Probability And Statistics By Example Volume 2 Markov Chains Pdf

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Remote sensing can be used to acquire spatio-temporal series of geographical data and to perform land use and land cover change LUCC analysis []. Obtained data can be processed using geographical information system GIS techniques and varied modelling approaches thus providing.

Understanding Markov Chains

Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples gambling processes and random walks are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters. An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals.

The concepts presented are illustrated by examples and by 72 exercises and their complete solutions. It is completed by almost a hundred pages of solutions of exercises. Often the reader is guided through the less trivial concepts by means of appropriate examples and additional comments, including diagrams and graphs. Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available. Understanding Markov Chains Examples and Applications.

Pages Probability Background. Gambling Problems. Random Walks. Discrete-Time Markov Chains. First Step Analysis. Classification of States. Long-Run Behavior of Markov Chains. Branching Processes. Continuous-Time Markov Chains. Discrete-Time Martingales. Spatial Poisson Processes. Reliability Theory. Back Matter Pages About the authors Nicolas Privault is an associate professor from the Nanyang Technological University NTU and is well-established in the field of stochastic processes and a highly respected probabilist.

Aside from these two Springer titles, he has authored several others. The manuscript has been developed over the years from his courses on Stochastic Processes.

Markov chain

A Markov chain is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes, [1] [4] [5] [6] such as studying cruise control systems in motor vehicles , queues or lines of customers arriving at an airport, currency exchange rates and animal population dynamics. Markov processes are the basis for general stochastic simulation methods known as Markov chain Monte Carlo , which are used for simulating sampling from complex probability distributions, and have found application in Bayesian statistics , thermodynamics , statistical mechanics , physics , chemistry , economics , finance , signal processing , information theory and artificial intelligence. The adjective Markovian is used to describe something that is related to a Markov process. A Markov process is a stochastic process that satisfies the Markov property [1] sometimes characterized as " memorylessness ". In simpler terms, it is a process for which predictions can be made regarding future outcomes based solely on its present state and—most importantly—such predictions are just as good as the ones that could be made knowing the process's full history.

Markov Chain Modeling of HIV, Tuberculosis, and Hepatitis B Transmission in Ghana

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Probability theory , a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.

Markov Chain Modeling of HIV, Tuberculosis, and Hepatitis B Transmission in Ghana

Several mathematical and standard epidemiological models have been proposed in studying infectious disease dynamics. These models help to understand the spread of disease infections. However, most of these models are not able to estimate other relevant disease metrics such as probability of first infection and recovery as well as the expected time to infection and recovery for both susceptible and infected individuals. That is, most of the standard epidemiological models used in estimating transition probabilities TPs are not able to generalize the transition estimates of disease outcomes at discrete time steps for future predictions. This paper seeks to address the aforementioned problems through a discrete-time Markov chain model.

It is an open access peer-reviewed textbook intended for undergraduate as well as first-year graduate level courses on the subject. This probability textbook can be used by both students and practitioners in engineering, mathematics, finance, and other related fields. The print version of the book is available through Amazon here. Since the textbook's initial publication, many requested the distribution of solutions to the problems in the textbook.


Start reading Probability and Statistics by Example: Volume 2, Markov Chains: A Primer in Random Processes and their Applications for free online and get.


Probability theory books

This is the book on Bayesian analysis. Probability is at the very deep level of many machine learning algorithms. Main topics are stopping times random walks conditional expectation discrete time martingales Markov chains exchangeability renewal and ergodic theory.

Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples gambling processes and random walks are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters. An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals. The concepts presented are illustrated by examples and by 72 exercises and their complete solutions. It is completed by almost a hundred pages of solutions of exercises.

1 Comments

  1. Juanelo N. 16.06.2021 at 01:01

    Skip to main content Skip to table of contents.