Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Markov Chain”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17Linked to original sources
PubMed2004

[Cluster analysis in geographical epidemiology: the use of several statistical methods and comparison of their results].

BACKGROUND: The increasing interest in environmental epidemiology has been followed by the development of many statistical tests for detecting disease clustering near a point source. The objectives of this study were to compare several tests to detect disease clustering, among which modelisation using Markov Chain Monte Carlo methods. METHODS: We compared six statistical methods for detecting disease clustering of bladder cancer around an industrial centre of Isère (France) for the period 1983-1997: Stone's test, score test, and two log-linear modelisations (with and without corrections for extra-Poisson variations) using two ways of parameters estimation (maximum likelihood and Markov Chain Monte Carlo methods). RESULTS: The results of the Stone test and the score test are not in favour of a higher risk of bladder cancer around the considered point source. The conclusions brought by the log linear modelisations are the same, but the results obtained using the Markov Chain Monte Carlo Method are very dependant of prior distributions determined for the different parameters. CONCLUSION: Markov Chain Monte Carlo methods, which allow taking into account complex geographical effects, seem well adapted to cluster analysis in geographical epidemiology. However, they remain difficult to implement.

Adolescent↗
PubMed2005

A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability.

A discrete-time Markov chain model, a continuous-time Markov chain model, and a stochastic differential equation model are compared for a population experiencing demographic and environmental variability. It is assumed that the environment produces random changes in the per capita birth and death rates, which are independent from the inherent random (demographic) variations in the number of births and deaths for any time interval. An existence and uniqueness result is proved for the stochastic differential equation system. Similarities between the models are demonstrated analytically and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models satisfy certain consistency conditions.

Animals↗
PubMed1993

DNA damage in non-proliferating cells subjected to ionizing irradiation at high or low dose rates.

Ionizing radiation damage to the genome of a non-cycling mammalian cell is analyzed using continuous time Markov chains. Immediate damage induced by the radiation is modeled as a batch Poisson arrival process of DNA double strand breaks (DSBs). Different kinds of radiation, for example gamma rays or alpha particles, have different batch probabilities. Enzymatic modulation of the immediate damage is modeled as a Markov process similar to the processes described by the master equation of stochastic chemical kinetics. An illustrative example is the restitution/complete exchange model, which postulates that radiation induced DSBs can subsequently either undergo enzymatically mediated repair (restitution) or can participate pairwise in chromosome exchanges, some of which make irremediable lesions such as dicentric chromosome aberrations. One may have rapid irradiation followed by enzymatic DSB processing or have prolonged irradiation with both DSB arrival and enzymatic DSB processing continuing throughout the irradiation period. A complete solution of the Markov chain is known for the case that the exchange rate constant is negligible so that no irremediable chromosome lesions are produced and DSBs are the only damage to the genome. Using PDEs for generating functions, a perturbation calculation is made assuming the exchange rate constant is small compared to the repair rate constant. Some non-perturbative results applicable to very prolonged irradiation are also obtained using matrix methods: Perron-Frobenius theory, variational methods and numerical approximations of eigenvalues. Applications to experimental results on expected values, variances and statistical distributions of DNA lesions are briefly outlined. Continuous time Markov chain models are the most systematic of those current radiation damage models which treat DSB-DSB interactions within the cell nucleus as homogeneous (e.g. ignore diffusion limitations). They contain most other homogeneous models as special cases, limiting cases or approximations. However, applying the continuous time Markov chain models to studying spatial dependence of DSB interactions, which is generally believed to be very important in some situations, presents difficulties.

Animals↗
PubMed1992

A stochastic analysis of three viral sequences.

This paper analyzes the nucleotide sequences of three viruses: Kunjin, west Nile, and yellow fever. Each virus has one long open reading frame of greater than 10,200 nucleotides that codes for four structural and seven nonstructural genes. The Kunjin and west Nile viruses are the most closely related pair, when assessed on the basis of matches between their nucleotide sequences. As would be expected, the matching is least for bases at third-position codon sites and is greatest for second-position sites. Statistics are presented for the numbers of mismatches that are transitions or transversions. Nucleotide base usage is also reported. To each of the 33 virus-gene segments, nonhomogeneous Markov chain models have been fitted to describe the sequences of nucleotide bases. The models allow for different transition probabilities ("transition" is used in the mathematical sense here) and for different degrees of dependency, at the three sites in the codons. Reasonably satisfactory fits can be obtained for many of the genes by using models that are first order for both first- and second-position sites in the codon but that are second order for third-position sites. One consequence of such a model is that the correlation between one amino acid and the next is limited to the correlation of the last base of the former with the first base of the latter. Other consequences are that the model can (and does) prohibit the occurrence of stop codons within a gene and that subsequences of only first-position bases, or only third-position bases, are also first-order Markov chains. In theory, second-position subsequences may not be Markov chains at all. In practice, the data suggest that each of these subsequences is effectively a zero-order Markov chain, i.e., bases spaced three apart are statistically independent. Stationarity of nucleotide base distributions can be interpreted in either of two ways: (1) spatially along the sites or (2) temporally at each site. These interpretations must often be inconsistent, when the former allows for Markov dependence between adjacent sites whereas the latter assumes independence between sites. The inconsistency can be overcome, for these viruses, if subsequences at different codon positions are analyzed separately.

Base Sequence↗
PubMedDate not supplied

[Successions in the forest-steppe under climate changes: a modelling approach].

The paper represents an attempt to apply the general principles of modelling vegetation dynamics under climate changes to a study of the long-term vegetation dynamics in the forest-steppe zone of the European territory of Russia, with a purpose to forecast under special climatic scenarios. An original technique is used to construct a Markov chain as a model of vegetation succession. The technique emanated from gebotanic knowledge generalized as a scheme of successional transitions with estimates of the average duration for certain stages of succession. Whenever the knowledge related the stage duration to certain (climate-sensitive) factors of the environment, the fundamental potentiality arises to model the temporal course of succession as a function of a given scenario for how the key factors change. In the formal terms, the model represents a random chain of the Markov kind with a finite number of states and discrete time of transitions by the given scheme. Relative square distributions of succession stages under concern at any time moment (within an adopted scenario) appear as the model outcome (forecasts), as well as estimates of the attainment time for certain states of the vegetation in the territory under study. A method is proposed to describe dynamics of the phytomass production and stores (and the corresponding model trajectories are obtained) for a given scenario.

Adaptation, Physiological↗
PubMed2001

A simple calculation for the buildup and decay of radon progeny.

A Markov chain in conjunction with an electronic spreadsheet is used to generate the buildup and decay patterns of radon progeny in a procedure involving only multiplication and addition. Markov chains are highly suitable for calculations of this type. Because the Markov matrix may not be readily available, and because some health physicists may not be familiar with this procedure, we give the values of a Markov matrix and demonstrate how it can be used to produce a Markov chain describing the buildup and decay of radon progeny.

Markov Chains↗
PubMed2006

Multipoint linkage analysis with many multiallelic or dense diallelic markers: Markov chain-Monte Carlo provides practical approaches for genome scans on general pedigrees.

Computations for genome scans need to adapt to the increasing use of dense diallelic markers as well as of full-chromosome multipoint linkage analysis with either diallelic or multiallelic markers. Whereas suitable exact-computation tools are available for use with small pedigrees, equivalent exact computation for larger pedigrees remains infeasible. Markov chain-Monte Carlo (MCMC)-based methods currently provide the only computationally practical option. To date, no systematic comparison of the performance of MCMC-based programs is available, nor have these programs been systematically evaluated for use with dense diallelic markers. Using simulated data, we evaluate the performance of two MCMC-based linkage-analysis programs--lm_markers from the MORGAN package and SimWalk2--under a variety of analysis conditions. Pedigrees consisted of 14, 52, or 98 individuals in 3, 5, or 6 generations, respectively, with increasing amounts of missing data in larger pedigrees. One hundred replicates of markers and trait data were simulated on a 100-cM chromosome, with up to 10 multiallelic and up to 200 diallelic markers used simultaneously for computation of multipoint LOD scores. Exact computation was available for comparison in most situations, and comparison with a perfectly informative marker or interprogram comparison was available in the remaining situations. Our results confirm the accuracy of both programs in multipoint analysis with multiallelic markers on pedigrees of varied sizes and missing-data patterns, but there are some computational differences. In contrast, for large numbers of dense diallelic markers, only the lm_markers program was able to provide accurate results within a computationally practical time. Thus, programs in the MORGAN package are the first available to provide a computationally practical option for accurate linkage analyses in genome scans with both large numbers of diallelic markers and large pedigrees.

Alleles↗
PubMed1998

Selecting a decision model for economic evaluation: a case study and review.

The increased use of modelling techniques as a methodological tool in the economic evaluation of health care technologies has, in the main, been limited to two approaches--decision trees and Markov chain models. The former are suited to modelling simple scenarios that occur over a short time period, whilst Markov chain models allow longer time periods to be modelled, in continuous time, where the timing of an event is uncertain. In the context of economic evaluation, a less well developed technique is discrete event simulation, which may allow even greater flexibility. Taking the economic evaluation of adjuvant therapies for breast cancer as an illustrative example, the process of building a decision tree, a Markov chain model, and a discrete event simulation model are described. The potential benefits and problems of each approach are discussed. The suitability of the modelling techniques to economic evaluations of health care programmes in general is then discussed. This section aims to illustrate the areas in which the alternative modelling methods may be most appropriately employed.

Adult↗
PubMed2000

Convergence diagnosis for Gibbs sampling output.

Gibbs sampling is a technique to calculate a complex posterior distribution as steady state measure of a Markov chain. The fundamental problem of inference from Markov chain simulation is that there will always be areas of the target distribution that have not been covered by the finite chain. Deciding when to stop the chain in order to have reached enough coverage of the support of the target distribution is an important matter. Techniques based on one long single chain and on multiple chains are discussed in the framework of a linear mixed effects model. The diagnostics used do not provide a consistent view on the convergence. Practical consequences on the estimates are shown.

Arteriosclerosis↗
PubMed2003

Recursions for statistical multiple alignment.

Algorithms are presented that allow the calculation of the probability of a set of sequences related by a binary tree that have evolved according to the Thorne-Kishino-Felsenstein model for a fixed set of parameters. The algorithms are based on a Markov chain generating sequences and their alignment at nodes in a tree. Depending on whether the complete realization of this Markov chain is decomposed into the first transition and the rest of the realization or the last transition and the first part of the realization, two kinds of recursions are obtained that are computationally similar but probabilistically different. The running time of the algorithms is O(Pi id=1 Li), where Li is the length of the ith observed sequences and d is the number of sequences. An alternative recursion is also formulated that uses only a Markov chain involving the inner nodes of a tree.

Algorithms↗
PubMed2003

Hierarchical Bayesian modeling of spatially correlated health service outcome and utilization rates.

We present Bayesian hierarchical spatial models for spatially correlated small-area health service outcome and utilization rates, with a particular emphasis on the estimation of both measured and unmeasured or unknown covariate effects. This Bayesian hierarchical model framework enables simultaneous modeling of fixed covariate effects and random residual effects. The random effects are modeled via Bayesian prior specifications reflecting spatial heterogeneity globally and relative homogeneity among neighboring areas. The model inference is implemented using Markov chain Monte Carlo methods. Specifically, a hybrid Markov chain Monte Carlo algorithm (Neal, 1995, Bayesian Learning for Neural Networks; Gustafson, MacNab, and Wen, 2003, Statistics and Computing, to appear) is used for posterior sampling of the random effects. To illustrate relevant problems, methods, and techniques, we present an analysis of regional variation in intraventricular hemorrhage incidence rates among neonatal intensive care unit patients across Canada.

Bayes Theorem↗
PubMed1980

An ancestral amplification of DNA in primates.

Newly evolved, tandemly arrayed, highly repeated DNAs from three primates were compared using Markov-chain and random-simulation approaches. Markov-chain calculations suggested that the repeated DNA sequences derived from the amplification of a progenitor sequence some 55 million years ago. Divergence of the products of this ancestral amplification could have created a library of related DNA sequences from which newly evolved repeated DNA was drawn - by recent amplifications of library members. The ancestral DNA amplification may have provided the genetic flexibility for creating the primate order; more recent amplifications in old-world primates probably led to the present subfamilies. The random-simulation approach verified the idea that repeated DNA evolves nonrandomly. A variable region was identified within the sequence.

Animals↗
PubMedDate not supplied

Engineering in software testing: statistical testing based on a usage model applied to medical device development.

When a population is too large for exhaustive study, as is the case for all possible uses of a software system, a statistically correct sample must be drawn as a basis for inferences about the population. A Markov chain usage model is an engineering formalism that represents the population of possible uses for which a product is to be tested. In statistical testing of software based on a Markov chain usage model, the rich body of analytical results available for Markov chains provides numerous insights that can be used in both product development and test planing. A usage model is based on specifications rather than code, so insights that result from model building can inform product decisions in the early stages of a project when the opportunity to prevent problems is the greatest. Statistical testing based on a usage model provides a sound scientific basis for quantifying the reliability of software.

Equipment Safety↗
PubMed1993

Entropy and convergence in dynamics and demography.

Demographic dynamics is formally equivalent to the dynamics of a Markov chain, as is true of some nonlinear dynamical systems. Convergence to demographic equilibrium can be studied in terms of convergence in the Markov chain. Tuljapurkar (1982) showed that population entropy (Kolmogorov-Sinai entropy) provides information on the rate of this convergence. This paper begins by considering finite state Markov chains, providing elementary proofs of the relationship between convergence rate and entropy, and discusses in detail the uses and limitations of entropy as a convergence measure; these results also apply to Markovian dynamical systems. Next, new qualitative and quantitative arguments are used to discuss the demographic meaning of entropy. An exact relationship is established giving population entropy in terms of the eigenvalues of the Leslie matrix characteristic equation. Finally, the significance of imprimitive and periodic limits is discussed in relation to population entropy.

Demography↗
PubMed2006

MCMC data association and sparse factorization updating for real time multitarget tracking with merged and multiple measurements.

In several multitarget tracking applications, a target may return more than one measurement per target and interacting targets may return multiple merged measurements between targets. Existing algorithms for tracking and data association, initially applied to radar tracking, do not adequately address these types of measurements. Here, we introduce a probabilistic model for interacting targets that addresses both types of measurements simultaneously. We provide an algorithm for approximate inference in this model using a Markov chain Monte Carlo (MCMC)-based auxiliary variable particle filter. We Rao-Blackwellize the Markov chain to eliminate sampling over the continuous state space of the targets. A major contribution of this work is the use of sparse least squares updating and downdating techniques, which significantly reduce the computational cost per iteration of the Markov chain. Also, when combined with a simple heuristic, they enable the algorithm to correctly focus computation on interacting targets. We include experimental results on a challenging simulation sequence. We test the accuracy of the algorithm using two sensor modalities, video, and laser range data. We also show the algorithm exhibits real time performance on a conventional PC.

Algorithms↗
PubMed1995

Application of Markov process modelling to health status switching behaviour of infants.

BACKGROUND: This study is an attempt to apply Markov process modelling to health status switching behaviour of infants. The data for the study consist of monthly records of diagnosed illnesses for 1152 children, each observed from the month of first contact with Kasangati Health Centre, Kampala, Uganda, until age 18 months. METHODS: Only two states of health are considered in the study, a 'Health' state, denoted by W: (for Well), and an 'Illness' state denoted by S: (for Sick). The data are thus reduced to monthly records (W or S) of the states of health of the study sample. The simplest model of dependence of current health state on the past is one that links the current state to the immediately preceding month only; that is a Markov model. The starting point of this study was therefore to determine the proportions of children making the transitions W-->W, W-->S, S-->W, S-->S, from one month to the next, for each month from birth (month 0) to 18 months of age (month 18). These were used as estimates of the probabilities of making these transitions for each month from birth. This paper discusses the main features emerging from the study of these transition probabilities. RESULTS: In the first 5 months after birth, the probabilities of making the transitions W-->W, W-->S, S-->W, S-->S from one month to the next, showed some dependence on the age of the child. From the sixth month on, however, the dependence on age seemed to wear off. The transition probabilities remained the same from then on, suggesting that the switching pattern between health states behaves, eventually, like a time-homogeneous Markov Chain. This time-homogeneous chain attained a steady state distribution at about 12 months from birth. CONCLUSIONS: The study has shown that the transitions between Health and Illness for infants, from month to month, can be modelled by a Markov Chain for which the (single-step) transition probabilities are generally time-dependent or age-dependent. After the first few months of life the dependence on age may wear off, as in this study, leading to a time-homogeneous Markov Chain, which eventually attains a steady state distribution in about 12 months. Interpretations of the transition probabilities as measures of disease prevalence are discussed.

Age Factors↗
PubMedDate not supplied

[Statistical analysis of genome].

The chemical structure of DNA is characterized by sequences of four basic nitrogens occurring in one of two nucleic acid chains and in a complementary fashion in the other. Markov chain is the aspect of probability theory that analyzes discrete states in which transition is a fixed probability not affected by the history of the system. It is shown that DNA is represented in the form of regular Markov chain. Ergodicity property and law of large numbers follow from the statistical analysis of stationary transition probabilities.

Algorithms↗
PubMedDate not supplied

Cells coupled by voltage-dependent gap junctions: the asymptotic dynamical limit.

We study the steady state and dynamical properties of a pair of cells coupled by a voltage-dependent gap junction. The cells have linear membrane properties, and the gap junction is modelled using a simple Markov chain with a voltage-dependent transition matrix. We first show that the voltage-independent case is globally convergent using energy dissipation as a Lyapunov function for the cells, and standard results on the convergence of homogeneous Markov chains for the junction. For the voltage-dependent case, we use the difference in cell and gap junction time scales to reduce the coupled equations for cells and the gap junction to a single equation for the gap junction, but with a transition matrix that depends upon the current gap junction state. We identify cooperativity as key property behind the global convergence of Markov chains and investigate convergence of the voltage-dependent system by establishing some conditions under which cooperativity is preserved.

Cell Communication↗