Hidden Markov Processes : Theory and Applications to Biology /

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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 mathematica...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Vidyasagar, M. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, [2014]
Edición:Course Book
Colección:Princeton Series in Applied Mathematics ; 44
Temas:
Computational biology.
Markov processes.
MATHEMATICS / Probability & Statistics / General.
BLAST theory.
BaumЗelch algorithm.
Bayes' rule.
Cramr's theorem.
GENSCAN algorithm.
GLIMMER algorithm.
Hankel matrix.
Hankel rank condition.
Hoeffding's inequality.
KullbackЌeibler divergence.
Markov chain.
Markov process.
Markov property.
Monte Carlo simulation.
PerronІrobenius theorem.
Probability theory.
Sanov's theorem.
Viterbi algorithm.
alignment.
alpha-mixing process.
amino acids.
canonical form.
complete realization problem.
computational biology.
concave function.
conditional entropy.
convex function.
entropy function.
entropy.
ergodicity.
expected value.
finite alphabet.
gene-finding problem.
genomics.
hidden Markov model.
hidden Markov processes.
hitting probability.
information theory.
irreducible matrices.
large deviation property.
large deviation theory.
likelihood estimation.
likelihood.
lower semi-continuous function.
lower semi-continuous relaxation.
maximal segmental score.
maximum likelihood estimate.
mean hitting time.
moment generating function.
nonnegative matrices.
nucleotide.
optimal gapped alignment.
periodic irreducible matrices.
post-genomic biology.
primitive matrices.
probability distribution.
probability.
protein classification.
proteomics.
quasi-realization.
random variable.
rate function.
recurrent state.
relative entropy rate.
relative entropy.
sequence alignment.
sequence.
state transition matrix.
stationary distribution.
total variation distance.
transient state.
ultra-mixing process.
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Tabla de Contenidos:
  • Frontmatter
  • Contents
  • Preface
  • PART 1. Preliminaries
  • Chapter One. Introduction to Probability and Random Variables
  • Chapter Two. Introduction to Information Theory
  • Chapter Three. Nonnegative Matrices
  • PART 2. Hidden Markov Processes
  • Chapter Four. Markov Processes
  • Chapter Five. Introduction to Large Deviation Theory
  • Chapter Six. Hidden Markov Processes: Basic Properties
  • Chapter Seven. Hidden Markov Processes: The Complete Realization Problem
  • PART 3. Applications to Biology
  • Chapter Eight. Some Applications to Computational Biology
  • Chapter Nine. BLAST Theory
  • Bibliography
  • Index
  • Backmatter

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