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Relevant bibliographies by topics / Transition probability matrix

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Academic literature on the topic 'Transition probability matrix'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 June 2025

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Journal articles on the topic "Transition probability matrix"

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Hasegawa, Shigeaki F., and Takenori Takada. "Probability of Deriving a Yearly Transition Probability Matrix for Land-Use Dynamics." Sustainability 11, no. 22 (2019): 6355. http://dx.doi.org/10.3390/su11226355.

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Takada’s group developed a method for estimating the yearly transition matrix by calculating the mth power roots of a transition matrix with an interval of m years. However, the probability of obtaining a yearly transition matrix with real and positive elements is unknown. In this study, empirical verification based on transition matrices from previous land-use studies and Monte-Carlo simulations were conducted to estimate the probability of obtaining an appropriate yearly transition probability matrix. In 62 transition probability matrices of previous land-use studies, 54 (87%) could provide a positive or small-negative solution. For randomly generated matrices with differing sizes or power roots, the probability of obtaining a positive or small-negative solution is low. However, the probability is relatively large for matrices with large diagonal elements, exceeding 90% in most cases. These results indicate that Takada et al.’s method is a powerful tool for analyzing land-use dynamics.

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Yuting Hu, Rong Xie, and Wenjun Zhang. "Transition Probability Matrix Based Tourists Flow Prediction." INTERNATIONAL JOURNAL ON Advances in Information Sciences and Service Sciences 5, no. 1 (2013): 194–201. http://dx.doi.org/10.4156/aiss.vol5.issue1.24.

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Kawabata, T., and K. Nishikawa. "Protein structure comparison using transition probability matrix." Seibutsu Butsuri 39, supplement (1999): S116. http://dx.doi.org/10.2142/biophys.39.s116_3.

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Eastman, J. Ronald, and Jiena He. "A Regression-Based Procedure for Markov Transition Probability Estimation in Land Change Modeling." Land 9, no. 11 (2020): 407. http://dx.doi.org/10.3390/land9110407.

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Land change models commonly model the expected quantity of change as a Markov chain. Markov transition probabilities can be estimated by tabulating the relative frequency of change for all transitions between two dates. To estimate the appropriate transition probability matrix for any future date requires the determination of an annualized matrix through eigendecomposition followed by matrix powering. However, the technique yields multiple solutions, commonly with imaginary parts and negative transitions, and possibly with no non-negative real stochastic matrix solution. In addition, the computational burden of the procedure makes it infeasible for practical use with large problems. This paper describes a Regression-Based Markov (RBM) approximation technique based on quadratic regression of individual transitions that is shown to always yield stochastic matrices, with very low error characteristics. Using land cover data for the 48 conterminous US states, median errors in probability for the five states with the highest rates of transition were found to be less than 0.00001 and the maximum error of 0.006 was of the same order of magnitude experienced by the commonly used compromise of forcing small negative transitions estimated by eigendecomposition to 0. Additionally, the technique can solve land change modeling problems of any size with extremely high computational efficiency.

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Riveros, Guillermo A., and Manuel E. Rosario-Pérez. "Deriving the transition probability matrix using computational mechanics." Engineering Computations 35, no. 2 (2018): 692–709. http://dx.doi.org/10.1108/ec-02-2017-0051.

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Purpose The combined effects of several complex phenomena cause the deterioration of elements in steel hydraulic structures (SHSs) within the US lock system: corrosion, cracking and fatigue, impact and overloads. Predicting the future condition state of these structures by the use of current condition state inspection data can be achieved through the probabilistic chain deterioration model. The purpose of this study is to derive the transition probability matrix using final elements modeling of a miter gate. Design/methodology/approach If predicted accurately, this information would yield benefits in determining the need for rehabilitation or replacement of SHS. However, because of the complexity and difficulties on obtaining sufficient inspection data, there is a lack of available condition states needed to formulate proper transition probability matrices for each deterioration case. Findings This study focuses on using a three-dimensional explicit finite element analysis (FEM) of a miter gate that has been fully validated with experimental data to derive the transition probability matrix when the loss of flexural capacity in a corroded member is simulated. Practical implications New methodology using computational mechanics to derive the transition probability matrices of navigation steel structures has been presented. Originality/value The difficulty of deriving the transition probability matrix to perform a Markovian analysis increases when limited amount of inspection data is available. The used state of practice FEM to derive the transition probability matrix is not just necessary but also essential when the need for proper maintenance is required but limited amount of the condition of the structural system is unknown.

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Permana, D., U. S. Pasaribu, S. W. Indratno, and S. Suprayogi. "Convergence of Transition Probability Matrix in CLVMarkov Models." IOP Conference Series: Materials Science and Engineering 335 (April 2018): 012046. http://dx.doi.org/10.1088/1757-899x/335/1/012046.

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Yavin, Tzahi, Eugene Wang, Hu Zhang, and Michael A. Clayton. "Transition probability matrix methodology for incremental risk charge." Journal of Financial Engineering 01, no. 01 (2014): 1450010. http://dx.doi.org/10.1142/s234576861450010x.

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As part of Basel II's incremental risk charge (IRC) methodology, this paper summarizes our extensive investigations of constructing transition probability matrices (TPMs) for unsecuritized credit products in the trading book. The objective is to create monthly or quarterly TPMs with predefined sectors and ratings that are consistent with the bank's Basel PDs. Constructing a TPM is not a unique process. We highlight various aspects of three types of uncertainties embedded in different construction methods: (1) the available historical data and the bank's rating philosophy; (2) the merger of one-year Basel PD and the chosen Moody's TPMs; and (3) deriving a monthly or quarterly TPM when the generator matrix does not exist. Given the fact that TPMs and specifically their PDs are the most important parameters in IRC, it is our view that banks may need to make discretionary choices regarding their methodology, with uncertainties well understood and managed.

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F. Ahmed, Alaa. "A Proposed Bayesian Estimation of Transitional Probability for a Markov Chain with Random Times via Swarm Algorithm." Journal of Al-Rafidain University College For Sciences ( Print ISSN: 1681-6870 ,Online ISSN: 2790-2293 ) 56, no. 1 (2025): 411–20. https://doi.org/10.55562/jrucs.v56i1.37.

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The transition matrix estimators of the Markov chain are not accurate and the transition matrix is considered given. There are many methods that are used to estimate the transition probabilities matrix for different cases, the most famous of which is the Maximum Likelihood Method, in order to find a good and new estimator for the transition probabilities matrix of the Markov chain, a method was proposed, which is a modification of the Bayes method, to reach the transition probabilities with the least variance. This method assumes that the values of in the initial probability are estimated by two methods: Maximum Likelihood Method (MLE), and the algorithm of particle swarm (PSO), The Escherichia Coli (E.Coli) gene chain was chosen as an applied aspect of the study due to its importance in medical research and for the purpose of discovering and manufacturing treatments by knowing the final form of its gene chain. After testing the E.Coli gene chain, it was found that is represents a Markov chain, and then both the transition probabilities matrix and the transition probabilities variance were estimated, and it was found that the proposed method for transitional probabilities is better than the method of greatest possibility depending on the variance.

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Wang, Xiaoxiao, and Yaotang Li. "On the Uniqueness of the Stationary Probability Matrix of Transition Probability Tensors." Frontiers of Mathematics 18, no. 6 (2023): 1421–45. http://dx.doi.org/10.1007/s11464-021-0165-9.

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Kyeong Lee, Jae, Mi Hwan Hyun, and Dong Gu Shin. "A study on website log data analysis methodology by transition probability." International Journal of Engineering & Technology 7, no. 2.12 (2018): 171. http://dx.doi.org/10.14419/ijet.v7i2.12.11118.

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Background/Objectives: To measure occupancy using transition probability matrix as a data analysis method to predict future requirements for web use. From this study, Executives facing business challenges can enhance the decision-making process for management and can be provided quantified evidence.Methods/Statistical analysis: Transition matrix and transition probability matrix are estimated if web users’ webpage use patterns are tied with frequency, using web log data. Occupancy is forecasted based on a Markov chain model.Findings: Data analysis from the perspective of web log-based marketing mostly focuses on increasing traffic and improving transition rates. However, general-purpose tools such as Google Analytics provide diverse web log data. In assumption of independence on users’ page reload, occupancy can be easily estimated through matrix on page reload (transition). As a result, we obtained slightly different results from the usual method that reported only frequency. In particular, rather than making business decisions with the frequency of absolute concepts, we were able to identify the top priority services through the percentage value of relative concepts.Improvements/Applications: The occupancy prediction using transition matrix is about future prediction based on previous information. However, it differs from marketing techniques in that it is estimated based on probability. In addition, it is able to predict more accurately through a probability model.

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Dissertations / Theses on the topic "Transition probability matrix"

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Zhang, Xiaojing. "A simulation study of confidence intervals for the transition matrix of a reversible Markov chain." Kansas State University, 2016. http://hdl.handle.net/2097/32737.

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Nasseri, Sahand. "Application of an improved transition probability matrix based crack rating prediction methodology in Forida's highway network." [Tampa, Fla] : University of South Florida, 2008. http://purl.fcla.edu/usf/dc/et/SFE0002379.

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Nasseri, Sahand. "Application of an Improved Transition Probability Matrix Based Crack Rating Prediction Methodology in Florida’s Highway Network." Scholar Commons, 2008. https://scholarcommons.usf.edu/etd/424.

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With the growing need to maintain roadway systems for provision of safety and comfort for travelers, network level decision-making becomes more vital than ever. In order to keep pace with this fast evolving trend, highway authorities must maintain extremely effective databases to keep track of their highway maintenance needs. Florida Department of Transportation (FDOT), as a leader in transportation innovations in the U.S., maintains Pavement Condition Survey (PCS) database of cracking, rutting, and ride information that are updated annually. Crack rating is an important parameter used by FDOT for making maintenance decisions and budget appropriation. By establishing a crack rating threshold below which traveler comfort is not assured, authorities can screen the pavement sections which are in need of Maintenance and Rehabilitation (M&R). Hence, accurate and reliable prediction of crack thresholds is essential to optimize the rehabilitation budget and manpower. Transition Probability Matrices (TPM) can be utilized to accurately predict the deterioration of crack ratings leading to the threshold. Such TPMs are usually developed by historical data or expert or experienced maintenance engineers' opinion. When historical data are used to develop TPMs, deterioration trends have been used vii indiscriminately, i.e. with no discrimination made between pavements that degrade at different rates. However, a more discriminatory method is used in this thesis to develop TPMs based on classifying pavements first into two groups. They are pavements with relatively high traffic and, pavements with a history of excessive degradation due to delayed rehabilitation. The new approach uses a multiple non-linear regression process to separately optimize TPMs for the two groups selected by prior screening of the database. The developed TPMs are shown to have minimal prediction errors with respect to crack ratings in the database that were not used in the TPM formation. It is concluded that the above two groups are statistically different from each other with respect to the rate of cracking. The observed significant differences in the deterioration trends would provide a valuable tool for the authorities in making critical network-level decisions. The same methodology can be applied in other transportation agencies based on the corresponding databases.

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Отич, Т. "Механізм визначення ефективної ставки резервування за кредитними операціями у період кризових явищ в економіці". Thesis, Національний університет ДПС України, 2011. http://essuir.sumdu.edu.ua/handle/123456789/62456.

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В роботі розглядаються механізм формування резервів за кредитними операціями на основі перехідних матриць ймовірностей.<br>The paper considers the mechanism of formation of reserves for credit operations on the basis of transition probabilities matrices.

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Freitas, Evandro de. "O uso de matriz de transição para o cálculo de probabilidades em jogos." Universidade Federal de Juiz de Fora (UFJF), 2013. https://repositorio.ufjf.br/jspui/handle/ufjf/3242.

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Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2016-08-17T13:35:24Z No. of bitstreams: 1 evandrodefreitas.pdf: 1325640 bytes, checksum: 5e6a80ba2ec417aa23d9dad0d4cff87f (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-02T11:09:46Z (GMT) No. of bitstreams: 1 evandrodefreitas.pdf: 1325640 bytes, checksum: 5e6a80ba2ec417aa23d9dad0d4cff87f (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-07T11:59:37Z (GMT) No. of bitstreams: 1 evandrodefreitas.pdf: 1325640 bytes, checksum: 5e6a80ba2ec417aa23d9dad0d4cff87f (MD5)<br>Made available in DSpace on 2017-02-07T11:59:37Z (GMT). No. of bitstreams: 1 evandrodefreitas.pdf: 1325640 bytes, checksum: 5e6a80ba2ec417aa23d9dad0d4cff87f (MD5) Previous issue date: 2013-08-15<br>CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>Neste trabalho apresentamos alguns métodos para a resolução de problemas de probabilidade. Dois deles são estudados no Ensino Médio: a árvore de probabilidades e as técnicas de contagem. O terceiro é o triângulo de Pascal visto aqui como instrumento de cálculo de probabilidades. O quarto e último método é um recurso não usualmente apresentado, mas de entendimento acessível no Ensino Médio: a matriz de transição.<br>This work presents some methods for solving probability problems. Two of them are studied in high school: the tree of probability and counting techniques. The third is the Pascal triangle seen here as a tool for calculating probabilities. The fourth and final method is a feature not usually presented, but understanding accessible in high school: the transition matrix.

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Torp, Emil, and Patrik Önnegren. "Driving Cycle Generation Using Statistical Analysis and Markov Chains." Thesis, Linköpings universitet, Fordonssystem, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-94147.

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A driving cycle is a velocity profile over time. Driving cycles can be used for environmental classification of cars and to evaluate vehicle performance. The benefit by using stochastic driving cycles instead of predefined driving cycles, i.e. the New European Driving Cycle, is for instance that the risk of cycle beating is reduced. Different methods to generate stochastic driving cycles based on real-world data have been used around the world, but the representativeness of the generated driving cycles has been difficult to ensure. The possibility to generate stochastic driving cycles that captures specific features from a set of real-world driving cycles is studied. Data from more than 500 real-world trips has been processed and categorized. The driving cycles are merged into several transition probability matrices (TPMs), where each element corresponds to a specific state defined by its velocity and acceleration. The TPMs are used with Markov chain theory to generate stochastic driving cycles. The driving cycles are validated using percentile limits on a set of characteristic variables, that are obtained from statistical analysis of real-world driving cycles. The distribution of the generated driving cycles is investigated and compared to real-world driving cycles distribution. The generated driving cycles proves to represent the original set of real-world driving cycles in terms of key variables determined through statistical analysis. Four different methods are used to determine which statistical variables that describes the features of the provided driving cycles. Two of the methods uses regression analysis. Hierarchical clustering of statistical variables is proposed as a third alternative, and the last method combines the cluster analysis with the regression analysis. The entire process is automated and a graphical user interface is developed in Matlab to facilitate the use of the software.<br>En körcykel är en beskriving av hur hastigheten för ett fordon ändras under en körning. Körcykler används bland annat till att miljöklassa bilar och för att utvärdera fordonsprestanda. Olika metoder för att generera stokastiska körcykler baserade på verklig data har använts runt om i världen, men det har varit svårt att efterlikna naturliga körcykler. Möjligheten att generera stokastiska körcykler som representerar en uppsättning naturliga körcykler studeras. Data från över 500 körcykler bearbetas och kategoriseras. Dessa används för att skapa överergångsmatriser där varje element motsvarar ett visst tillstånd, med hastighet och acceleration som tillståndsvariabler. Matrisen tillsammans med teorin om Markovkedjor används för att generera stokastiska körcykler. De genererade körcyklerna valideras med hjälp percentilgränser för ett antal karaktäristiska variabler som beräknats för de naturliga körcyklerna. Hastighets- och accelerationsfördelningen hos de genererade körcyklerna studeras och jämförs med de naturliga körcyklerna för att säkerställa att de är representativa. Statistiska egenskaper jämfördes och de genererade körcyklerna visade sig likna den ursprungliga uppsättningen körcykler. Fyra olika metoder används för att bestämma vilka statistiska variabler som beskriver de naturliga körcyklerna. Två av metoderna använder regressionsanalys. Hierarkisk klustring av statistiska variabler föreslås som ett tredje alternativ. Den sista metoden kombinerar klusteranalysen med regressionsanalysen. Hela processen är automatiserad och ett grafiskt användargränssnitt har utvecklats i Matlab för att underlätta användningen av programmet.

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Rimkevičiūtė, Inga. "Daugiapakopių procesų būsenų modeliavimas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20100614_133830-67546.

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Pagrindinis šio darbo tikslas yra sukurti daugiapakopių procesų būsenų modelį, kuriuo būtų galima modeliuoti įvairių galimų bet kokios sistemos trikdžių scenarijus ir atlikti demonstracinius skaičiavimus. Atsiradus sutrikimui ar pažeidimams sutrikdomas kitų sistemoje dalyvaujančių pakopų darbas ir turime tam tikras pasekmes, kurios iššaukia problemas, liečiančias aplinkui funkcionuojančius sektorius. Todėl yra labai svarbu nustatyti daugiapakopių procesų būsenų modelio galimų būsenų scenarijus, išanalizuoti jų tikėtinumą bei dažnumą ir įvertinti. Daugiausiai dėmesio skiriama perėjimo tikimybių iš vienos pakopos būsenų į kitos pakopos būsenas matricų modeliavimui ir skaičiavimo algoritmo kūrimui. Tada atliekame stebėjimą kaip elgiasi trikdžių pasirodymo tikimybės per 100 perėjimų. Tam naudojami Markovo grandinės bei procesai ir tikimybiniai skirstiniai.<br>The main purpose of this research is to develop multi-stage process states model that could simulate a possible range of any system failures and demonstrational calculations. In the event of disruption or irregularities affects the other systems involved in stage work and we have certain consequences, which triggered concerns about the functioning around the sector. It is very important to establish a multi-stage process states model, the possible states of scenarios, analyze their probability and the frequency and to assess it. Focuses on the transition probabilities between states in the next tier level status matrix modeling and computing algorithm. Then perform the behavior tracking script and the likelihood of interference, the likelihood of the appearance of over 100 transitions. For this purpose, Markov chains and processes, and probabilistic distributions are used.

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Panthi, Kamalesh. "A Methodological Framework for Modeling Pavement Maintenance Costs for Projects with Performance-based Contracts." FIU Digital Commons, 2009. http://digitalcommons.fiu.edu/etd/120.

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Performance-based maintenance contracts differ significantly from material and method-based contracts that have been traditionally used to maintain roads. Road agencies around the world have moved towards a performance-based contract approach because it offers several advantages like cost saving, better budgeting certainty, better customer satisfaction with better road services and conditions. Payments for the maintenance of road are explicitly linked to the contractor successfully meeting certain clearly defined minimum performance indicators in these contracts. Quantitative evaluation of the cost of performance-based contracts has several difficulties due to the complexity of the pavement deterioration process. Based on a probabilistic analysis of failures of achieving multiple performance criteria over the length of the contract period, an effort has been made to develop a model that is capable of estimating the cost of these performance-based contracts. One of the essential functions of such model is to predict performance of the pavement as accurately as possible. Prediction of future degradation of pavement is done using Markov Chain Process, which requires estimating transition probabilities from previous deterioration rate for similar pavements. Transition probabilities were derived using historical pavement condition rating data, both for predicting pavement deterioration when there is no maintenance, and for predicting pavement improvement when maintenance activities are performed. A methodological framework has been developed to estimate the cost of maintaining road based on multiple performance criteria such as crack, rut and, roughness. The application of the developed model has been demonstrated via a real case study of Miami Dade Expressways (MDX) using pavement condition rating data from Florida Department of Transportation (FDOT) for a typical performance-based asphalt pavement maintenance contract. Results indicated that the pavement performance model developed could predict the pavement deterioration quite accurately. Sensitivity analysis performed shows that the model is very responsive to even slight changes in pavement deterioration rate and performance constraints. It is expected that the use of this model will assist the highway agencies and contractors in arriving at a fair contract value for executing long term performance-based pavement maintenance works.

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Bayrak, Hakan. "Lifetime Condition Prediction For Bridges." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613793/index.pdf.

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Infrastructure systems are crucial facilities. They supply the necessary transportation, water and energy utilities for the public. However, while aging, these systems gradually deteriorate in time and approach the end of their lifespans. As a result, they require periodic maintenance and repair in order to function and be reliable throughout their lifetimes. Bridge infrastructure is an essential part of the transportation infrastructure. Bridge management systems (BMSs), used to monitor the condition and safety of the bridges in a bridge infrastructure, have evolved considerably in the past decades. The aim of BMSs is to use the resources in an optimal manner keeping the bridges out of risk of failure. The BMSs use the lifetime performance curves to predict the future condition of the bridge elements or bridges. The most widely implemented condition-based performance prediction and maintenance optimization model is the Markov Decision Process-based models (MDP). The importance of the Markov Decision Process-based model is that it defines the time-variant deterioration using the Markov Transition Probability Matrix and performs the lifetime cost optimization by finding the optimum maintenance policy. In this study, the Markov decision process-based model is examined and a computer program to find the optimal policy with discounted life-cycle cost is developed. The other performance prediction model investigated in this study is a probabilistic Bi-linear model which takes into account the uncertainties for the deterioration process and the application of maintenance actions by the use of random variables. As part of the study, in order to further analyze and develop the Bi-linear model, a Latin Hypercube Sampling-based (LHS) simulation program is also developed and integrated into the main computational algorithm which can produce condition, safety, and life-cycle cost profiles for bridge members with and without maintenance actions. Furthermore, a polynomial-based condition prediction is also examined as an alternative performance prediction model. This model is obtained from condition rating data by applying regression analysis. Regression-based performance curves are regenerated using the Latin Hypercube sampling method. Finally, the results from the Markov chain-based performance prediction are compared with Simulation-based Bi-linear prediction and the derivation of the transition probability matrix from simulated regression based condition profile is introduced as a newly developed approach. It has been observed that the results obtained from the Markov chain-based average condition rating profiles match well with those obtained from Simulation-based mean condition rating profiles. The result suggests that the Simulation-based condition prediction model may be considered as a potential model in future BMSs.

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Florence, Lindsay Walker. "Skill Evaluation in Women's Volleyball." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2286.pdf.

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Book chapters on the topic "Transition probability matrix"

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Sitenko, Aleksei G. "The Scattering Matrix and Transition Probability." In Springer Series in Nuclear and Particle Physics. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-84034-0_2.

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Xu, Guanshuo, Shang Gao, Yun Qing Shi, RuiMin Hu, and Wei Su. "Camera-Model Identification Using Markovian Transition Probability Matrix." In Digital Watermarking. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03688-0_26.

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Chen, Dongming, Chang Liu, Xinyu Huang, Dongqi Wang, and Jiarui Yan. "A Probability Transition Matrix-Based Recommendation Algorithm for Bipartite Networks." In Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-32456-8_99.

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Chen, Luyi, Shilin Wang, Shenghong Li, and Jianhua Li. "New Feature Presentation of Transition Probability Matrix for Image Tampering Detection." In Digital Forensics and Watermarking. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32205-1_30.

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Shang, Zhiqiang, Yerong Hu, Xiangyin Chen, Shiyu Liu, and Zejun Zhang. "Technical Degradation Prediction of Bridge Components Based on Semi-Markov Degradation Model." In Lecture Notes in Civil Engineering. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-4355-1_2.

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AbstractTo overcome the limitations of traditional Markov bridge degradation prediction models, which fail to consider the interactions between different component degradation mechanisms and struggle to accurately capture the true degradation conditions of bridge components, introducing an improved version of the traditional Markov model by incorporating the Weibull distribution. This enhancement results in a semi-Markov model that offers a probability distribution for predicting the technical condition of bridge components. Taking advantage of periodic inspection data from a highway section in Shandong Province, China. With this data, the states of bridge components are defined in the semi-Markov degradation model. The improved semi-Markov model integrates a two-parameter Weibull distribution and involves determining the parameters of the Weibull distribution, transition probability matrix, and state distribution vector. The semi-Markov degradation model, in contrast to commonly used Markov degradation models, accounts for both the state and duration of each state, resulting in significantly more accurate predictions of the degradation process of bridge components, achieving a prediction accuracy of 96%. The developed semi-Markov bridge degradation model facilitates the timely detection of changes in the technical condition of bridge components by updating the transition probability matrix according to variations in the duration of each state, thereby improving the efficiency of subsequent bridge maintenance decision-making.

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Saini, Gurdeep, Naveen Yadav, Biju R. Mohan, and Nagaraj Naik. "Time Series Forecasting Using Markov Chain Probability Transition Matrix with Genetic Algorithm Optimisation." In Modeling, Simulation and Optimization. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-15-9829-6_34.

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Joo, Yongjin, Chulmin Jun, and Soohong Park. "Design of a Dynamic Land-Use Change Probability Model Using Spatio-Temporal Transition Matrix." In Computational Science and Its Applications – ICCSA 2010. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12156-2_8.

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Li, Dong-Xu, Xun Deng, Bo-Wei Zhao, et al. "A Novel Graph Representation Learning Model for Drug Repositioning Using Graph Transition Probability Matrix Over Heterogenous Information Networks." In Lecture Notes in Computer Science. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-4749-2_16.

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Vidyasagar, M. "Markov Processes." In Hidden Markov Processes. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691133157.003.0004.

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This chapter deals with Markov processes. It first defines the “Markov property” and shows that all the relevant information about a Markov process assuming values in a finite set of cardinality n can be captured by a nonnegative n x n matrix known as the state transition matrix, and an n-dimensional probability distribution of the initial state. It then invokes the results of the previous chapter on nonnegative matrices to analyze the temporal evolution of Markov processes. It also estimates the state transition matrix and considers the dynamics of stationary Markov chains, recurrent and transient states, hitting probability and mean hitting times, and the ergodicity of Markov chains.

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Grimmett, Geoffrey R., and David R. Stirzaker. "Markov chains." In One Thousand Exercises in Probability. Oxford University PressOxford, 2001. http://dx.doi.org/10.1093/oso/9780198572213.003.0006.

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Abstract Show that any sequence of independent random variables taking values in the countable set S is a Markov chain. Under what condition is this chain homogeneous? A die is rolled repeatedly. Which of the following are Markov chains? For those that are, supply the transition matrix.

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Conference papers on the topic "Transition probability matrix"

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Chen, Youwang, Yunkai Deng, and Weiming Tian. "Model Switching Detection-Aided Adaptive Transition Probability Matrix IMM Algorithm." In 2024 IEEE International Conference on Signal, Information and Data Processing (ICSIDP). IEEE, 2024. https://doi.org/10.1109/icsidp62679.2024.10869288.

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Brenna, Andrea, Luciano Lazzari, and Marco Ormellese. "Probabilistic Model Based on Markov Chain for the Assessment of Localized Corrosion of Stainless Steels." In CORROSION 2014. NACE International, 2014. https://doi.org/10.5006/c2014-4091.

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Abstract Pitting, crevice and stress corrosion cracking are the most damaging corrosion forms of stainless steels in industrial applications. Generally, pitting and crevice susceptibility depends on a variety of factors related to the metal (chemical composition, differences in the metallurgical structure, inclusions), the environment (chloride content, pH, temperature, differential aeration) and the geometry of the system. Due to their unpredictable occurrence, localized corrosion events cannot be explained without using a proper statistical method. In this work a probabilistic approach based on Markov chains for the assessment of pitting and crevice corrosion initiation is proposed. A Markov chain is a stochastic process that undergoes transitions from one state to another through a finite number of possible states, until a so-called "absorbing state” from which the system has no tendency to evolve is attained. Formally, a Markov chain is characterized by a set of states and a transition probability matrix. The model calculates the probability to have pitting (and vice versa to maintain a stable passive condition) involving a large number of operating parameters related to both metal and environment. Experimental tests were carried out to validate the model which requires more accurate investigations.

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Takei, Masahiro, Mitsuaki Ochi, Yoshifuru Saito, and Kiyoshi Horii. "Density Distribution Evaluation of Free Fall Particles Using CT and State Transition Matrix." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45213.

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Spatial particle density distribution images in a pipe cross section have been evaluated by means of state transition matrix, which is a parameter indicating the dominant particle density transition patterns among time series images consisting of CT 2D-space and 1D-time. State transition characterizes the transition patterns for positions in a cross section as monotonous transitions, sudden transitions, and extreme value transitions. In free fall particles in a vertical pipe, high, sudden and extreme value transitions do not occur, because particle flow rate at this position is low, and therefore the probability of collision among particles is also low. A high, sudden and extreme value transitions occur near the pipe center when the particle flow rate is high, because the probability of collision among particles is high.

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Zhang, Ziqi, Yuexiang Li, Hongxin Wei, Kai Ma, Tao Xu, and Yefeng Zheng. "Alleviating Noisy-label Effects in Image Classification via Probability Transition Matrix." In British Machine Vision Conference 2021. British Machine Vision Association, 2021. https://doi.org/10.5244/c.35.41.

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Wijesinghe, P., U. Gunawardana, and R. Liyanapathirana. "Transition Matrix Monte Carlo technique for outage probability estimation in MIMO channels." In 2011 Australian Communications Theory Workshop (AusCTW). IEEE, 2011. http://dx.doi.org/10.1109/ausctw.2011.5728750.

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Yang, Xing, Yubao Liu, Zhan Li, and Jiajie Mo. "Privacy Preserving Naïve Bayesian Classifier Based on Transition Probability Matrix." In 2011 Seventh International Conference on Computational Intelligence and Security (CIS). IEEE, 2011. http://dx.doi.org/10.1109/cis.2011.135.

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Kotenko, Igor V., Igor B. Parashchuk, and Vasily A. Desnitsky. "Determination of the Transition Probability Matrix for an IoT Fuzzy Security Model." In 2023 IEEE International Conference on Internet of Things and Intelligence Systems (IoTaIS). IEEE, 2023. http://dx.doi.org/10.1109/iotais60147.2023.10346032.

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Bi, Xin, Jinsong Du, Jie Gao, Wei Wang, and Yang Gao. "The IMM tracking algorithm for maneuvering target with adaptive Markov transition probability matrix." In 2015 IEEE 10th Conference on Industrial Electronics and Applications (ICIEA). IEEE, 2015. http://dx.doi.org/10.1109/iciea.2015.7334305.

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Ahn, B. K., and W. A. Curtin. "Effects of Stress Concentrations at the Slipping Fiber/Matrix Interface on Tensile Strength of Ceramic Matrix Composites." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0686.

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Abstract Ceramic matrix composites can exhibit a transition from strong, tough behavior to brittle behavior as the interfacial sliding resistance τ between the fibers and the matrix increases. The detailed micromechanical reasons for this dangerous transition are not well understood, but are clearly important for optimizing performance in such composite systems. One mechanism of weakening involves a transition, with increasing τ, from “global” to “local” load transfer from broken to unbroken fibers near the slipping interface. These stress concentrations have been nicely investigated previously by Steif and coworkers (1991) for 2d geometries and by Weitsman and coworkers (1993) using shear-lag for an axisymmetric problem, but the precise implications of these stress concentrations on actual tensile composite failure have not been fully investigated. Here, the problem of stress concentrations in the fiber is revised using the very accurate yet efficient Axisymmetric Damage Model of Pagano (1993) to calculate the axial fiber stresses. The geometry is axisymmetric with a transverse matrix crack and a debond crack along the fiber/matrix interface having a constant sliding resistance τ. The stress concentrations obtained are compared to previous results, and generally increase with increasing τ. More importantly, the fiber surface stresses are then used to determine the probability of fiber fails by surface flaws having a Weibull probability distribution, and the overall composite strength is calculated in a manner similar to that originally suggested by Thouless and Evans for a single matrix crack. The results show a decrease in strength with increasing τ, relative to the common approximation of assuming uniform stresses across the fiber cross-section. The nature of the tough to brittle transition will be discussed in light of these results.

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Zhang, Yujie, Yongsheng Ou, Xinyu Wu, and Wei Feng. "Robust dissipative filtering for discrete-time Markov jump Lur'e systems with uncertain transition probability matrix." In 2015 54th IEEE Conference on Decision and Control (CDC). IEEE, 2015. http://dx.doi.org/10.1109/cdc.2015.7402900.

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Reports on the topic "Transition probability matrix"

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Pasupuleti, Murali Krishna. Phase Transitions in High-Dimensional Learning: Understanding the Scaling Limits of Efficient Algorithms. National Education Services, 2025. https://doi.org/10.62311/nesx/rr1125.

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Abstract: High-dimensional learning models exhibit phase transitions, where small changes in model complexity, data size, or optimization dynamics lead to abrupt shifts in generalization, efficiency, and computational feasibility. Understanding these transitions is crucial for scaling modern machine learning algorithms and identifying critical thresholds in optimization and generalization performance. This research explores the role of high-dimensional probability, random matrix theory, and statistical physics in analyzing phase transitions in neural networks, kernel methods, and convex vs. non-convex optimization. Key focus areas include the computational-to-statistical gap, double descent phenomena, and spectral phase transitions that impact model efficiency. The study also investigates the scaling limits of iterative optimization methods, highlighting when gradient-based learning succeeds or fails in high-dimensional regimes. By integrating theoretical analysis and empirical validation, this report provides a structured framework for designing scalable, efficient, and robust AI systems that can adapt to phase transitions and scaling laws in high-dimensional learning. Keywords: Phase transitions in learning, high-dimensional probability, scaling laws, statistical physics in AI, random matrix theory, computational-to-statistical gap, neural network overparameterization, double descent phenomenon, convex vs. non-convex optimization, spectral phase transitions, kernel methods in high dimensions, scaling limits in deep learning, gradient-based optimization, iterative learning algorithms, eigenvalue distributions in machine learning, large-scale AI efficiency, threshold effects in generalization, scaling-aware machine learning, AI robustness in high dimensions.

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