LEADER 06899nam 2201585 450 001 9910828783803321 005 20230803203840.0 010 $a1-4008-5051-7 024 7 $a10.1515/9781400850518 035 $a(CKB)3710000000204272 035 $a(EBL)1680802 035 $a(OCoLC)885122066 035 $a(SSID)ssj0001290892 035 $a(PQKBManifestationID)11722461 035 $a(PQKBTitleCode)TC0001290892 035 $a(PQKBWorkID)11245465 035 $a(PQKB)11006836 035 $a(MiAaPQ)EBC1680802 035 $a(StDuBDS)EDZ0001756160 035 $a(DE-B1597)447402 035 $a(OCoLC)888550795 035 $a(OCoLC)979630034 035 $a(OCoLC)984676792 035 $a(OCoLC)987942185 035 $a(OCoLC)992455040 035 $a(OCoLC)999360571 035 $a(DE-B1597)9781400850518 035 $a(Au-PeEL)EBL1680802 035 $a(CaPaEBR)ebr10901474 035 $a(CaONFJC)MIL633490 035 $a(EXLCZ)993710000000204272 100 $a20140812h20142014 uy 0 101 0 $aeng 135 $aur|nu---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aHidden Markov processes $etheory and applications to biology /$fM. Vidyasagar 205 $aCourse Book 210 1$aPrinceton, New Jersey ;$aOxford, England :$cPrinceton University Press,$d2014. 210 4$dİ2014 215 $a1 online resource (303 p.) 225 1 $aPrinceton Series in Applied Mathematics 300 $aDescription based upon print version of record. 311 0 $a0-691-13315-8 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tPreface --$tPART 1. Preliminaries --$tChapter One. Introduction to Probability and Random Variables --$tChapter Two. Introduction to Information Theory --$tChapter Three. Nonnegative Matrices --$tPART 2. Hidden Markov Processes --$tChapter Four. Markov Processes --$tChapter Five. Introduction to Large Deviation Theory --$tChapter Six. Hidden Markov Processes: Basic Properties --$tChapter Seven. Hidden Markov Processes: The Complete Realization Problem --$tPART 3. Applications to Biology --$tChapter Eight. Some Applications to Computational Biology --$tChapter Nine. BLAST Theory --$tBibliography --$tIndex --$tBack matter 330 $aThis book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. The book starts from first principles, so that no previous knowledge of probability is necessary. However, the work is rigorous and mathematical, making it useful to engineers and mathematicians, even those not interested in biological applications. A range of exercises is provided, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory. Biological applications are taken from post-genomic biology, especially genomics and proteomics. The topics examined include standard material such as the Perron-Frobenius theorem, transient and recurrent states, hitting probabilities and hitting times, maximum likelihood estimation, the Viterbi algorithm, and the Baum-Welch algorithm. The book contains discussions of extremely useful topics not usually seen at the basic level, such as ergodicity of Markov processes, Markov Chain Monte Carlo (MCMC), information theory, and large deviation theory for both i.i.d and Markov processes. The book also presents state-of-the-art realization theory for hidden Markov models. Among biological applications, it offers an in-depth look at the BLAST (Basic Local Alignment Search Technique) algorithm, including a comprehensive explanation of the underlying theory. Other applications such as profile hidden Markov models are also explored. 410 0$aPrinceton series in applied mathematics. 606 $aComputational biology 606 $aMarkov processes 610 $aBLAST theory. 610 $aBaum?elch algorithm. 610 $aBayes' rule. 610 $aCramr's theorem. 610 $aGENSCAN algorithm. 610 $aGLIMMER algorithm. 610 $aHankel matrix. 610 $aHankel rank condition. 610 $aHoeffding's inequality. 610 $aKullback?eibler divergence. 610 $aMarkov chain. 610 $aMarkov process. 610 $aMarkov property. 610 $aMonte Carlo simulation. 610 $aPerron?robenius theorem. 610 $aProbability theory. 610 $aSanov's theorem. 610 $aViterbi algorithm. 610 $aalignment. 610 $aalpha-mixing process. 610 $aamino acids. 610 $acanonical form. 610 $acomplete realization problem. 610 $acomputational biology. 610 $aconcave function. 610 $aconditional entropy. 610 $aconvex function. 610 $aentropy function. 610 $aentropy. 610 $aergodicity. 610 $aexpected value. 610 $afinite alphabet. 610 $agene-finding problem. 610 $agenomics. 610 $ahidden Markov model. 610 $ahidden Markov processes. 610 $ahitting probability. 610 $ainformation theory. 610 $airreducible matrices. 610 $alarge deviation property. 610 $alarge deviation theory. 610 $alikelihood estimation. 610 $alikelihood. 610 $alower semi-continuous function. 610 $alower semi-continuous relaxation. 610 $amaximal segmental score. 610 $amaximum likelihood estimate. 610 $amean hitting time. 610 $amoment generating function. 610 $anonnegative matrices. 610 $anucleotide. 610 $aoptimal gapped alignment. 610 $aperiodic irreducible matrices. 610 $apost-genomic biology. 610 $aprimitive matrices. 610 $aprobability distribution. 610 $aprobability. 610 $aprotein classification. 610 $aproteomics. 610 $aquasi-realization. 610 $arandom variable. 610 $arate function. 610 $arecurrent state. 610 $arelative entropy rate. 610 $arelative entropy. 610 $asequence alignment. 610 $asequence. 610 $astate transition matrix. 610 $astationary distribution. 610 $atotal variation distance. 610 $atransient state. 610 $aultra-mixing process. 615 0$aComputational biology. 615 0$aMarkov processes. 676 $a570.285 686 $aSK 820$2rvk 700 $aVidyasagar$b M$g(Mathukumalli),$f1947-$08077 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910828783803321 996 $aHidden Markov processes$94072157 997 $aUNINA