Asymptotic Properties of the Markov Chain Model method of finding Markov chains Generators of Empirical Transition Matrices in Credit Ratings Applications

As practitioners we are interested in the likelihood of the population containing a copy of the optimum. The dynamic systems approach, however, does not help us to calculate that quantity. Markov chain analysis can be used in principle to calculate the quantity. However, since the associated transition matrices are enormous even for modest problems, it follows that in practice these calculations are usually computationally infeasible. Therefore, some improvements on this situation are desirable. In this paper, we present a method for modeling the behavior of finite population evolutionary algorithms (EAs), and show that if the population size is greater than 1 and much less than the cardinality of the search space, the resulting exact model requires considerably less memory space for theoretically running the stochastic search process of the original EA than the Nix and Vose-style Markov chain model. We also present some approximate models that use still less memory space than the exact model. Furthermore, based on our models, we examine the selection pressure by fitness-proportionate selection, and observe that on average over all population trajectories, there is no such strong bias toward selecting the higher fitness individuals as the fitness landscape suggests.

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Determination of the Order of a Markov Chain for Daily Rainfall Data of North East India: "Application AIC criterion"

Journal of Applied and Natural Science ◽

10.31018/jans.v10i1.1583 ◽

2018 ◽

Vol 10 (1) ◽

pp. 80-87

Author(s):

Surobhi Deka

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Akaike Information Criterion ◽

Markov Chain Model ◽

Information Criterion ◽

Chain Model ◽

Adequate Model ◽

First Order ◽

North East India ◽

North East

The paper aims at demonstrating the application of the Akaike information criterion to determine the order of two state Markov chain for studying the pattern of occurrence of wet and dry days during the rainy season (April to September) in North-East India. For each station, each day is classified as dry day if the amount of rainfall is less than 3 mm and wet day if the amount of rainfall is greater than or equal to 3 mm. We apply Markov chain of order up to three to the sequences of wet and dry days observed at seven distantly located stations in North East region of India. The Markov chain model of appropriate order for analyzing wet and dry days is determined. This is done using the Akaike Information Criterion (AIC) by checking the minimum of AIC estimate. Markov chain of order one is found to be superior to the majority of the stations in comparison to the other order Markov chains. More precisely, first order Markov chain model is an adequate model for the stations North Bank, Tocklai, Silcoorie, Mohanbari and Guwahati. Further, it is observed that second order and third order Markov chains are competing with first order in the stations Cherrapunji and Imphal, respectively. A fore-knowledge of rainfall pattern is of immense help not only to farmers, but also to the authorities concerned with planning of irrigation schemes. The outcomes are useful for taking decisions well in advance for transplanting of rice as well as for other input management and farm activities during different stages of the crop growing season.

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Hospital patients arrival prediction using Markov chain model method

2016 4th International Conference on Cyber and IT Service Management ◽

10.1109/citsm.2016.7577590 ◽

2016 ◽

Cited By ~ 2

Author(s):

Alwis Nazir ◽

Lia Anggraini ◽

Lola Octavia ◽

Fadhilah Syafria

Keyword(s):

Markov Chain ◽

Markov Chain Model ◽

Chain Model ◽

Model Method ◽

Hospital Patients

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Higher order Markov Chain Model for Synthetic Generation of Daily Streamflows

TEMA (São Carlos) ◽

10.5540/tema.2018.019.03.449 ◽

2018 ◽

Vol 19 (3) ◽

pp. 449

Author(s):

A. G. C. Pereira ◽

F. A. S. Sousa ◽

B. B. Andrade ◽

Viviane Simioli Medeiros Campos

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Markov Chain Model ◽

Chain Model ◽

Order Markov Chain ◽

Chain Order ◽

Higher Order Markov Chain ◽

Best Fit ◽

Synthetic Generation ◽

Better Than

The aim of this study is to get further into the two-state Markov chain model for synthetic generation daily streamflows. The model proposed in Aksoy and Bayazit (2000) and Aksoy (2003) is based on a two Markov chains for determining the state of the stream. The ascension curve of the hydrograph is modeled by a two-parameter Gamma probability distribution function and is assumed that a recession curve of the hydrograph follows an exponentially function. In this work, instead of assuming a pre-defined order for the Markov chains involved in the modelling of streamflows, a BIC test is performed to establish the Markov chain order that best fit on the data. The methodology was applied to data from seven Brazilian sites. The model proposed here was better than that one proposed by Aksoy but for two sites which have the lowest time series and are located in the driest regions.

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Nonlinear Markov Chain Modelling of the Novel Coronavirus (Covid-19) Pandemic

10.1101/2020.04.21.20073668 ◽

2020 ◽

Author(s):

Muammer Catak ◽

Necati Duran

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Markov Chain Model ◽

Chain Model ◽

The Novel ◽

The World ◽

The Usa ◽

Novel Coronavirus ◽

Almost All ◽

Markov Chain Modelling

Almost all countries around the world are struggling against the novel coronavirus (Covid-19) pandemic. In this paper, a nonlinear Markov chains model is proposed in order to analyse and to understand the behaviour of the Covid-19 pandemic. The data from China was used to build up the presented model. Thereafter, the nonlinear Markov chain model is employed to estimate the daily new Covid-19 cases in some countries including Italy, Spain, France, UK, the USA, Germany, Turkey, and Kuwait. In addition, the correlation between the daily new Covid-19 cases and the daily number of deaths is examined.

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Markov chain based modelling and prediction of natural gas allocation structure in Pakistan

International Journal of Energy Sector Management ◽

10.1108/ijesm-12-2019-0002 ◽

2020 ◽

Vol 14 (5) ◽

pp. 911-933

Author(s):

Hussaan Ahmad ◽

Nasir Hayat

Keyword(s):

Markov Chain ◽

Natural Gas ◽

Polynomial Regression ◽

Markov Chain Model ◽

Chain Model ◽

Transition Matrices ◽

Allocation Pattern ◽

Content Type ◽

Structural Prediction ◽

Order Polynomial

Purpose The purpose of this paper is to analyze the historical gas allocation pattern for seeking appropriate arrangement and utilization of potentially insufficient natural gas supply available in Pakistan up to 2030. Design/methodology/approach This study presents Markov chain-based modeling of historical gas allocation data followed by its validation through error evaluation. Structural prediction using classical Chapman–Kolmogorov method and varying-order polynomial regression in the historical transition matrices are presented. Findings Markov chain model reproduces the terminal state vector with 99.8 per cent accuracy, thus demonstrating its validity for capturing the history. Lower order polynomial regression results in better structural prediction compared with higher order ones in terms of closeness with Markov approach-based prediction. Research limitations/implications The data belongs to a certain geographic region with specific gas demand and supply profile. The proposition may be tested further by researchers to check the validity for other comparable structural predictions/analyses. Practical implications This study can facilitate policy-making in the field of natural gas allocation and management in Pakistan specifically and other comparable countries generally. Originality/value Two major literature gaps filled through this study are: first, Markov chain model becomes stationary when projected using Chapman–Kolmogorov relation in terms of a fixed, average transition matrix resulting in an equilibrium state after a finite number of future steps. Second, most of the previous studies analyze various gas consumption sectors individually, thus lacking integrated gas allocation policy.

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A Comparison of Stochastic Models for the Interarrival Times of Packets in a Computer Network

Optimal Information Modeling Techniques ◽

10.4018/978-1-931777-09-4.ch023 ◽

2011 ◽

pp. 248-257 ◽

Cited By ~ 1

Author(s):

Dennis Guster ◽

Semyon Litvinov ◽

Mary Richardson ◽

David Robinson

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Power Law ◽

Stochastic Models ◽

Computer Network ◽

Markov Chain Model ◽

Actual Data ◽

Chain Model ◽

Power Law Process ◽

Simulation Techniques

Because of the complexity and over-subscription of today’s networks, the importance of valid simulation techniques to aid in determining sound network design is paramount. A number of studies have shown that the theoretical exponential packet interarrival rates are not appropriate for many network installations. This chapter compares two other modeling techniques: the power law process and Markov chains to the exponential and actual data taken from a ten-minute segment. The results reveal that the exponential and power law models are a poor match to the actual data. The Markov chain model, although not perfect, yielded some promising results.

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Application of Markov Chains to Identification of Turbine Engine Dynamic Models

Volume 2: Turbo Expo 2002, Parts A and B ◽

10.1115/gt2002-30038 ◽

2002 ◽

Cited By ~ 2

Author(s):

V. Yu. Arkov ◽

G. G. Kulikov ◽

T. V. Breikin

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Gas Turbines ◽

Dynamic Models ◽

Markov Chain Model ◽

Dynamic Modelling ◽

Parametric Models ◽

Chain Model ◽

Model Estimation ◽

Identifiability Analysis

The paper addresses the problem of dynamic modelling of gas turbines for condition monitoring purposes. Identification of dynamic models is performed using a novel Markov chain technique. This includes identifiability analysis and model estimation. When identifying the model, experimental data should be sufficiently informative for identification. So far, identifiability analysis is weak formed and workable solutions are still to be developed. A possible technique is proposed based on non-parametric models in the form of controllable Markov chains. The second step in systems identification is the model estimation. At this stage, Markov chains are introduced to provide more functionality and versatility for dynamic modelling of gas turbines. The Markov chain model combines the deterministic and stochastic components of the engine dynamics within a single model, thus providing more exact and adequate description of the real system behaviour and leading to far more accurate health monitoring.

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Semantic-Enhanced Multi-Dimensional Markov Chains on Semantic Trajectories for Predicting Future Locations

Sensors ◽

10.3390/s18103582 ◽

2018 ◽

Vol 18 (10) ◽

pp. 3582 ◽

Cited By ~ 7

Author(s):

Antonios Karatzoglou ◽

Dominik Köhler ◽

Michael Beigl

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Markov Chain Model ◽

Predictive Performance ◽

Chain Model ◽

Semantic Level ◽

Trajectory Mining ◽

Solid Foundation ◽

Semantic Similarity Analysis ◽

High Level

In this work, we investigate the performance of Markov Chains with respect to modelling semantic trajectories and predicting future locations. In the first part, we examine whether and to what degree the semantic level of semantic trajectories affects the predictive performance of a spatial Markov model. It can be shown that the choice of the semantic level when describing trajectories has a significant impact on the accuracy of the models. High-level descriptions lead to better results than low-level ones. The second part introduces a multi-dimensional Markov Chain construct that considers, besides locations, additional context information, such as time, day and the users’ activity. While the respective approach is able to outperform our baseline, we could also identify some limitations. These are mainly attributed to its sensitivity towards small-sized training datasets. We attempt to overcome this issue, among others, by adding a semantic similarity analysis component to our model that takes the varying role of locations due each time to the respective purpose of visiting the particular location explicitly into consideration. To capture the aforementioned dynamics, we define an entity, which we refer to as Purpose-of-Visit-Dependent Frame (PoVDF). In the third part of this work, we describe in detail the PoVDF-based approach and we evaluate it against the multi-dimensional Markov Chain model as well as with a semantic trajectory mining and prefix tree based model. Our evaluation shows that the PoVDF-based approach outperforms its competition and lays a solid foundation for further investigation.

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On convergence to diffusion processes of Markov chains related to population genetics

Advances in Applied Probability ◽

10.1017/s0001867800032985 ◽

1979 ◽

Vol 11 (04) ◽

pp. 673-700

Author(s):

Norio Okada

Keyword(s):

Population Genetics ◽

Markov Chain ◽

Natural Selection ◽

Diffusion Process ◽

Diffusion Processes ◽

Markov Chain Model ◽

Asymptotic Properties ◽

Chain Model ◽

Selection Effects ◽

Successive Generations

A Markov chain model related to population genetics and its convergence to a diffusion process on the multi-dimensional bounded domain are treated. We discuss the case where natural selection is random and the different selection effects over successive generations are independent. Our model is a multi-allelic version of the haploid model of Karlin and Levikson. The asymptotic properties of the limiting diffusion are stated.

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