Hidden Markov Processes

Theory and Applications to Biology

M. Vidyasagar

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

This book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. The book starts from first principles, so that no previous knowledge of probability is necessary. However, the work is rigorous and mathematical, making it useful to engineers and mathematicians, even those not interested in biological applications. A range of exercises is provided, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory. Biological applications are taken from post-genomic biology, especially genomics and proteomics.

The topics examined include standard material such as the Perron-Frobenius theorem, transient and recurrent states, hitting probabilities and hitting times, maximum likelihood estimation, the Viterbi algorithm, and the Baum-Welch algorithm. The book contains discussions of extremely useful topics not usually seen at the basic level, such as ergodicity of Markov processes, Markov Chain Monte Carlo (MCMC), information theory, and large deviation theory for both i.i.d and Markov processes. The book also presents state-of-the-art realization theory for hidden Markov models. Among biological applications, it offers an in-depth look at the BLAST (Basic Local Alignment Search Technique) algorithm, including a comprehensive explanation of the underlying theory. Other applications such as profile hidden Markov models are also explored.

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Schlagwörter

Statistic, Scientific notation, Conditional probability, Nonnegative matrix, Rate function, Real number, Sequence alignment, Canonical form, Computation, Integer, Addition, Gene, Joint probability distribution, Parameter, Algorithm, Monte Carlo method, Conditional probability distribution, Estimation, Almost surely, Finite set, Independent and identically distributed random variables, Stationary distribution, Equation, Computational biology, Permutation, Markov process, Protein, Stochastic matrix, Dynamic programming, Without loss of generality, Nucleotide, Quantity, Random variable, Hidden Markov model, Convex function, Cardinality, Biologist, Biology, Eigenvalues and eigenvectors, Applied mathematics, Summation, Subset, Theorem, Convex combination, Upper and lower bounds, Markov property, Probability, Large deviations theory, Likelihood function, Probability measure, Mathematics, Moment-generating function, Block matrix, Probability theory, State space, Existential quantification, Expected value, Convergence of random variables, Notation, Empirical distribution function, Markov chain, Stochastic process, Markov chain Monte Carlo, Natural number, Stationary process, Countable set, Probability distribution, Entropy rate, Instance (computer science), Markov model