Multivariate Markov Chain Model Research Articles

Incorporating Cyber Layer Failures in Composite Power System Reliability Evaluations

This paper proposes a novel approach to analyze the impacts of cyber layer failures (i.e., protection failures and monitoring failures) on the reliability evaluation of composite power systems. The reliability and availability of the cyber layer and its protection and monitoring functions with various topologies are derived based on a reliability block diagram method. The availability of the physical layer components are modified via a multi-state Markov chain model, in which the component protection and monitoring strategies, as well as the cyber layer topology, are simultaneously considered. Reliability indices of composite power systems are calculated through non-sequential Monte-Carlo simulation. Case studies demonstrate that operational reliability downgrades in cyber layer function failure situations. Moreover, protection function failures have more significant impact on the downgraded reliability than monitoring function failures do, and the reliability indices are especially sensitive to the change of the cyber layer function availability in the range from 0.95 to 1.

Synchronization of elastically coupled processive molecular motors and regulation of cargo transport.

The collective work of motor proteins plays an important role in cellular transport processes. Since measuring intermotor coupling and hence a comparison to theoretical predictions is difficult, we introduce the synchronization as an alternative observable for motor cooperativity. This synchronization can be determined from the ratio of the mean times of motor resting and stepping. Results from a multistate Markov chain model and Brownian dynamics simulations, describing the elastically coupled motors, coincide well. Our model can explain the experimentally observed effect of strongly increased transport velocities and powers by the synchronization and coupling of myosin V and kinesin I.

Bivariate Semi-Markov Process for Counterparty Credit Risk

We consider the problem of constructing an appropriate multivariate model to study counterparty credit risk in the credit rating migration problem. For this financial problem different multivariate Markov chain models were proposed. However, the Markovian assumption may be inappropriate for the study of the dynamics of credit ratings, which typically show non Markovian-like behavior. In this article, we develop a semi-Markov approach to study the counterparty credit risk by defining a new multivariate semi-Markov chain model. Methods are given for computing the transition probabilities, reliability functions and the price of a risky Credit Default Swap.

A New Multivariate Markov Chain Model for Adding a New Categorical Data Sequence

We propose a new multivariate Markov chain model for adding a new categorical data sequence. The number of the parameters in the new multivariate Markov chain model is only𝒪(3s) less than𝒪((s+1)2)the number of the parameters in the former multivariate Markov chain model. Numerical experiments demonstrate the benefits of the new multivariate Markov chain model on saving computational resources.

On Perturbation Bounds for the Joint Stationary Distribution of Multivariate Markov Chain Models

AbstractMultivariate Markov chain models have previously been proposed in for studying dependent multiple categorical data sequences. For a given multivariate Markov chain model, an important problem is to study its joint stationary distribution. In this paper, we use two techniques to present some perturbation bounds for the joint stationary distribution vector of a multivariate Markov chain with s categorical sequences. Numerical examples demonstrate the stability of the model and the effectiveness of our perturbation bounds.

A multivariate Markov Weather Model for O&M Simulation of Offshore Wind Parks

A multivariate Markov chain model is presented for generating sea state time series based on observed time series. The sea state is represented by the wave height, wind speed, wave period, wind direction and wave direction. Two ways of capturing the seasonal variation in the sea state parameters resulted in two distinct models. Their quality was assessed by comparing their statistical properties to what was obtained from observed time series. In one of the models (Model 1) transition probabilities were estimated separately for each month, while in the other (Model 2) a monthly transformation of the data were performed. Two different sea state data sets were considered in the validation, and it was found that both models compared favorably to the empirical data. It was concluded that Model 1 worked best for the longest data set considered, but was challenged by the shorter time series, where Model 2 worked best. Model 2 uses the observed data more efficiently, but relies on stationarity after removing the monthly variability. This seems to be a reasonable approximation for the data considered. The effect of changing the wave height resolution in the modeled time series was also investigated.

A New Improved Parsimonious Multivariate Markov Chain Model

We present a new improved parsimonious multivariate Markov chain model. Moreover, we find a new convergence condition with a new variability to improve the prediction accuracy and minimize the scale of the convergence condition. Numerical experiments illustrate that the new improved parsimonious multivariate Markov chain model with the new convergence condition of the new variability performs better than the improved parsimonious multivariate Markov chain model in prediction.

The strain-specific dynamics of Escherichia coli O157:H7 faecal shedding in cattle post inoculation

This study reports analysis of faecal shedding dynamics in cattle for three Escherichia coli O157:H7 (ECO157) strains (S1, S2 and S3) of different genotype and ecological history, using experimental inoculation data. The three strains were compared for their shedding frequency and level of ECO157 in faeces. A multistate Markov chain model was used to compare shedding patterns of S1 and S2. Strains S1 and S2 were detected seven to eight times more often and at 104 larger levels than strain S3. Strains S1 and S2 had similar frequencies and levels of shedding. However, the total time spent in the shedding state during colonization was on average four times longer for S1 (15 days) compared to S2 (4 days). These results indicate that an ECO157 strain effect on the frequency, level, pattern and the duration of faecal shedding may need to be considered in control of ECO157 in the cattle reservoir.

First order multivariate Markov chain model for generating annual weather data for Hong Kong

It becomes popular to use computer simulation technique to evaluate the performance of energy utilizations in buildings. The hourly weather data as simulation input is a crucial factor for the successful energy system simulation, and obtaining an accurate set of weather data is necessary to represent the long-term typical weather conditions throughout a year. This paper introduces a stochastic approach, which is called the first order multivariate Markov chain model, to generate the annual weather data for better evaluating and sizing different energy systems. The process for generating the weather data time series from the multivariate Markov transition probability matrices is described using 15-years actual hourly weather data of Hong Kong. The ability of this new model for retaining the statistical properties of the generated weather data series is examined and compared with the current existing TMY and TRY data. The main statistical properties used for this purpose are mean value, standard deviation, maximum value, minimum value, frequency distribution probability and persistency probability of the weather data sequence. The comparison between the observed weather data and the synthetically generated ones shows that the statistical characteristics of the developed set of weather data are satisfactorily preserved and the developed set of weather data can predict and evaluate different energy systems more accurately.

A Flexible Markov Chain Approach for Multivariate Credit Ratings

Modeling the dependence of credit ratings is an important issue for portfolio credit risk analysis. Multivariate Markov chain models are a feasible mathematical tool for modeling the dependence of credit ratings. Here we develop a flexible multivariate Markov chain model for modeling the dependence of credit ratings. The proposed model provides a parsimonious way to capture both the cross-sectional and temporal associations among ratings of individual entities. The number of model parameters is of the magnitude O(sm 2 + s 2 m), where m is the number of ratings categories and s is the number of entities in a credit portfolio. The proposed model is also easy to implement. The estimation method is formulated as a set of s linear programming problems and the estimation algorithm can be implemented easily in a Microsoft EXCEL worksheet, see Ching et al. Int J Math Educ Sci Eng 35:921---932 (2004). We illustrate the practical implementation of the proposed model using real ratings data. We evaluate risk measures, such as Value at Risk and Expected Shortfall, for a credit portfolio using the proposed model and compare the risk measures with those arising from Ching et al. IMRPreprintSeries (2007), Siu et al. Quant Finance 5:543---556 (2005).

PSA‐detected prostate cancer and the potential for dedifferentiation—estimating the proportion capable of progression

The aims were to determine whether prostate-specific antigen (PSA)-detected prostate cancers progress to higher Gleason score during the preclinical screen-detectable phase, and, if so, to estimate the proportion of tumours with progressive potential. We developed two multi-state Markov chain models to represent the natural history of two tumour populations, one with (Model I) and the other without (Model II) the potential for progression. For each, we derived the transition rates between the states and used these estimates to calculate the expected prevalence of preclinical low and intermediate-to-high Gleason score prostate cancers, using data from the Prostate Testing for Cancer and Treatment (ProtecT) study on 2,310 prostate cancers detected by PSA testing in 71,511 men 50-69 years. We compared the expected prevalence for each tumour population to that of the observed based on ProtecT and the European Randomised Study on Screening for Prostate Cancer (ERSPC)-Rotterdam Centre's first round screening data, the latter allowing independent assessment of the two models. The overall expected proportion of low Gleason score tumours was 0.56 under Model I and 0.81 under Model II, whereas the observed proportion based on either ProtecT or ERSPC-Rotterdam was 0.69. Using the observed prevalence from ERSPC-Rotterdam, we estimated that 22, 33 and 66% of the tumours in men aged 55-59, 60-64 and 65-69 years, respectively, had the potential for progression in the preclinical phase. PSA-detected prostate cancers are a mixture of progressive and non-progressive tumours with respect to Gleason score. The former may potentially benefit from screening. Identifying cancers with the potential for progression is important to target screening.

Multivariate Markov chain models for production planning

Markov models are commonly used in modelling many practical systems such as queueing networks, manufacturing systems and inventory systems. In this paper, we consider a multivariate Markov chain model for modelling multiple categorical data sequences. We develop new efficient estimation methods for the model parameters. We then apply the model and methods to demand predictions and production planning for a soft-drink company in Hong Kong. This problem is essentially a newsboy's problem in a multivariate Markov chain framework. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

An improved multivariate Markov chain model for credit risk

An improved multivariate Markov chain model for credit risk

Higher-order multivariate Markov chains and their applications

Markov chains are commonly used in modeling many practical systems such as queuing systems, manufacturing systems and inventory systems. They are also effective in modeling categorical data sequences. In a conventional n th order multivariate Markov chain model of s chains, and each chain has the same set of m states, the total number of parameters required to set up the model is O ( m ns ) . Such huge number of states discourages researchers or practitioners from using them directly. In this paper, we propose an n th-order multivariate Markov chain model for modeling multiple categorical data sequences such that the total number of parameters are of O ( ns 2 m 2 ) . The proposed model requires significantly less parameters than the conventional one. We develop efficient estimation methods for the model parameters. An application to demand predictions in inventory control is also discussed.

On a multivariate Markov chain model for credit risk measurement

In this paper, we use credibility theory to estimate credit transition matrices in a multivariate Markov chain model for credit rating. A transition matrix is estimated by a linear combination of the prior estimate of the transition matrix and the empirical transition matrix. These estimates can be easily computed by solving a set of linear programming (LP) problems. The estimation procedure can be implemented easily on Excel spreadsheets without requiring much computational effort and time. The number of parameters is O(s2 m2 ), where s is the dimension of the categorical time series for credit ratings and m is the number of possible credit ratings for a security. Numerical evaluations of credit risk measures based on our model are presented.

Multivariate Markov chain modeling for stock markets

We study a multivariate Markov chain model as a stochastic model of the price changes of portfolios in the framework of the mean field approximation. The time series of price changes are coded into the sequences of up and down spins according to their signs. We start with the discussion for small portfolios consisting of two stock issues. The generalization of our model to arbitrary size of portfolio is constructed by a recurrence relation. The resultant form of the joint probability of the stationary state coincides with Gibbs measure assigned to each configuration of spin glass model. Through the analysis of actual portfolios, it has been shown that the synchronization of the direction of the price changes is well described by the model.

A multivariate Markov chain model for categorical data sequences and its applications in demand predictions

Markov models are commonly used in modelling many practical systems such as telecommunication systems, manufacturing systems and inventory systems. In this paper we propose a multivariate Markov chain model for modelling multiple categorical data sequences. We develop efficient estimation methods for the model parameters. We then apply the model and method to demand predictions for a soft‐drink company in Hong Kong.

Multivariate Markovian modeling of tuberculosis: forecast for the United States.

We have developed a computer-implemented, multivariate Markov chain model to project tuberculosis (TB) incidence in the United States from 1980 to 2010 in disaggregated demographic groups. Uncertainty in model parameters and in the projections is represented by fuzzy numbers. Projections are made under the assumption that current TB control measures will remain unchanged for the projection period. The projections of the model demonstrate an intermediate increase in national TB incidence (similar to that which actually occurred) followed by continuing decline. The rate of decline depends strongly on geographic, racial, and ethnic characteristics. The model predicts that the rate of decline in the number of cases among Hispanics will be slower than among white non-Hispanics and black non-Hispanics a prediction supported by the most recent data.

00/00357 Effect of annealing on the electrical, optical and structural properties of hydrogenated amorphous silicon films deposited in an asymmetric R.F. plasma CVD system at room temperature

It becomes popular to use computer simulation technique to evaluate the performance of energy utilizations in buildings. The hourly weather data as simulation input is a crucial factor for the successful energy system simulation, and obtaining an accurate set of weather data is necessary to represent the long-term typical weather conditions throughout a year. This paper introduces a stochastic approach, which is called the first order multivariate Markov chain model, to generate the annual weather data for better evaluating and sizing different energy systems. The process for generating the weather data time series from the multivariate Markov transition probability matrices is described using 15-years actual hourly weather data of Hong Kong. The ability of this new model for retaining the statistical properties of the generated weather data series is examined and compared with the current existing TMY and TRY data. The main statistical properties used for this purpose are mean value, standard deviation, maximum value, minimum value, frequency distribution probability and persistency probability of the weather data sequence. The comparison between the observed weather data and the synthetically generated ones shows that the statistical characteristics of the developed set of weather data are satisfactorily preserved and the developed set of weather data can predict and evaluate different energy systems more accurately.

Source models for VBR broadcast-video traffic

Traffic from video services is expected to be a substantial portion of the traffic carried by emerging broadband integrated networks. For variable bit rate (VBR) coded video, statistical source models are needed to design networks that achieve acceptable picture quality at minimum cost and to design traffic shaping and control mechanisms. For video teleconference traffic Heyman et al. (1992) showed that traffic is sufficiently accurately characterized by a multistate Markov chain model that can be derived from three traffic parameters (mean, correlation, and variance). The present authors describe modeling results for sequences with frequent scene changes (the previously studied video teleconferences have very little scene variation) such as entertainment television, news, and sports broadcasts. The authors analyze 11 long sequences of broadcast video traffic data. Unlike video teleconferences, the different sequences studied have different details regarding distributions of cells per frame. The authors present source models applicable to the different sequences and evaluate their accuracy as predictors of cell losses in asynchronous transfer mode (ATM) networks. The modeling approach is the same for all of the sequences but use of a single model based on a few physically meaningful parameters and applicable to all sequences does not seem to be possible.