the degree of freedom. For reliability assessment, we derive the system reliability function and present an efficient Monte Carlo method for its evaluation. Further, we introduce an expectation–maximization algorithm for parameter estimation and design a bootstrap method for interval estimation. Comprehensive simulation studies are conducted to validate the effectiveness of the inference method. Finally, the proposed methodology is applied to analyze two real-world degradation datasets.

Graphical criteria for the identification of marginal causal effects in continuous-time survival and event-history analyses

Abstract We consider continuous-time survival and event-history settings, where our aim is to graphically represent causal structures allowing us to characterize when a causal parameter is identified from observational data. This causal parameter is formalized as the effect on an outcome event of a (possibly hypothetical) intervention on the intensity of a treatment process. To establish identifiability, we propose novel graphical rules indicating whether the observed information is sufficient to obtain the desired causal effect by suitable reweighting. This requires a different type of graph than in discrete time. We formally define causal semantics for the corresponding dynamic graphs that represent local independence models for multivariate counting processes. Importantly, our work highlights that causal inference from censored data relies on subtle structural assumptions on the censoring process beyond independent censoring; these can be verified graphically. Put together, our results are the first to establish graphical rules for nonparametric causal identifiability in event processes in this generality for the continuous-time case, not relying on particular parametric survival models. We conclude with a data example on Human papillomavirus (HPV) testing for cervical cancer screening, where the assumptions are illustrated graphically and the desired effect is estimated by reweighted cumulative incidence curves.

Data-driven sensor delay estimation in industrial processes using multivariate projection methods

A key step in preparing industrial data for multivariate statistical modelling of (batch-)continuous processes is the estimation of sensor delays along the production line, to use as a correction for understanding relationships between them. Without such a correction, the measurements collected from the sensors do not all relate to the same portion of material travelling through the plant, which is where from a physical point of view the correlations are expected to arise from. Most methods to do these corrections currently reported in literature are limited in that they optimize only correlations bivariately between the different sensors, despite the eventual goal of being understood as a multivariate process model. This work proposes several methods for multivariate sensor delay estimation, based on multivariate projection methods, and critically investigates these using simulated and empirical process data from two industrial facilities. The objective is to provide more clarity on if, how, and why taking into account these multivariate correlations using such projection methods is beneficial. One of the proposed methods, named PLS-SEQ, was shown to outperform bivariate sensor delay estimation, which is regarded as benchmark method in this work, for all datasets. The average reduction in delay estimation error achieved by using PLS-SEQ is between 6% and 64%. The other newly proposed multivariate projection-based methods did not show such unanimous improvement in accuracy, but helped identifying the presence of sensor clusters in industrial data as a novel key challenge for sensor delay estimation. The presented results illustrate that projection-based multivariate methods, in particular the newly proposed method PLS-SEQ, show promising potential for sensor delay estimation, outperforming the bivariate sensor delay estimation methods used as benchmark. Ultimately, using these methods can improve the predictive and descriptive quality of statistical models for key industrial processes.

Сonceptual basis for building a base of models for determining the value of a construction company's information assets

An actual area of research in the field of increasing the effectiveness of the functioning of modern information and communication technologies (ICT) is the principles and methods of establishing the value of information assets (IA) in order to effectively choose means of their protection.
 The object of research of this work is the decision support system (DSPR) for establishing the value of the information asset of the information and communication technologies of the construction company.
 The purpose of the study is to determine the conceptual foundations of building a base of system models, which would allow creating a flexible dynamic decision support system for the implementation of decision-making processes, having a flexible structure that provides for the possibility of implementing alternative scenarios (options) for establishing the value of information assets.
 The principles and conceptual foundations of building a base of models, a decision-making support system with a flexible structure, configured for the possibility of implementing alternative scenarios of expert evaluation, depending on the degree of certainty and availability of data, are proposed. As a conceptual basis, the structure of the model base, alternative and scenario modeling of decision-making processes, a classifier of scenario formation conditions, a database of models in the form of a class diagram, a multivariate process model of information technology for establishing the value of information assets in the form of a set of hierarchical process models of alternative network modeling are considered.
 In the proposed approach, increasing the probability of the obtained results is achieved due to the fact that the user is given the opportunity to choose the most appropriate and effective evaluation scenario, taking into account the goals and objectives of the evaluation, the availability and degree of certainty of the basic data, the existing resource, time and information limitations when making decisions.

How doctor image features engage health science short video viewers? Investigating the age and gender bias

PurposeShort-form health science videos have become an important medium for disseminating health knowledge and improving public health literacy. However, the factors that determine viewer engagement are not well understood. This study aims to address this research gap by investigating the association between doctor image features and viewer engagement behavior, building on the personal branding theory and information signaling theory.Design/methodology/approachA sample of 1245 health science short-form videos was collected, and key video features related to doctor images were extracted through manual labeling. Multi-variable regression analysis and SPSS process model were employed to test the hypotheses.FindingsThe results show that doctor image features are significantly associated with viewer engagement behavior. Videos featuring doctors in medical uniforms receive more viewer likes, comments and shares. Highlighting the doctor's title can increase viewer collections. Videos shot in a home, white wall, or study room setting receive more like, comments and sharing. The doctor's appearance demonstrates a positive nonlinear relationship with viewer likes and comments. Young doctors with title information tend to attract more video collections than older doctors with title information. The positive effect of the doctor's appearance and showing title information, become more significant among male doctors.Originality/valueThis research provides novel insights into the factors that determine viewer engagement behavior in short-form health science videos. Specific doctor image features can enhance viewer engagement by signaling doctor professionalism. The results also suggest that there may be age and gender biases in viewers' perceptions.

A Multivariate Stochastic Degradation Model for Dependent Performance Characteristics

Simultaneous degradation of multiple dependent performance characteristics (PCs) is a common phenomenon for industrial products. The associated degradation modeling is of practical importance yet challenging. The dependence of the PCs can usually be attributed to two sources, one being the overall system health status and the other the common operating environments. Based on the observation, this study proposes a parsimonious multivariate Wiener process model whose number of parameters increases linearly with the dimension. We introduce a common stochastic time scale shared by all the PCs to model the dependence from the dynamic operating environment. Conditional on the time scale, the degradation of each PC is modeled as the sum of two independent Wiener processes, where one represents the common effects shared by all the PCs, and the other represents degradation caused by randomness unique to this PC. An EM algorithm is developed for model parameter estimation, and extensive simulations are implemented to validate the proposed model and the algorithms. For efficient reliability evaluation under a multivariate degradation model, including the proposed one, a bridge sampling-based algorithm is further developed. The applicability and the advantages of the proposed methods are demonstrated using a multivariate degradation dataset of a coating material. Supplementary materials for this article are available online.

Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants.

We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation and inhibition. Such expressions can be used for the prediction and sensitivity analysis of the statistical behavior of the model over time and to estimate the probability densities of neuronal membrane potentials using Gram-Charlier expansions. Our results are shown to provide a better alternative to Monte Carlo estimates via stochastic simulations and computer codes based on combinatorial recursions are included.

Robust optimization with uncertainty using a stochastic multivariate Gaussian process model

In robust parameter design (RPD), estimating the response surface model from the noisy experimental data is critical for parameter optimization. The multivariate Gaussian process (MGP) model has become a popular tool for response surface modelling. However, most existing MGP models may not effectively evaluate the uncertainty of noisy data. This article proposes a stochastic MGP for efficient emulation and robust optimization by considering uncertainty. Firstly, the hierarchical modelling technique is adopted to estimate the relationship model with noisy data. Secondly, the hyperparameters are estimated by the Gibbs technique, and the Bayesian averaging method is used to measure the parameter uncertainty. Finally, a novel optimization model integrated with the Bayesian averaging and quality loss function is developed to find the optimal solution. Two case studies are used to illustrate the effectiveness of the proposed method. The results show that the proposed approach obtains smaller quality loss than the existing ones.

Performance Prediction of the Full-Scale KNR Biological Nutrient Removal Process Using Multivariate Dynamic Process Model with the Grammar-Based Genetic Programming (GBGP) System

Biological wastewater treatment systems are characterized by large temporal variability of inflow, variable concentrations of components in the incoming wastewater to the plant, and highly variable biological reactions within the process. This paper proposes an automatic process model induction system using an evolutionary computional intelligence, called grammar-based genetic programming (GBGP), that is specially designed to automatically discover multivariate dynamic process models that best fit observed process data. This automatic process model induction system combines an evolutionary self-organizing system of genetic programming paradigm with various mathematical functions for a multivariate nonlinear model evolution using a grammar system via the mechanism of genetics and natural selection. In the GBGP, a four-step modelling procedure was performed: (1) initialization: generatr an initial population of P models using contex-free grammar. generation K=0; (2) optimize each model (variables and constants) in the population; (3) execute and evaluate the fitness of each model in the population; (4) genetic loop: repeat until termination criterion is met (maximum generation Kmax). The results demonstrate that the multivariate dynamic process modelling technique presented using a grammar-based genetic programming (GBGP) provides a valuable tool for predicting the out puts with high levels of accuracy and identifying key operating variables for the full-scale KNR biological nutrient removal process. These modells are derived automatically in the form of understandable mathematical formulas that enable engineers to extract important knowledge hidden in the data and develop better operation and control strategies.

Multivariate Kalman filtering for spatio-temporal processes.

An increasing interest in models for multivariate spatio-temporal processes has been noted in the last years. Some of these models are very flexible and can capture both marginal and cross spatial associations amongst the components of the multivariate process. In order to contribute to the statistical analysis of these models, this paper deals with the estimation and prediction of multivariate spatio-temporal processes by using multivariate state-space models. In this context, a multivariate spatio-temporal process is represented through the well-known Wold decomposition. Such an approach allows for an easy implementation of the Kalman filter to estimate linear temporal processes exhibiting both short and long range dependencies, together with a spatial correlation structure. We illustrate, through simulation experiments, that our method offers a good balance between statistical efficiency and computational complexity. Finally, we apply the method for the analysis of a bivariate dataset on average daily temperatures and maximum daily solar radiations from 21 meteorological stations located in a portion of south-central Chile.Supplementary InformationThe online version contains supplementary material available at 10.1007/s00477-022-02266-3.

The Mediating Role of Competitiveness Between Entrepreneurial Challenges and Willingness of Female Business Graduates

This research examines the challenges of female business graduate entrepreneurs; we have developed a modified conceptual framework in which willingness to become an entrepreneur has been taken as a dependent variable. However, financial, cultural, marketing, and technological challenges are independent variables. Additionally, we incorporated competitiveness as a mediation variable between independent and dependent variables. The competitiveness could be beneficial to the female business graduates’ entrepreneurs and might be reduced by their financial, marketing, cultural, and technological challenges. The data was collected through a modified structured questionnaire from the entrepreneurs of female business graduates. The information was collected from Pakistan, India, Bangladesh, and Sri Lanka; we have collected 386 responses for the period from February 2021 to July 2021. We employed a structural equation modelingbased (SEM-based) multivariate approach and conditional process modeling for the data analysis. The findings of this research exhibit that the financial challenges, cultural challenges, marketing challenges, and technological challenges have a significant negative impact on female business entrepreneurs. These are the constraints that restrict female business graduates’ entrepreneurial opportunities. On the other hand, the mediation analysis showed that competitiveness has a positive and significant impact between financial challenges, cultural challenges, marketing challenges, & technological challenges, and willingness to become an entrepreneur. The perfect mediation of competitiveness established that the business success of SMEs does not rely on the individuals’ competencies and success factors only, but organizational competitiveness is equally essential for organizational performance.

Improving exoplanet detection power: Multivariate Gaussian process models for stellar activity

The radial velocity method is one of the most successful techniques for detecting exoplanets. It works by detecting the velocity of a host star, induced by the gravitational effect of an orbiting planet, specifically, the velocity along our line of sight which is called the radial velocity of the star. Low-mass planets typically cause their host star to move with radial velocities of 1 m/s or less. By analyzing a time series of stellar spectra from a host star, modern astronomical instruments can, in theory, detect such planets. However, in practice, intrinsic stellar variability (e.g., star spots, convective motion, pulsations) affects the spectra and often mimics a radial velocity signal. This signal contamination makes it difficult to reliably detect low-mass planets. A principled approach to recovering planet radial velocity signals in the presence of stellar activity was proposed by Rajpaul et al. (Mon. Not. R. Astron. Soc. 452 (2015) 2269–2291). It uses a multivariate Gaussian process model to jointly capture time series of the apparent radial velocity and multiple indicators of stellar activity. We build on this work in two ways: (i) we propose using dimension reduction techniques to construct new high-information stellar activity indicators; and (ii) we extend the Rajpaul et al. (Mon. Not. R. Astron. Soc. 452 (2015) 2269–2291) model to a larger class of models and use a power-based model comparison procedure to select the best model. Despite significant interest in exoplanets, previous efforts have not performed large-scale stellar activity model selection or attempted to evaluate models based on planet detection power. In the case of main sequence G2V stars, we find that our method substantially improves planet detection power, compared to previous state-of-the-art approaches.

The Impact of Proactive Environmental Strategy on Competitive and Sustainable Development of Organizations

The purpose of this research is to evaluate the impact of proactive environmental strategy, competitive differentiation advantage & cost-leadership competitive advantage for the competitive, sustainable development of an organization in terms of its performances, for instance, product strategy, production, process & financial performances. We incorporated technological eco-innovation as a mediating factor & corporate image as a moderator between exogenous & endogenous variables. We have collected 798 responses from China, India, Pakistan, Bangladesh, United Arab Emirates, and Vietnam. For the data analyses, we employed a structural equation modeling-based multivariate approach and conditional process modeling. The novelty and significance of the undertaken study rested in multifaceted outcomes; for instance, the proactive environmental strategy, the competitive advantage of differentiation & competitive advantage of cost leadership have a significant & positive impact on the sustainable development of an organization in terms of its performances, for example, product strategic, production & financial performances. The findings further demonstrate that technological eco-innovation as a mediating factor & corporate image as a moderating factor played vital and significant influencers between exogenous and endogenous variables. Finally, the Toda- Yamamoto causality showed the two-ways directionality between exogenous & endogenous variables. The outcomes have provided critical practical and societal implications for the industry and society. The companies may incorporate the environment as a cornerstone in short & longterm strategies for sustainable development. On the other hand, organizations may provide an eco-friendly environment to society.

Partial separability and functional graphical models for multivariate Gaussian processes

SummaryThe covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting challenging. For example, Gaussian graphical models have recently been extended to the setting of multivariate functional data by applying multivariate methods to the coefficients of truncated basis expansions. However, compared with multivariate data, a key difficulty is that the covariance operator is compact and thus not invertible. This paper addresses the general problem of covariance modelling for multivariate functional data, and functional Gaussian graphical models in particular. As a first step, a new notion of separability for the covariance operator of multivariate functional data is proposed, termed partial separability, leading to a novel Karhunen–Loève-type expansion for such data. Next, the partial separability structure is shown to be particularly useful in providing a well-defined functional Gaussian graphical model that can be identified with a sequence of finite-dimensional graphical models, each of identical fixed dimension. This motivates a simple and efficient estimation procedure through application of the joint graphical lasso. Empirical performance of the proposed method for graphical model estimation is assessed through simulation and analysis of functional brain connectivity during a motor task.

On multivariate copula modeling of dependent degradation processes

Multivariate degradation processes have been observed in many engineering systems. Most existing multivariate degradation modeling techniques, such as multivariate general path models or multivariate Wiener process models, assume an underlying Gaussian dependence structure. Unfortunately, in reality, the dependencies among degradation processes are often nonlinear, asymmetric and greatly tail-skewed, and thus limit the usefulness of the conventional modeling techniques in practice. To overcome these limitations, in this paper, we develop a copula-based multivariate modeling framework. Three fundamental copula classes are applied to model the complex dependence structure among correlated degradation processes. Statistical inference and model selection techniques, including two graphical diagnostic tools, a test of independence and a goodness-of-fit test, are employed to identify the best model. The advantages of the proposed modeling framework are demonstrated through simulation studies. And we also discuss the effect of ignoring tail dependence on system failure probability assessment. Finally, the applications of the copula-based multivariate degradation models on both system reliability evaluation and remaining useful life prediction are provided. The proposed methodology is illustrated using a numerical example.

Multivariate gaussian process incorporated predictive model for stream turbine power plant

Steam power turbine-based power plant approximately contributes 90% of the total electricity produced in the United States. Mainly steam turbine consists of multiple types of turbine, boiler, attemperator, reheater, etc. Power is produced through the steam with high pressure and temperature that is conducted by the turbines. The total power generation of the power plant is highly nonlinear considering all these elements in the model. We perform a predictive modeling approach to detect the power generation from these turbines by the Gaussian process (GP) model. As there are multiple interconnected turbines, we consider a multivariate Gaussian process (MGP) modeling to predict the power generation from these turbines which can capture the cross-correlations between the turbines. Also, the sensitivity analysis of the input parameters is constructed for each turbine to find out the most important parameters.

Energy ETF return jump contagion: a multivariate Hawkes process approach

Compared with investing in individual stocks, ETF investment is capable of diversifying the non-systematic risk or exposure to broad market or industry sectors. The aim of this paper is to develop a jump contagion modeling framework to understand the contagion effect of market jump events of energy sector ETFs using multivariate Hawkes process modeling approach. Through analyzing intraday high-frequency market data, we find that negative index jumps lead index price discovery processes, and their influences disappear faster than the positive index jumps in both the S&P500 and the crude oil futures. And on average, the self contagion in negative jumps is stronger than the self contagion in the positive jumps across all ETF groups. However, the ETFs focused on the master limited partnership (MLP) segment show less negative self contagion and relatively stronger positive self contagion than the other energy ETFs. Overall, the influence of negative jumps on ETFs from both the equity index and the energy future index is stronger than that of the positive jumps. And the influence of the equity index (S&P500) jump on ETFs lasts longer than that of the crude oil futures index (CLC1).

Nonstationary multivariate Gaussian processes for electronic health records

Advances in the modeling and analysis of electronic health records (EHR) have the potential to improve patient risk stratification, leading to better patient outcomes. The modeling of complex temporal relations across the multiple clinical variables inherent in EHR data is largely unexplored. Existing approaches to modeling EHR data often lack the flexibility to handle time-varying correlations across multiple clinical variables, or they are too complex for clinical interpretation. Therefore, we propose a novel nonstationary multivariate Gaussian process model for EHR data to address the aforementioned drawbacks of existing methodologies. Our proposed model is able to capture time-varying scale, correlation and smoothness across multiple clinical variables. We also provide details on two inference approaches: Maximum a posteriori and Hamilton Monte Carlo. Our model is validated on synthetic data and then we demonstrate its effectiveness on EHR data from Kaiser Permanente Division of Research (KPDOR). Finally, we use the KPDOR EHR data to investigate the relationships between a clinical patient risk metric and the latent processes of our proposed model and demonstrate statistically significant correlations between these entities.