Markov Chain Method Research Articles

A Flexible Framework for Synthesizing Categorical Sequences with Application to Human Activity Patterns

The ability to synthesize realistic data in a parametrizable way is valuable for a number of reasons, including privacy, missing data imputation, and evaluating the performance of statistical and computational methods. When the underlying data generating process is complex, data synthesis requires approaches that balance realism and simplicity. In this paper, we address the problem of synthesizing sequential categorical data of the type that is increasingly available from mobile applications and sensors that record participant status continuously over the course of multiple days and weeks. We propose the paired Markov Chain (paired-MC) method, a flexible framework that produces sequences that closely mimic real data while providing a straightforward mechanism for modifying characteristics of the synthesized sequences. We demonstrate the paired-MC method on two datasets, one reflecting daily human activity (time use) patterns collected via a smartphone application, and one encoding the intensities of physical activity measured by wearable accelerometers. In both settings, sequences synthesized by paired-MC better capture key characteristics of the real data than alternative approaches. Supplemental materials for this article are available online.

Brazilian Road Bridge Management Based On Probabilistic Markov Process Deterioration Models

Objective: The objective of this study is to investigate the feasibility of applying the Markov chain method, with the aim of obtaining deterioration models for road bridges in Brazil. Theoretical Framework: The concept of Condition Index (CI), the determination of the probability transition matrix and deterioration models based on Markov chains are presented. Method: The methodology is based on inspection records of highway bridges inspected by the Agência Nacional de Transporte Terrestre (ANTT) in three sections of different federal highways, based on annual records of condition indexes from 2010 to 2016. Results and Discussion: The deterioration models indicate that in the bridges of the analyzed highway sections, BR-040/MG/RJ, BR-101/RJ and BR-116/BA, the transition from CI=4 to CI=3 is observed in 10 years. The bridges on the BR-040/MG/RJ highway also drop from maximum CI=5 to CI=3 in just 10 years. Research Implications: The results obtained can be applied or influence practices in the field of Transportation Engineering in Brazil. The implications cover the passenger and cargo transportation sectors. Originality/Value: The study uses real data from inspections of highway bridges from a specific period of time. The relevance and value of this research are evidenced by the achievement of bridge deterioration models, which constitute fundamental tools for planning, managing and preparing public works concession notices.

The structure of the Hungarian insurance market and the invariant distribution of market shares

The Hungarian economy exhibits a notable underinsurance phenomenon, with insurance penetration at a mere 2.8%, significantly lower than the European Union average of 8%. This situation indicates substantial growth potential within the Hungarian insurance market, particularly in the life and non-life insurance sectors, contingent upon the development of solvent demand and favorable demand-stimulating factors. Anticipated transformations in the structure of the Hungarian insurance market may arise due to both endogenous and exogenous influences, likely resulting in heightened market concentration and alterations in competitive dynamics. This study aims to conduct an analysis of the historical and expected future transformations of the Hungarian insurance market structure by utilizing publicly available data on gross premium income. The analysis employs traditional market structure indicators, such as market shares, concentration ratios, and the Herfindahl-Hirschman Index (HHI), while also examining market share transitions through the application of the Markov chain method. Markov transition probabilities offer a more accurate representation of historical market structure processes compared to conventional market structure indicators. Furthermore, the calculation of these transition probabilities facilitates the prediction of anticipated future changes in market shares. The stationary (ergodic) distribution of market shares, derived from the transition probability matrix, denotes a market share distribution toward which the market converges under stable conditions. This approach also enables the computation of an equilibrium market share distribution achievable in the future under specified conditions, driven by the internal mechanisms of the market. The analysis reveals an upward trend in the market shares of larger companies and an increase in market concentration across both the life and non-life insurance sectors in Hungary. Traditional methods of indirect measurement indicate a prospective rise in market concentration and a potential decline in competitive conditions. However, when considering stationarity, the invariant distributions estimated via the Markov chain methodology suggest a decrease in the market shares of the largest companies, accompanied by a leveling effect among leading firms. This indicates that, assuming unchanged conditions over the past decade, the intrinsic processes of the market could lead to a less concentrated market structure in both the life and non-life insurance sectors of the Hungarian insurance market. Removing the stationarity assumption presents new opportunities for determining the equilibrium state of the insurance market under specific conditions. Future research will venture further in this direction. The objective is to develop a model capable of indirectly measuring market power, which will provide essential insights for competition authorities and management of market participants, even within asymmetric information contexts, regarding the anticipated trajectory of market structure transformation.

Optimal Design of One-Sided Exponential Adaptive EWMA Scheme Based on Median Run Length

High-quality processes, characterized by low defect rates, typically exhibit an exponential distribution for time-between-events (TBE) data. To effectively monitor TBE data, one-sided exponential Adaptive Exponentially Weighted Moving Average (AEWMA) schemes are introduced. However, the run length (RL) distribution varies with the magnitude of the process mean shift, rendering the median run length (MRL) a more pertinent performance metric. This paper investigates the RL properties of one-sided exponential AEWMA schemes using a Markov chain method. An optimal design procedure based on MRL is developed to enhance the one-sided exponential AEWMA scheme. Comparative analyses reveal that the one-sided exponential AEWMA scheme provides better balanced protection against both minor and major shifts in the process mean compared to EWMA-type and Shewhart schemes. Finally, two practical case studies illustrate the application of AEWMA schemes in manufacturing.

Reliability Assessment of Competitive Failure Systems Based on Three Parameter Weibull Distribution and Wiener Process

Considering the competitive failure that exists in the operation of industrial systems, including degradation failure and sudden failure, this paper presents a reliability assessment method based on the three-parameter Weibull distribution and the Wiener process. Nonlinear functions are proposed to establish the relationship between the different failure processes, and the reliability model is derived. The Metropolis-Hastings (MH) sampling algorithm of the Monte Carlo Markov Chain (MCMC) method is employed to estimate the parameters in this study. The reliability assessment results are obtained by the real degradation samples. The results show that the reliability model incorporating the three-parameter Weibull distribution produces more comprehensive and dependable results. Furthermore, MH sampling can solve the issues of complex likelihood functions that cannot directly obtain parameter evaluation results. Additionally, this paper analyzes the sensitivity of the model parameters, thereby offering theoretical support for enhancing the safe operation of the system.

How Sticky is the Per Capita Income?

In our settlement-level study using the Markov chain method and dynamic regression panel models, we found that in the period 2011-2021, income in the previous year strongly affects income status, i.e., income shows high persistence. Despite the steady increase in per capita income over the period under study, the spatial structure of the income distribution shows a fixed state, with a high degree of stability: poor municipalities remain poor, while rich municipalities remain rich. Only in the Central and Western Transdanubian regions is there a greater chance of a municipality's population moving into a higher income category. The results of the regression models show that, in addition to the income level of previous years, the higher number of self-employed, the greater distance of settlements from cities and Budapest, the employment structure and the higher share of job seekers have a significant impact on the income of the population.

Calculating Insurance Premiums for Stroke Patients Using the Multistate Markov Chain Method

Health insurance premium is one of the important elements in the insurance industry that needs to be calculated correctly so that insurance companies can minimize risks and losses. In this study, insurance premiums for stroke patients are calculated by utilizing the Markov Chain method. This method is used to model the movement of a patient's health condition over time, considering various conditions such as recovery, relapse, or death. Each condition is represented by a state in the Markov Chain model, and the transition between states is calculated based on patient history data and transition probabilities. Based on the modeling results, a more accurate premium estimation is obtained compared to conventional methods, as it is able to consider the dynamics of changing health conditions. This research provides important insights for the insurance industry in risk management as well as more optimal premium calculations for patients with chronic diseases such as stroke.

PERAMALAN HARGA SAHAM PT UNILEVER INDONESIA MENGGUNAKAN FUZZY TIME SERIES MARKOV CHAIN ABSOLUTE DIFFERENCES K-MEANS CLUSTERING DAN FUZZY TIME SERIES MARKOV CHAIN TREE PARTITION METHOD

Stocks are an investment instrument that is in high demand and can provide large profits for investors, especially stocks from large and popular companies, such as PT Unilever Indonesia. However, the boycott action causes its share price to tend to decline and makes it difficult for investors to make investment decisions. In this research, the development of the Fuzzy Time Series Markov Chain (FTSMC) method, namely Fuzzy Time Series Markov Chain Absolute Differences K-Means Clustering (FTSMC-ADKC) and Fuzzy Time Series Markov Chain Tree Partition Method (FTSMC-TPM) is used in forecasting the stock price of PT Unilever Indonesia. Both methods have a good ability to forecast volatile time series data and do not require data distribution assumptions such as classical forecasting methods. Furthermore, the accuracy of the two methods is compared through the Mean Absolute Percentage Error (MAPE) value, resulting in FTSMC-ADKC being more accurate with a MAPE of 0.71% compared to FTSMC-TPM with a MAPE of 1.21%. By using FTSMC-ADKC, the closing price of PT Unilever Indonesia shares on March 27, 2024 is estimated to be Rp2724.46, which has decreased from the previous day.

Markov Chain Method for Calculating Insurance Premiums

Markov Chain Method for Calculating Insurance Premiums

Assessment of cloud service trusted state based on fuzzy entropy and Markov chain

In the era of cloud service popularization, the trustworthiness of service is particularly important. If users cannot prevent the potential trustworthiness problem of the service during long-term use, once the trustworthiness problem occurs, it will cause significant losses. In order to objectively assess the cloud service trustworthiness, and predict its change, this paper establishes a special hierarchical model of cloud service trustworthiness attributes. This paper proposes corresponding management countermeasures around the model, defines the cloud service trustworthiness level, defines the cloud service trusted state based on fuzzy entropy and Markov chain, constructs the membership function of the cloud service trusted state, and realizes the assessment of cloud service trustworthiness and its changes according to the prediction method of Markov chain. Through case analysis and method comparison, it shows that the method proposed in this paper is effective and feasible. This method can provide objective and comprehensive assessment data for the cloud service trustworthiness and its change, makes up the deficiency of fuzzy entropy assessment method. This research has important reference value and significance for the research of cloud service trustworthiness assessment.

Instrument Selection in Panel Data Models with Endogeneity: A Bayesian Approach

This paper proposes the use of Bayesian inference techniques to search for and obtain valid instruments in dynamic panel data models where endogenous variables may exist. The use of Principal Component Analysis (PCA) allows for obtaining a reduced number of instruments in comparison to the high number of instruments commonly used in the literature, and Monte Carlo Markov Chain (MCMC) methods enable efficient exploration of the instrument space, deriving accurate point estimates of the elements of interest. The proposed methodology is illustrated in a simulated case and in an empirical application, where the partial effect of a series of determinants on the attraction of international bank flows is quantified. The results highlight the importance of promoting and developing the private sector in these economies, as well as the importance of maintaining good levels of creditworthiness.

Degree Distribution of Evolving Network with Node Preference Deletion

Discussing evolutionary network models and corresponding degree distributions under different mechanisms is applied basic research in network science. This study proposes a new evolutionary network model, which integrates node preference deletion and edge reconnection mechanisms and is also an extension of the existing evolutionary network model. In order to analyze the key statistical property of the model, the steady-state distribution, we propose a Markov chain method based on the enhanced stochastic process rule (ESPR). The ESPR method makes the evolving network’s topological structure and statistical properties consistent with those observed in the natural evolution process, ensures the theoretical results of the degree distribution of the evolving network model, and overcomes the limitations of using empirical methods for approximate analysis. Finally, we verify the accuracy of the steady-state distribution and tail feature estimation of the model through Monte Carlo simulation. This work has laid a solid theoretical foundation for the future development of evolutionary network models and the study of more complex network statistical properties.

An Assessment of Markov Chain as a Predictive Tool for the Global Performance of an Institution of Higher Learning

The Markov chain (MC) technique is used to make prediction of the ranking of a university in South Africa. The ranking is approached as a stochastic variable. The data were extracted from Scimago in the prediction process. A university was randomly selected to evaluate the level of prediction of the MC method. The university was relatively low ranked. The MC states for this study were adopted from a previous one, based on performance brackets. The Markov chain displayed a satisfactory level of prediction for the probability of a university moving from one level to another. The distribution of university rankings could be well defined to determine the performance of a university.

Hybrid energy management strategy based on neural networks robust to fluctuations in operational load

Hybrid energy management strategy based on neural networks robust to fluctuations in operational load

A game theoretic complex network model to estimate the epidemic threshold under individual vaccination behaviour and adaptive social connections

In today’s interconnected world, the spread of information is closely linked to infectious disease dynamics. Public awareness plays a crucial role, as individual vaccination decisions significantly impact collective efforts to combat emerging health threats. This study explores disease transmission within a framework integrating social connections, information sharing, and individual vaccination decisions. We introduce a behaviour-prevalence model on an adaptive multiplex network, where the physical layer (Layer-II) captures disease transmission under vaccination. In contrast, the virtual layer (Layer-I) represents adaptive social contacts and the flow of information, shaping vaccination decisions within a socially influenced environment. We derive analytical expressions for the epidemic threshold using the microscopic Markov Chain Method (MMCM). Simulation results highlight that adaptive social contacts lead to a higher epidemic threshold than non-adaptive networks. Additionally, network characteristics, such as the power-law exponent in scale-free networks, significantly impact infection spread within populations. Our results reveal that changes in perceived infection risk and an individual’s sensitivity to non-vaccinated neighbour’s status strongly influence vaccine uptake across populations. These insights can guide public health officials in developing targeted vaccination programs that address the evolving dynamics of social connections, information dissemination, and vaccination choice in the digital era.

A Spatial–Temporal Bayesian Model for a Case-Crossover Design with Application to Extreme Heat and Claims Data

Epidemiological approaches for examining human health responses to environmental exposures in observational studies frequently address confounding by employing advanced matching techniques and statistical methods grounded in conditional likelihood. This study incorporates a recently developed Bayesian hierarchical spatiotemporal model within a conditional logistic regression framework to capture the heterogeneous effects of environmental exposures in a case-crossover (CCO) design. Spatial and temporal dependencies are modeled through random effects incorporating multivariate conditional autoregressive priors. Flexible frailty structures are introduced to explore strategies for managing temporal variables. Parameter estimation and inference are conducted using a Monte Carlo Markov chain method within a Bayesian framework. Model fit and optimal model selection are evaluated using the deviance information criterion. Simulations assess and compare model performance across various scenarios. Finally, the approach is illustrated with workers’ compensation claims data from New York and Florida to examine spatiotemporal heterogeneity in hospitalization rates related to heat prostration.

The spatio-temporal characteristics and dynamic evolution of coupling and coordinated development of innovation factor allocation and green economy in China

IntroductionMeasuring the coupling coordination degree between the innovation factor allocation system and the green economy development system, and deeply exploring the changing trends in the coupling coordination between innovation factors allocation, including their subsystems, and green economy development, are essential prerequisites for achieving a high degree of coupling coordination between the two systems.MethodsThis paper, based on panel data from 30 provincial regions in China from 2013 to 2022, measures the coupling coordination degree between innovation factor allocation and green economy development, including their subsystems, and explores the spatial differentiation characteristics of this coupling coordination across the provinces in China and its three major regions. First, an evaluation index system for the innovation factor allocation system and the green economy development system is constructed from both input and output perspectives. The entropy weighted TOPSIS method and the coupling coordination degree model are then employed to explore the temporal characteristics of the coupling coordination between innovation factor allocation and green economy development. Second, Dagum's Gini coefficient is used to reveal the directional distribution of coupling coordination and the sources of spatial disparities. Third, kernel density estimation and spatial Markov chain methods are applied to uncover the dynamic evolution of this coupling coordination.Results and discussionThe study finds that the overall coupling coordination degree between innovation factor allocation and green economy development in China is relatively low, but it exhibits a continuous upward trend. From the perspective of regional disparities, the coupling level between innovation factor allocation and green economy development across Chinese provinces shows an imbalanced spatial distribution, characterized by higher levels in the east and lower levels in the west, with spatial disparities tending to widen. Inter-regional differences are the primary source of these spatial disparities, followed by intra-regional differences. While internal disparities within Eastern China are narrowing, they are expanding within the Central and Western China. The development processes in these regions are often influenced by neighboring spatial spillover effects. Finally, recommendations are proposed to enhance the coupling coordination degree between innovation factor allocation and green economy development in China.

Modeling the delay propagation dynamics in high-speed railway networks with a traffic-driven SIS epidemic model

The propagation of delays is a prevalent issue in high-speed railway (HSR) networks. However, the underlying properties of delay propagation have not been fully explored, hindering the effective management of this problem. In this paper, considering the impact of traffic flow, we model the delay propagation as a traffic-driven susceptible–infected–susceptible (SIS) epidemic spreading process. We introduce a traffic frequency matrix to estimate the traffic rate and further derive the propagation dynamic equations using a continuous-time Markov chain method. We then derive the epidemic threshold of the model, which is proportional to the recovery rate and inversely proportional to the average path length. Finally, through simulation, we study the impacts of various factors including the infection rate, recovery rate, and the degree and number of initial delay stations. Our work provides some insights for the prediction and control of delay propagation in HSR networks.

A novel construction and evaluation framework for driving cycle of electric vehicles based on energy consumption and emission analysis

A novel construction and evaluation framework for driving cycle of electric vehicles based on energy consumption and emission analysis

The X-ray re-brightening of GRB afterglow revisited: a possible signature from activity of the central engine

ABSTRACT Long-duration gamma-ray bursts (GRBs) are thought to be from core collapse of massive stars, and a rapidly spinning magnetar or black hole may be formed as the central engine. The extended emission in the prompt emission, flares, and plateaus in X-ray afterglow, are proposed to be as the signature of central engine re-activity. However, the direct evidence from observations of identifying the central engines remains an open question. In this paper, we systemically search for long-duration GRBs that consist of bumps in X-ray afterglow detected by Swift/XRT and find that the peak time of the X-ray bumps exhibit bimodal distribution (defined as ‘early’ and ‘late’ bumps) with division line at $t=7190$ s. Although we cannot rule out that such a bimodality arises from selection effects. We proposed that the long-duration GRBs with an early (or late) bumps may be originated from the fall-back accretion onto a new-born magnetar (or black hole). By adopting Monte Carlo Markov Chain (MCMC) method to fit the early (or late) bumps of X-ray afterglow with the fall-back accretion of magnetar (or black hole), it is found that the initial surface magnetic field and period of magnetars for most early bumps are clustered around $5.88\times 10^{13}$ G and 1.04 ms, respectively. Meanwhile, the derived accretion mass of black hole for late bumps is in the range of $[4\times 10^{-4}, 1.8\times 10^{-2}]\,{\rm M}_{\odot }$, and the typical fall-back radius is distributed range of $[1.04, 4.23]\times 10^{11}$ cm, which is consistent with the typical radius of a Wolf–Rayet star. However, we also find that the fall-back accretion magnetar model is disfavoured by the late bumps, but the fall-back accretion of black hole model cannot be ruled out to interpret the early bumps of X-ray afterglow.