Maintainability of structures in Markov chain models under recruitment control

1975 ◽  
Vol 12 (2) ◽  
pp. 376-382 ◽  
Author(s):  
G. S. Davies
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Chain Model ◽  
Fixed Size ◽  
Markov Chain Models ◽  
The Family

We consider a fixed size Markov chain model which suffers losses and admits controlled recruitment. The family of n-step maintainable structures is described geometrically and examined.

Maintainability of structures in Markov chain models under recruitment control

1975 ◽  
Vol 12 (02) ◽  
pp. 376-382 ◽  
Author(s):  
G. S. Davies
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Chain Model ◽  
Fixed Size ◽  
Markov Chain Models ◽  
The Family

We consider a fixed size Markov chain model which suffers losses and admits controlled recruitment. The family of n-step maintainable structures is described geometrically and examined.

Manifest and Latent Markov Chain Models for Categorical Panel Data

1988 ◽  
Vol 13 (4) ◽  
pp. 299-312 ◽  
Author(s):  
Rolf Langeheine
Keyword(s):  
Markov Chain ◽  
Discrete Time ◽  
Markov Chain Model ◽  
Order Effects ◽  
Chain Model ◽  
Continuous Time Markov Chain ◽  
Discrete Time Markov Chain ◽  
Markov Chain Models ◽  
Starting Point ◽  
Recent Developments

The starting point of this paper is a 3 × 3 × 3 table of repeated behavior ratings of children, which has been previously analyzed by Plewis (1981) using manifest discrete time and continuous time Markov chain models. Potential reasons for the ubiquitous misfit of the manifest discrete time Markov chain model are outlined. It is proposed, instead, to make use of more recent developments in latent discrete time Markov chain modeling that simultaneously address the main problems of heterogeneity, measurement error, stationarity, and order effects.

MARKOV CHAIN MODELING AND ANALYSIS OF COMPLICATED PHENOMENA IN COUPLED CHAOTIC OSCILLATORS

2010 ◽  
Vol 19 (04) ◽  
pp. 801-818 ◽  
Author(s):  
YOSHIFUMI NISHIO ◽  
YUTA KOMATSU ◽  
YOKO UWATE ◽  
MARTIN HASLER
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Chain Model ◽  
Chaotic Oscillators ◽  
Modeling And Analysis ◽  
Markov Chain Models ◽  
Simulation Results ◽  
Markov Chain Modeling

In this paper, we propose a Markov chain modeling of complicated phenomena observed from coupled chaotic oscillators. Once we obtain the transition probability matrix from computer simulation results, various statistical quantities can be easily calculated from the model. It is shown that various statistical quantities are easily calculated by using the Markov chain model. Various features derived from the Markov chain models of chaotic wandering of synchronization states and switching of clustering states are compared with those obtained from computer simulations of original circuit equations.

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

2013 ◽  
Vol 3 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Wen Li ◽  
Lin Jiang ◽  
Wai-Ki Ching ◽  
Lu-Bin Cui
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Categorical Data ◽  
Markov Chain Model ◽  
Chain Model ◽  
Perturbation Bounds ◽  
Markov Chain Models ◽  
Joint Stationary Distribution ◽  
Distribution Vector ◽  
The Stability

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.

scholarly journals Markov Chain Models for Hydrological Drought Characteristics

2012 ◽  
Vol 13 (1) ◽  
pp. 298-309 ◽  
Author(s):  
Dilek Eren Akyuz ◽  
Mehmetcik Bayazit ◽  
Bihrat Onoz
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Second Order ◽  
Chain Model ◽  
Return Periods ◽  
Annual Streamflow ◽  
Drought Duration ◽  
Drought Characteristics ◽  
Markov Chain Models ◽  
Order Markov Chain

Abstract Estimation of drought characteristics such as probabilities and return periods of droughts of various lengths is of major importance in drought forecast and management and in solving water resources problems related to water quality and navigation. This study aims at applying first- and second-order Markov chain models to dry and wet periods of annual streamflow series to reproduce the stochastic structure of hydrological droughts. Statistical evaluation of drought duration and intensity is usually carried out using runs analysis. First-order Markov chain model (MC1) for dry and wet periods is not adequate when autocorrelation of the original hydrological series is high. A second-order Markov chain model (MC2) is proposed to estimate the probabilities and return periods of droughts. Results of these models are compared with those of a simulation study assuming a lag-1 autoregressive [AR(1)] process widely used to model annual streamflows. Probability distribution and return periods of droughts of various lengths are estimated and compared with the results of MC1 and MC2 models using efficacy evaluation statistics. It is found that the MC2 model in general gives results that are in better agreement with simulation results as compared with the MC1 model. Skewness is found to have little effect on return periods except when autocorrelation is very high. MC1 and MC2 models are applied to droughts observed in some annual streamflow series, with the result that the MC2 model has a relatively good agreement considering the limited duration of the records.

An Efficient Markov Chain Model for the Simulation of Heterogeneous Soil Structure

2004 ◽  
Vol 68 (2) ◽  
pp. 346 ◽  
Author(s):  
Keijan Wu ◽  
Naoise Nunan ◽  
John W. Crawford ◽  
Iain M. Young ◽  
Karl Ritz
Keyword(s):  
Markov Chain ◽  
Soil Structure ◽  
Markov Chain Model ◽  
Chain Model ◽  
Heterogeneous Soil

Data Mining Technique Applied To DNA Sequencing

2015 ◽  
Vol 2 (7) ◽  
pp. 18
Author(s):  
R. Jamuna
Keyword(s):  
Data Mining ◽  
Dna Methylation ◽  
Markov Chain ◽  
Human Genome ◽  
Transition Probabilities ◽  
Markov Chain Model ◽  
Effective Means ◽  
Cpg Islands ◽  
Chain Model ◽  
The Given

CpG islands (CGIs) play a vital role in genome analysis as genomic markers.  Identification of the CpG pair has contributed not only to the prediction of promoters but also to the understanding of the epigenetic causes of cancer. In the human genome [1] wherever the dinucleotides CG occurs the C nucleotide (cytosine) undergoes chemical modifications. There is a relatively high probability of this modification that mutates C into a T. For biologically important reasons the mutation modification process is suppressed in short stretches of the genome, such as ‘start’ regions. In these regions [2] predominant CpG dinucleotides are found than elsewhere. Such regions are called CpG islands. DNA methylation is an effective means by which gene expression is silenced. In normal cells, DNA methylation functions to prevent the expression of imprinted and inactive X chromosome genes. In cancerous cells, DNA methylation inactivates tumor-suppressor genes, as well as DNA repair genes, can disrupt cell-cycle regulation. The most current methods for identifying CGIs suffered from various limitations and involved a lot of human interventions. This paper gives an easy searching technique with data mining of Markov Chain in genes. Markov chain model has been applied to study the probability of occurrence of C-G pair in the given   gene sequence. Maximum Likelihood estimators for the transition probabilities for each model and analgously for the  model has been developed and log odds ratio that is calculated estimates the presence or absence of CpG is lands in the given gene which brings in many  facts for the cancer detection in human genome.

Evaluating basketball player’s rotation line-ups performance via statistical markov chain modelling

2021 ◽  
pp. 174795412110090
Author(s):  
Pavlos Kolias ◽  
Nikolaos Stavropoulos ◽  
Alexandra Papadopoulou ◽  
Theodoros Kostakidis
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Specific Rotation ◽  
Multiple Regression Model ◽  
Chain Model ◽  
Know How ◽  
Basketball Game ◽  
Long Run ◽  
Rotation Line ◽  
Rating Category

Coaches in basketball often need to know how specific rotation line-ups perform in either offense or defense and choose the most efficient formation, according to their specific needs. In this research, a sample of 1131 ball possession phases of Greek Basket League was utilized, in order to estimate the offensive and defensive performance of each formation. Offensive and defensive ratings for each formation were calculated as a function of points scored or received, respectively, over possessions, where possessions were estimated using a multiple regression model. Furthermore, a Markov chain model was implemented to estimate the probabilities of the associated formation’s performance in the long run. The model could allow us to distinguish between overperforming and underperforming formations and revealed the probabilities over the evolution of the game, for each formation to be in a specific rating category. The results indicated that the most dominant formation, in terms of offense, is Point Guard-Point Guard-Small Forward-Power Forward-Center, while defensively schema Point Guard-Shooting Guard-Small Forward-Center-Center had the highest rating. Such results provide information, which could operate as a supplementary tool for the coach’s decisions, related to which rotation line-up patterns are mostly suitable during a basketball game.

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