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PubMed1999

Markov chain Monte Carlo analysis of human Y-chromosome microsatellites provides evidence of biased mutation.

We describe a Markov Chain Monte Carlo analysis of five human Y- chromosome microsatellite polymorphisms based on samples from five diverse populations. Our analysis provides strong evidence for mutational bias favoring increase in length at all loci. Estimates of population coalescent times and population size from our two largest samples, one African and one European, suggest that the African population is older but smaller and that the English East Anglian population has undergone significant expansion, being larger but younger. We conclude that Markov Chain Monte Carlo analysis of microsatellite haplotypes can uncover information not apparent when the microsatellites are considered independently. Incorporation of population size as a variable should allow us to estimate the timing and magnitude of major historical population trends.

Algorithms↗

PubMed1990

Markov chains as a shortcut method to estimate age distributions in herds of beef cattle under different culling strategies.

Markov chains were used to estimate the age distribution at equilibrium and average age in herds of beef cattle and the age distribution and average age of culled cows. These estimates are essential in systems simulation and economic analyses of beef production alternatives because the biological input and output from a beef production system depend on the age structure of the cows in the system. Ten sets of data on age-specific probabilities of culling for different reasons were found in the literature and used in simulation of different culling strategies. Three different culling strategies were simulated using these data. In addition to culling on maximum age, culling was either based on health alone, health and reproductive failure in one year (not pregnant) or health and reproductive failure in two consecutive years (not pregnant twice). The average herd age in the data sets reviewed under the actual culling strategies ranged from 4.58 to 6.73 yr and the average age of culled cows ranged from 5.41 to 9.94 yr. Description of the culling process as a Markov chain enables calculations of the age distribution at equilibrium by simple matrix operations, an advantage over the methods presently used. The scarcity of estimated age-specific probabilities of health and reproductive failure points to the need for more population analyses of beef cattle.

Age Factors↗

PubMed1981

Markov chain as a model of Hill's theory on circulation.

Establishing a model for various kinds of vivid metabolic systems of living organisms is an subject, uneasy but of great significance. Hill has constructed a theoretical framework for discussions of metabolic systems, such as active transport, muscle contraction, etc. The basic method of his framework is diagram calculation for the cycle flux on the metabolic cycles of those systems [2, 7] He has successively found that the result from diagram calculations agrees with the data of the numbers of completing different cycles given by random test (Monte Carlo test), but has not yet proved that the former is just the circulation rate in the sense of trajectory. In this paper, the model of a Markov chain is used to define the circulation rate in the sense of trajectories and, by deriving the remaining Markov chains, we calculate the expression of circulation rate which coincides with Hill's result obtained from diagrams. And hence we verify that Hill's cycle flux is equivalent to the circulation rate defined by trajectory. Besides, this paper establishes a connection between Hill's free energy of small systems and the potential of a Markov chain which is suggested by Hou Zhenting.

Markov Chains↗

PubMed1997

Markov chain Monte Carlo segregation and linkage analysis for oligogenic models.

A new method for segregation and linkage analysis, with pedigree data, is described. Reversible jump Markov chain Monte Carlo methods are used to implement a sampling scheme in which the Markov chain can jump between parameter subspaces corresponding to models with different numbers of quantitative-trait loci (QTL's). Joint estimation of QTL number, position, and effects is possible, avoiding the problems that can arise from misspecification of the number of QTL's in a linkage analysis. The method is illustrated by use of a data set simulated for the 9th Genetic Analysis Workshop; this data set had several oligogenic traits, generated by use of a 1,497-member pedigree. The mixing characteristics of the method appear to be good, and the method correctly recovers the simulated model from the test data set. The approach appears to have great potential both for robust linkage analysis and for the answering of more general questions regarding the genetic control of complex traits.

Computer Simulation↗

PubMed1999

Monte Carlo Markov chain methods for genome screening.

We used Monte Carlo Markov chain (MCMC) methods to analyze a quantitative trait, MAO level, and a discrete trait, Collaborative Study on the Genetics of Alcoholism (COGA) alcoholism. Segregation, linkage, and haplotype sharing were analyzed and effects of marker map features were examined. For MAO, modest signals were found on chromosomes 1 and 17 for raw data, and 15 for covariate-adjusted data. For alcoholism, a strong signal was found on chromosome 1 with modest signals on chromosomes 4 and 10.

Alcoholism↗

PubMed1997

Markov chain Monte Carlo methods for radiation hybrid mapping.

The ordering of genetic loci is central to genetic mapping at all levels. Markov chain Monte Carlo (MCMC) techniques can provide estimates of the posterior density of orders while accounting naturally for missing data, data errors, and unknown parameters. MCMC sampling schemes have been proposed for mapping problems such as linkage mapping and radiation hybrid mapping. The sampling schemes tend, however, to suffer from poor mixing caused by strong correlations between the model parameters. The method described here investigates the effect of using a modified sampling scheme, simulated tempering, on the mixing characteristics of the Markov chain. The method is illustrated by the analysis of haploid radiation hybrid mapping data; the principles are, however, applicable to a range of mapping problems. The results demonstrate that simulated tempering greatly improves the performance of the MCMC sampling scheme. For the radiation hybrid problem, the approach is probably not suitable for simultaneously ordering very large number of loci (> 100); it could, however, be useful for fine scale mapping of subsections of chromosomes.

Algorithms↗

PubMed1977

A Markov chain characterization of human neutrophil locomotion under neutral and chemotactic conditions.

The locomotion of human neutrophils is modelled by a continuous-time Markov chain model consisting of five states: state O, where the cell is stationary, and four motile states whose directions are defined by the four quadrants of a Cartesian plane. In this paper, the Markov property is verified experimentally in special cases. Further experimental evidence for the model is provided by the waiting-time distributions in each of the five states, which are well approximated by exponential distributions. Using the steady-state distribution of the Markov chain as a measure of the ultimate motion of the cells, it is possible to detect the effect of known chemotactic agents upon neutrophil locomotion. Other useful parameters describing neutrophil locomotion are presented.

Cell Movement↗

PubMed2001

Statistical measures of DNA sequence dissimilarity under Markov chain models of base composition.

In molecular biology, the issue of quantifying the similarity between two biological sequences is very important. Past research has shown that word-based search tools are computationally efficient and can find some new functional similarities or dissimilarities invisible to other algorithms like FASTA. Recently, under the independent model of base composition, Wu, Burke, and Davison (1997, Biometrics 53, 1431 1439) characterized a family of word-based dissimilarity measures that defined distance between two sequences by simultaneously comparing the frequencies of all subsequences of n adjacent letters (i.e., n-words) in the two sequences. Specifically, they introduced the use of Mahalanobis distance and standardized Euclidean distance into the study of DNA sequence dissimilarity. They showed that both distances had better sensitivity and selectivity than the commonly used Euclidean distance. The purpose of this article is to extend Mahalanobis and standardized Euclidean distances to Markov chain models of base composition. In addition, a new dissimilarity measure based on Kullback-Leibler discrepancy between frequencies of all n-words in the two sequences is introduced. Applications to real data demonstrate that Kullback-Leibler discrepancy gives a better performance than Euclidean distance. Moreover, under a Markov chain model of order kQ for base composition, where kQ is the estimated order based on the query sequence, standardized Euclidean distance performs very well. Under such a model, it performs as well as Mahalanobis distance and better than Kullback-Leibler discrepancy and Euclidean distance. Since standardized Euclidean distance is drastically faster to compute than Mahalanobis distance, in a usual workstation/PC computing environment, the use of standardized Euclidean distance under the Markov chain model of order kQ of base composition is generally recommended. However, if the user is very concerned with computational efficiency, then the use of Kullback-Leibler discrepancy, which can be computed as fast as Euclidean distance, is recommended. This can significantly enhance the current technology in comparing large datasets of DNA sequences.

Algorithms↗

PubMed2000

Bayesian analysis of discrete survival data with a hidden Markov chain.

This paper considers the discrete survival data from a Bayesian point of view. A sequence of the baseline hazard functions, which plays an important role in the discrete hazard function, is modeled with a hidden Markov chain. It is explained how the resultant model is implemented via Markov chain Monte Carlo methods. The model is illustrated by an application of real data.

Bayes Theorem↗

PubMed2005

Markov chain modelling for geriatric patient care.

OBJECTIVES: To show that Markov chain modelling can be applied to data on geriatric patients and use these models to assess the effects of covariates. METHODS: Phase-type distributions were fitted by maximum likelihood to data on times spent by the patients in hospital and in community-based care. Data on the different events that ended the patients' periods of care were used to estimate the dependence of the probabilities of these events on the phase from which the time in care ended. The age of the patients at admission to care and the year of admission were also included as covariates. RESULTS: Differential effects of these covariates were shown on the various parameters of the fitted model, and interpretations of these effects made. CONCLUSIONS: Models based on phase-type distributions were appropriate for describing times spent in care, as the ordered phases had an interpretable structure corresponding to increasing amounts of care being given.

Aged↗

PubMed2005

Finite-size scaling analysis of percolation in three-dimensional correlated binary Markov chain random fields.

Percolation and finite-size scaling properties in three-dimensional binary correlated Markov-chain random fields on a cubic lattice are computed by extensive Monte Carlo simulation. At short correlation scales, the percolation threshold in correlated random fields decreases as the correlation scale increases. The rate of decrease rapidly diminishes for correlation lengths larger than 2-3 lattice sites. At correlation scales of 4-6 lattice sites, the percolation threshold is found to be 0.126 +/- 0.001 for the Markov chain random fields, similar to that for sequential Gaussian and indicator random fields, which are evaluated for comparison. The average percolation threshold in finite-size lattices is a function of both, the correlation length and the finite lattice size. The universal scaling constants for mean cluster size and backbone fraction are found to be consistent with results on uncorrelated lattices. But prefactors of scaling relationships vary with correlation length. The squared radius of gyration of non-percolating clusters is found to scale with gamma/nu and its scaling prefactors are independent of the correlation scale. Prefactors are similar between the three random field generators evaluated. The percolation properties derived here are useful to account for finite-size effects on percolation in natural or man-made correlated systems.

Journal Article↗

PubMed1999

Interpolated markov chains for eukaryotic promoter recognition.

MOTIVATION: We describe a new content-based approach for the detection of promoter regions of eukaryotic protein encoding genes. Our system is based on three interpolated Markov chains (IMCs) of different order which are trained on coding, non-coding and promoter sequences. It was recently shown that the interpolation of Markov chains leads to stable parameters and improves on the results in microbial gene finding (Salzberg et al., Nucleic Acids Res., 26, 544-548, 1998). Here, we present new methods for an automated estimation of optimal interpolation parameters and show how the IMCs can be applied to detect promoters in contiguous DNA sequences. Our interpolation approach can also be employed to obtain a reliable scoring function for human coding DNA regions, and the trained models can easily be incorporated in the general framework for gene recognition systems. RESULTS: A 5-fold cross-validation evaluation of our IMC approach on a representative sequence set yielded a mean correlation coefficient of 0.84 (promoter versus coding sequences) and 0.53 (promoter versus non-coding sequences). Applied to the task of eukaryotic promoter region identification in genomic DNA sequences, our classifier identifies 50% of the promoter regions in the sequences used in the most recent review and comparison by Fickett and Hatzigeorgiou ( Genome Res., 7, 861-878, 1997), while having a false-positive rate of 1/849 bp.

Algorithms↗

PubMed2003

Connective tissue polarity unraveled by a markov-chain mechanism of collagen fibril segment self-assembly.

The well-established occurrence of pyroelectricity (Lang, 1966) in tissues of living organisms has found a first explanation by a Markov-chain mechanism taking place during collagen fibril self-assembly in extracytoplasmic channels. Recently reported biochemical findings on the longitudinal fusion reactivity of small fibril segments (which undergo C-, N- and C-, C- but not N-, N-terminal fusions; see Graham et al., 2000; Kadler et al., 1996) may provide a mechanism by which a difference in the fusion probabilities P(CC), P(NN) drives the self-assembly into partial macroscopic polar order. In principle, a Markov-chain growth process can lower the noncentrosymmetric infinity 2 symmetry describing dielectric properties of a growing limb (as managed by fibroblasts) into the polar infinity group. It is proposed that macroscopically polar properties enter the biological world by a stochastic mechanism of unidirectional growth. Polarity formation in organisms shows similarity to effects reported for molecular crystals (Hulliger et al., 2002).

Cell Division↗

PubMed1998

Compound Poisson and Poisson process approximations for occurrences of multiple words in Markov chains.

We derive a Poisson process approximation for the occurrences of clumps of multiple words and a compound Poisson process approximation for the number of occurrences of multiple words in a sequence of letters generated by a stationary Markov chain. Using the Chen-Stein method, we provide a bound on the error in the approximations. For rare words, these errors tend to zero as the length of the sequence increases to infinity. Modeling a DNA sequence as a stationary Markov chain, we show as an application that the compound Poisson approximation is efficient for the number of occurrences of rare stem-loop motifs.

Base Sequence↗

PubMedDate not supplied

[The application of Markov chains to demographic projections in smaller geopolitical areas].

"This article deals with the use of Markov chains to project population in smaller geopolitical areas. The method consists of projecting only the relative distribution which, applied to a previous demographic projection, gives figures for the population by subregion. An algorithm is worked out, allowing for an estimate to be made of the transitional probabilities of the chain based on easily available data: the total population residing in two or more regions or states in only two specific moments. Once those probabilities have been determined, the projection of the probabilities and of the relative distribution is direct. This method is applied to the metropolitan zone of Mexico City, for which population and territorial extension are projected." (SUMMARY IN ENG)

Americas↗

PubMed2005

Is anoxic depolarisation associated with an ADC threshold? A Markov chain Monte Carlo analysis.

A Bayesian nonlinear hierarchical random coefficients model was used in a reanalysis of a previously published longitudinal study of the extracellular direct current (DC)-potential and apparent diffusion coefficient (ADC) responses to focal ischaemia. The main purpose was to examine the data for evidence of an ADC threshold for anoxic depolarisation. A Markov chain Monte Carlo simulation approach was adopted. The Metropolis algorithm was used to generate three parallel Markov chains and thus obtain a sampled posterior probability distribution for each of the DC-potential and ADC model parameters, together with a number of derived parameters. The latter were used in a subsequent threshold analysis. The analysis provided no evidence indicating a consistent and reproducible ADC threshold for anoxic depolarisation.

Algorithms↗

PubMed1986

Markov chain model and its application.

This paper examines the use of the Markov chain model to study the condition of asthma patients with respect to seasonal variations. The model can be utilized for predicting the health status of these patients.

Asthma↗

PubMed2004

Markov chain analysis of succession in a rocky subtidal community.

We present a Markov chain model of succession in a rocky subtidal community based on a long-term (1986-1994) study of subtidal invertebrates (14 species) at Ammen Rock Pinnacle in the Gulf of Maine. The model describes successional processes (disturbance, colonization, species persistence, and replacement), the equilibrium (stationary) community, and the rate of convergence. We described successional dynamics by species turnover rates, recurrence times, and the entropy of the transition matrix. We used perturbation analysis to quantify the response of diversity to successional rates and species removals. The equilibrium community was dominated by an encrusting sponge (Hymedesmia) and a bryozoan (Crisia eburnea). The equilibrium structure explained 98% of the variance in observed species frequencies. Dominant species have low probabilities of disturbance and high rates of colonization and persistence. On average, species turn over every 3.4 years. Recurrence times varied among species (7-268 years); rare species had the longest recurrence times. The community converged to equilibrium quickly (9.5 years), as measured by Dobrushin's coefficient of ergodicity. The largest changes in evenness would result from removal of the dominant sponge Hymedesmia. Subdominant species appear to increase evenness by slowing the dominance of Hymedesmia. Comparison of the subtidal community with intertidal and coral reef communities revealed that disturbance rates are an order of magnitude higher in coral reef than in rocky intertidal and subtidal communities. Colonization rates and turnover times, however, are lowest and longest in coral reefs, highest and shortest in intertidal communities, and intermediate in subtidal communities.

Animals↗