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82
Hidden Markov models in computational biology: applications to protein modeling
 JOURNAL OF MOLECULAR BIOLOGY
, 1994
"... Hidden.Markov Models (HMMs) are applied t.0 the problems of statistical modeling, database searching and multiple sequence alignment of protein families and protein domains. These methods are demonstrated the on globin family, the protein kinase catalytic domain, and the EFhand calcium binding moti ..."
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Cited by 524 (35 self)
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Hidden.Markov Models (HMMs) are applied t.0 the problems of statistical modeling, database searching and multiple sequence alignment of protein families and protein domains. These methods are demonstrated the on globin family, the protein kinase catalytic domain, and the EFhand calcium binding motif. In each case the parameters of an HMM are estimated from a training set of unaligned sequences. After the HMM is built, it is used to obtain a multiple alignment of all the training sequences. It is also used to search the. SWISSPROT 22 database for other sequences. that are members of the given protein family, or contain the given domain. The Hi " produces multiple alignments of good quality that agree closely with the alignments produced by programs that incorporate threedimensional structural information. When employed in discrimination tests (by examining how closely the sequences in a database fit the globin, kinase and EFhand HMMs), the '\ HMM is able to distinguish members of these families from nonmembers with a high degree of accuracy. Both the HMM and PROFILESEARCH (a technique used to search for relationships between a protein sequence and multiply aligned sequences) perform better in these tests than PROSITE (a dictionary of sites and patterns in proteins). The HMM appecvs to have a slight advantage over PROFILESEARCH in terms of lower rates of false
Sequential Monte Carlo Methods for Dynamic Systems
 Journal of the American Statistical Association
, 1998
"... A general framework for using Monte Carlo methods in dynamic systems is provided and its wide applications indicated. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ..."
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Cited by 461 (8 self)
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A general framework for using Monte Carlo methods in dynamic systems is provided and its wide applications indicated. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ingredients: importance sampling and resampling, rejection sampling, and Markov chain iterations. We deliver a guideline on how they should be used and under what circumstance each method is most suitable. Through the analysis of differences and connections, we consolidate these methods into a generic algorithm by combining desirable features. In addition, we propose a general use of RaoBlackwellization to improve performances. Examples from econometrics and engineering are presented to demonstrate the importance of RaoBlackwellization and to compare different Monte Carlo procedures. Keywords: Blind deconvolution; Bootstrap filter; Gibbs sampling; Hidden Markov model; Kalman filter; Markov...
Hidden Markov processes
 IEEE Trans. Inform. Theory
, 2002
"... Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finite ..."
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Cited by 173 (3 self)
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Abstract—An overview of statistical and informationtheoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discretetime finitestate homogeneous Markov chain observed through a discretetime memoryless invariant channel. In recent years, the work of Baum and Petrie on finitestate finitealphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet. In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximumlikelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. New algorithms were developed for estimating the state, parameter, and order of an HMP, for universal coding and classification of HMPs, and for universal decoding of hidden Markov channels. These and other related topics are reviewed in this paper. Index Terms—Baum–Petrie algorithm, entropy ergodic theorems, finitestate channels, hidden Markov models, identifiability, Kalman filter, maximumlikelihood (ML) estimation, order estimation, recursive parameter estimation, switching autoregressive processes, Ziv inequality. I.
Dirichlet Mixtures: A Method for Improving Detection of Weak but Significant Protein Sequence Homology
, 1996
"... This paper presents the mathematical foundations of Dirichlet mixtures, which have been used to improve database search results for homologous sequences, when a variable number of sequences from a protein family or domain are known. We present a method for condensing the information in a protein dat ..."
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Cited by 130 (22 self)
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This paper presents the mathematical foundations of Dirichlet mixtures, which have been used to improve database search results for homologous sequences, when a variable number of sequences from a protein family or domain are known. We present a method for condensing the information in a protein database into a mixture of Dirichlet densities. These mixtures are designed to be combined with observed amino acid frequencies, to form estimates of expected amino acid probabilities at each position in a profile, hidden Markov model, or other statistical model. These estimates give a statistical model greater generalization capacity, such that remotely related family members can be more reliably recognized by the model. Dirichlet mixtures have been shown to outperform substitution matrices and other methods for computing these expected amino acid distributions in database search, resulting in fewer false positives and false negatives for the families tested. This paper corrects a previously p...
Combining phylogenetic and hidden Markov models in biosequence analysis
 J. Comput. Biol
, 2004
"... A few models have appeared in recent years that consider not only the way substitutions occur through evolutionary history at each site of a genome, but also the way the process changes from one site to the next. These models combine phylogenetic models of molecular evolution, which apply to individ ..."
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Cited by 104 (13 self)
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A few models have appeared in recent years that consider not only the way substitutions occur through evolutionary history at each site of a genome, but also the way the process changes from one site to the next. These models combine phylogenetic models of molecular evolution, which apply to individual sites, and hidden Markov models, which allow for changes from site to site. Besides improving the realism of ordinary phylogenetic models, they are potentially very powerful tools for inference and prediction—for gene finding, for example, or prediction of secondary structure. In this paper, we review progress on combined phylogenetic and hidden Markov models and present some extensions to previous work. Our main result is a simple and efficient method for accommodating higherorder states in the HMM, which allows for contextsensitive models of substitution— that is, models that consider the effects of neighboring bases on the pattern of substitution. We present experimental results indicating that higherorder states, autocorrelated rates, and multiple functional categories all lead to significant improvements in the fit of a combined phylogenetic and hidden Markov model, with the effect of higherorder states being particularly pronounced.
Bayesian Methods for Hidden Markov Models  Recursive Computing in the 21st Century
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2002
"... Markov chain Monte Carlo (MCMC) sampling strategies can be used to simulate hidden Markov model (HMM) parameters from their posterior distribution given observed data. Some MCMC methods (for computing likelihood, conditional probabilities of hidden states, and the most likely sequence of states) use ..."
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Cited by 87 (8 self)
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Markov chain Monte Carlo (MCMC) sampling strategies can be used to simulate hidden Markov model (HMM) parameters from their posterior distribution given observed data. Some MCMC methods (for computing likelihood, conditional probabilities of hidden states, and the most likely sequence of states) used in practice can be improved by incorporating established recursive algorithms. The most important is a set of forwardbackward recursions calculating conditional distributions of the hidden states given observed data and model parameters. We show how to use the recursive algorithms in an MCMC context and demonstrate mathematical and empirical results showing a Gibbs sampler using the forwardbackward recursions mixes more rapidly than another sampler often used for HMM's. We introduce an augmented variables technique for obtaining unique state labels in HMM's and finite mixture models. We show how recursive computing allows statistically efficient use of MCMC output when estimating the hidden states. We directly calculate the posterior distribution of the hidden chain's state space size by MCMC, circumventing asymptotic arguments underlying the Bayesian information criterion, which is shown to be inappropriate for a frequently analyzed data set in the HMM literature. The use of loglikelihood for assessing MCMC convergence is illustrated, and posterior predictive checks are used to investigate application specific questions of model adequacy.
Nucleotides of Transcription Factor Binding Sites Exert Interdependent Effects on the Binding Affinities of Transcription Factors
, 2002
"... We can determine the effects of many possible sequence variations in transcription factor binding sites using microarray binding experiments. Analysis of wildtype and mutant Zif268 (Egr1) zinc fingers bound to microarrays containing all possible central 3 bp triplet binding sites indicates that the ..."
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Cited by 84 (4 self)
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We can determine the effects of many possible sequence variations in transcription factor binding sites using microarray binding experiments. Analysis of wildtype and mutant Zif268 (Egr1) zinc fingers bound to microarrays containing all possible central 3 bp triplet binding sites indicates that the nucleotides of transcription factor binding sites cannot be treated independently. This indicates that the current practice of characterizing transcription factor binding sites by mutating individual positions of binding sites one base pair at a time does not provide a true picture of the sequence specificity. Similarly, current bioinformatic practices using either just a consensus sequence, or even mononucleotide frequency weight matrices to provide more complete descriptions of transcription factor binding sites, are not accurate in depicting the true binding site specificities, since these methods rely upon the assumption that the nucleotides of binding sites exert independent effects on binding affinity. Our results stress the importance of complete reference tables of all possible binding sites for comparing protein binding preferences for various DNA sequences. We also show results suggesting that microarray binding data using particular subsets of all possible binding sites can be used to extrapolate the relative binding affinities of all possible fulllength binding sites, given a known binding site for use as a starting sequence for site preference refinement.
Probabilistic and Statistical Properties of Words: An Overview
 Journal of Computational Biology
, 2000
"... In the following, an overview is given on statistical and probabilistic properties of words, as occurring in the analysis of biological sequences. Counts of occurrence, counts of clumps, and renewal counts are distinguished, and exact distributions as well as normal approximations, Poisson process a ..."
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Cited by 83 (1 self)
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In the following, an overview is given on statistical and probabilistic properties of words, as occurring in the analysis of biological sequences. Counts of occurrence, counts of clumps, and renewal counts are distinguished, and exact distributions as well as normal approximations, Poisson process approximations, and compound Poisson approximations are derived. Here, a sequence is modelled as a stationary ergodic Markov chain; a test for determining the appropriate order of the Markov chain is described. The convergence results take the error made by estimating the Markovian transition probabilities into account. The main tools involved are moment generating functions, martingales, Stein’s method, and the ChenStein method. Similar results are given for occurrences of multiple patterns, and, as an example, the problem of unique recoverability of a sequence from SBH chip data is discussed. Special emphasis lies on disentangling the complicated dependence structure between word occurrences, due to selfoverlap as well as due to overlap between words. The results can be used to derive approximate, and conservative, con � dence intervals for tests. Key words: word counts, renewal counts, Markov model, exact distribution, normal approximation, Poisson process approximation, compound Poisson approximation, occurrences of multiple words, sequencing by hybridization, martingales, moment generating functions, Stein’s method, ChenStein method. 1.
Using Dirichlet Mixture Priors to Derive Hidden Markov Models for Protein Families
 PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON INTELLIGENT SYSTEMS FOR MOLECULAR BIOLOGY
, 1993
"... A Bayesian method for estimating the amino acid distributions in the states of a hidden Markov model (HMM) for a protein family or the columns of a multiple alignment of that family is introduced. This method uses Dirichlet mixture densities as priors over amino acid distributions. These mixtu ..."
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Cited by 73 (6 self)
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A Bayesian method for estimating the amino acid distributions in the states of a hidden Markov model (HMM) for a protein family or the columns of a multiple alignment of that family is introduced. This method uses Dirichlet mixture densities as priors over amino acid distributions. These mixture densities are determined from examination of previously constructed HMMs or multiple alignments. It is shown that this Bayesian method can improve the quality of HMMs produced from small training sets. Specific experiments on the EFhand motif are reported, for which these priors are shown to produce HMMs with higher likelihood on unseen data, and fewer false positives and false negatives in a database search task.
MetaMEME: motifbased hidden Markov models of protein families
 Comput Appl Biosci
, 1997
"... Motivation: Modeling families of related biological sequences using Hidden Markov models (HMMs), although increasingly widespread, faces at least one major problem: because of the complexity of these mathematical models, they require a relatively large training set in order to accurately recognize a ..."
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Cited by 72 (8 self)
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Motivation: Modeling families of related biological sequences using Hidden Markov models (HMMs), although increasingly widespread, faces at least one major problem: because of the complexity of these mathematical models, they require a relatively large training set in order to accurately recognize a given family. For families in which there are few known sequences, a standard linear HMM contains too many parameters to be trained adequately. Results: This work attempts to solve that problem by generating smaller HMMs which precisely model only the conserved regions of the family. These HMMs are constructed from motif models generated by the EM algorithm using the MEME software. Because motifbased HMMs have relatively few parameters, they can be trained using smaller data sets. Studies of short chain alcohol dehydrogenases and 4Fe4S ferredoxins support the claim that motifbased HMMs exhibit increased sensitivity and selectivity in database searches, especially when training sets contain few sequences.