Churchill, G. A. 1989. Stochastic models for heterogeneous DNA sequences. Bull Math Biol 51:79#94.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Bioinformatics Research Center, www.birc.dk, funded by Aarhus University Research Foundation are also applied in other areas than speech recognition. One prominent example of this is the area of computational biology where they have found many applications, e.g. modeling of DNA sequences [5], protein secondary structure prediction [2] gene nding [11] recognition of transmembrane proteins [16] and characterization of biological sequence families by modeling how the biological sequences relate by substitutions, insertions, and deletions to the consensus sequence of the family ....

G. A. Churchill. Stochastic models for heterogeneous DNA sequences. Bulletin of Mathematical Biology, 51:7994, 1989.

....successful. The actual models constructed by Haussler et al. are HMM s, with the amino acids constituting the observables, and a Markov process, with carefully constructed state space and restricted transitions, constituting the hidden process. A very similar approach is taken by Churchill [15] in constructing HMM s for the sequence of bases constituting a DNA molecule. Transition probabilities are estimated from existing data bases, as are statedependent distributions on the twenty available amino acids. Here again the conditional Markov structure of the unobserved (in fact, virtual) ....

G.A. Churchill. Stochastic models in heterogeneous DNA sequences. Bulletin of Mathematical Biology, 51:79--94, 1989.

....the error, whereas in the (k; h) segmentation problem with h k several segments have to use the same source. While the (k; k) segmentation problem has been considered often, to the best of our knowledge the problem of (k; h) segmentation has not been studied extensively. In 1989 Churchill [6] stated a related problem for the purpose of partitioning genomic sequences into segments. In his formulation he uses hidden Markov states to model different compositional properties within each DNA segment, and his solution uses the Viterbi algorithm to determine the most probable sequence of ....

G. A. Churchill. Stochastic models for heterogeneous DNA sequences. Bulletin of Mathematical Biology, 51:79 -- 94, 1989. 1 1.5 2 2.5 3 3.5 4 4.5 5 7 0 1 2 3 131 4 0 1 3 1 0 1 2 1 2 1 4 0 1 3 Gene

....and the most likely path for a given sequence is the corresponding sequence of words. Rabiner [124] gives a good introduction to the theory of hidden Markov models and their applications to speech recognition. Hidden Markov models were introduced in computational biology in 1989 by Churchill [27]. Durbin et al. 35] and Eddy [36, 37] are good overviews of the use of hidden Markov models in computational biology. One of the most popular applications is to use them to characterise sequence families by using so called profile hidden Markov models introduced by Krogh et al. 80] For a ....

G. A. Churchill. Stochastic models for heterogeneous DNA sequences.

....a very good overview of the theory of hidden Markov models and its applications to problems in speech recognition. Hidden Markov models were first applied to problems in computational biology in the late 1980 s and early 1990 s. Since then they have found many applications, e.g. modeling of DNA [38], protein secondary structure prediction [15] gene prediction [110] and recognition of transmembrane proteins [175] Probably the most popular application, introduced by Krogh et al. in [111] is to use profile hidden Markov models to characterize a sequence family by modeling how the sequences ....

....and the most likely path for a given sequence is the corresponding sequence of words. Rabiner [166] gives a good introduction to the theory of hidden Markov models and their applications to speech recognition. Hidden Markov models were introduced in computational biology in 1989 by Churchill [38]. Durbin et al. 46] and Eddy [48, 49] are good overviews of the use of hidden Markov models in computational biology. One of the most popular applications is to use them to characterize sequence families by using # Center for Biological Sequence Analysis, Center of the Danish National Research ....

G. A. Churchill. Stochastic models for heterogeneous DNA sequences.

....and the most likely path for a given sequence is the corresponding sequence of words. Rabiner [19] gives a good introduction to the theory of hidden Markov models and their applications to speech recognition. Hidden Markov models were introduced in computational biology in 1989 by Churchill [5]. Durbin et al. 6] and Eddy [7, 8] are good overviews of the use of hidden Markov models in computational biology. One of the most popular applications is to use them to characterise sequence families by using so called pro le hidden Markov models introduced by Krogh et al. 15] For a pro le ....

G. A. Churchill. Stochastic models for heterogeneous DNA sequences. Bulletin of Mathematical Biology, 51:79-94, 1989.

....Foundation probability re ects a sequence likely to belong to the class of sequences being modeled, instead of formalisms only distinguishing sequences as either belonging to the class being modeled or not. The two most widely used grammatical models in bioinformatics are hidden Markov models [1, 3, 8, 9, 16] and stochastic context free grammars [7, 14, 15] though other models have also been proposed [13, 18] These two types of stochastic models were originally developed as tools for speech recognition (see [2, 12] One can identify hidden Markov models as a stochastic version of regular languages ....

G. A. Churchill. Stochastic models for heterogeneous DNA sequences. Bulletin of Mathematical Biology, 51:7994, 1989.

....and the Prog. in Math. and Mol. Biology ## Partially supported by the IST Programme of the EU under contract number IST1999 14186 (ALCOM FT) # # # Bioinformatics Research Center, www.birc.dk, funded by the University of Aarhus Research Foundation applications, e.g. modeling of DNA sequences [5], protein secondary structure prediction [2] gene nding [11] recognition of transmembrane proteins [16] and characterization of biological sequence families [12] Applications of HMMs are often based on two fundamental questions. Given an HMM and a string we might want to determine the ....

G. A. Churchill. Stochastic models for heterogeneous DNA sequences. Bull. Math. Biol., 51:7994, 1989.

....Foundation probability re ects a sequence likely to belong to the class of sequences being modeled, instead of formalisms only distinguishing sequences as either belonging to the class being modeled or not. The two most widely used grammatical models in bioinformatics are hidden Markov models [1, 3, 8, 9, 16] and stochastic context free grammars [7, 14, 15] though other models have also been proposed [13, 18] These two types of stochastic models were originally developed as tools for speech recognition (see [2, 12] One can identify hidden Markov models as a stochastic version of regular languages ....

G. A. Churchill. Stochastic models for heterogeneous DNA sequences. Bulletin of Mathematical Biology, 51:7994, 1989.

.... already in the late 60 s by Baum and Petrie (1966) and thereafter the model has been extensively used in many areas such as speech processing (Baker, 1975; Juang and Rabiner, 1991) recognition of handwritten word (Kundu et al. 1989) and modeling and analysis of DNA and protein sequences (Churchill, 1989; Eddy, 1998) In the applications of HMMs, likelihood functions and estimates of the model parameters have been routinely computed. However, the more advanced statistical inference, like condence intervals, have been constantly ignored. As an exception, Klein et al. 1997) presented in general ....

Churchill, G. A. (1989). Stochastic models for heterogeneous DNA sequences, Bulletin of Mathematical Biology, 51, 79-94.

....of homogeneous regions. There are also segmentation methods that require speci cation of the number of types of domains # (e.g. C G rich and G C poor representtwotypes of domains, whereas C G high, intermediate, and low specify three types) Segmentation analysis of DNA sequences can be found in [18, 15, 9, 33]. One particularly attractive segmentation method is a divideand conquer approach [4, 28] similar recursion processes are also discussed in statistics and machine learning under the names of classi cation and regression tree [10] recursive partitioning [38] decision tree induction [30, ....

GA Churchill (1989), \Stochastic models for heterogeneous DNA sequences", Bulletin of Mathematical Biology, 51:79-94.

....the most likely path for a given sequence is the corresponding sequence of words. Rabiner (Rabiner 1989) gives a good introduction to the theory of hidden Markov models and their applications to speech recognition. Hidden Markov models were introduced in computational biology in 1989 by Churchill (Churchill 1989). Durbin et al. Durbin et al. 1998) and Eddy (Eddy 1996; 1998) are good overviews of the use of hidden Markov models in computational biology. One of the most popular applications is to use them to characterise sequence families by using so called pro le hidden Markov models introduced by Krogh ....

Churchill, G. A. 1989. Stochastic models for heterogeneous DNA sequences. Bulletin of Mathematical Biology 51:79-94.

....and the most likely path for a given sequence is the corresponding sequence of words. Rabiner [19] gives a good introduction to the theory of hidden Markov models and their applications to speech recognition. Hidden Markov models were introduced in computational biology in 1989 by Churchill [5]. Durbin et al. 6] and Eddy [7, 8] are good overviews of the use of hidden Markov models in computational biology. One of the most popular applications is to use them to characterise sequence families by using so called pro le hidden Markov models introduced by Krogh et al. 15] For a pro le ....

G. A. Churchill. Stochastic models for heterogeneous DNA sequences. Bulletin of Mathematical Biology, 51:79-94, 1989.

....of occurrence of a letter at a given position depends only on the m previous letters in the sequence (and not on the position) the independent case is a particular case with m =0. Hidden Markov models (HMMs) reveal however that the composition of a DNA sequence may vary over the sequence (Churchill (1989), Muri 1998) Durbin et al. 1998) and can be studied with HMMs. However, no statistical properties of words have been yet derived in such heterogeneous models. DNA sequences code for amino acid sequences (proteins) by non overlapping triplets called codons. The three positions of the codons have ....

Churchill, G.A. 1989. Stochastic models for heterogeneous DNA sequences. Bull. Math. Biol., 51, 79-94.

....Hidden Markov Models, identifiability, Maximum Likelihood Estimation. 1 Introduction. Hidden Markov Models (HMMs) form a wide class of discrete time stochastic processes, used in different areas such as speech recognition (Juang and Rabiner 1989) neurophysiology (Fredkin and Rice 1987) biology (Churchill 1989), econometrics (Chib et al. 1998) and time series analysis (De Jong and Shephard 1995, Chan and Ledolter 1995; see Mac Donald and Zucchini 1997 and the references therein) Most works on maximum likelihood estimation in such models have focused on iterative numerical methods, suitable for ....

Churchill, G.A. (1989) Stochastic models for heterogeneous DNA sequences. Bull. Math.

....Markov model is to provide a mechanism for modelling the type of homogeneous segment at each location in the sequence. Crucially, the model for base transitions depends on the hidden label process and the analysis must allow for the fact that these data are missing. Initial work on the model by Churchill (1989, 1992) adopted a maximum likelihood approach and used the EM algorithm to deal with the hidden process. More recently, Muri (1997, 1998) Muri et al. 1998) and Boys et al. 1999) have adopted a Bayesian perspective and described how prior information may be incorporated into a procedure for ....

Churchill, G. A. (1989) Stochastic models for heterogeneous DNA sequences. Bull. Math. Biol., 51, 79--94.

....(HMM) for Sequence Alignment The HMM, as initially introduced in the late 1960s, is a powerful statistical modeling tool and has been widely applied in signal processing, speech recognition, time series analysis, etc. Rabiner 1989) The method was first applied to model biological sequences by Churchill (1989) and has become very popular recently in multiple sequence alignment (Baldi et al. 1994; Krogh et al. 1994; Lazareva and Churchill 1997) The basic form of an HMM can be written as y t f t (y j h t ) 2) h t g t (h j h t Gamma1 ) 3) where f t and g t are probability distributions (known up ....

Churchill, G.A. (1989), "Stochastic Models for Heterogeneous DNA Sequences," Bulletin of Mathematical Biology 51, 79-94.

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Churchill, G. A. 1989. Stochastic models for heterogeneous DNA sequences. Bull Math Biol 51:79#94.

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Churchill, G.A.: Stochastic models for heterogeneous DNA sequences. Bull. Math. Biol. 51 (1989) 79--94

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G.A. Churchill, Stochastic Models for heterogeneous DNA Sequences, Bull. Mathematical Biology, 51, 79-94, 1989.

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Churchill, G.A. (1989). Stochastic models for heterogeneous DNA sequences. Bull. Math. Bio. 51, 79-94.

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Churchill,G.A. (1989) Stochastic models for heterogeneous DNA sequences. Bull. Math. Biol., 51, 79--94.

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Churchill, G.A. (1989), "Stochastic models for heterogeneous DNA sequences", Bull. Math. Biol., 51, 79-94. 28

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Churchill,G. (1989) Stochastic models for heterogeneous DNA sequences. Bull. Math. Biol., 51,79--94.

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Churchill, G.A. (1989). Stochastic models for heterogeneous DNA sequences. Bull. Math. Bio. 51, 79-94.

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