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 145 records · Page 8Linked to original sources
PubMed2001

Use of a Markov-chain Monte Carlo model to evaluate the time value of historical testing information in animal populations.

Quantitative risk assessments are now required to support many regulatory decisions involving infectious diseases of animals. Current methods, however, do not consider the relative values of historical and recent data. A Markov-chain model can use specific disease characteristics to estimate the present value of disease information collected in the past. Uncertainty about the disease characteristics and variability among animals and herds can be accounted for with Monte Carlo simulation modeling. This results in a transparent method of valuing historical testing information for use in risk assessments. We constructed such a model to value historical testing information in a more-transparent and -reproducible manner. Applications for this method include trade, food safety, and domestic animal-health regulations.

Animal Diseases↗
PubMed2000

Markov chain Monte Carlo for mapping a quantitative trait locus in outbred populations.

A Bayesian approach is presented for mapping a quantitative trait locus (QTL) using the 'Fernando and Grossman' multivariate Normal approximation to QTL inheritance. For this model, a Bayesian implementation that includes QTL position is problematic because standard Markov chain Monte Carlo (MCMC) algorithms do not mix, i.e. the QTL position gets stuck in one marker interval. This is because of the dependence of the covariance structure for the QTL effects on the adjacent markers and may be typical of the 'Fernando and Grossman' model. A relatively new MCMC technique, simulated tempering, allows mixing and so makes possible inferences about QTL position based on marginal posterior probabilities. The model was implemented for estimating variance ratios and QTL position using a continuous grid of allowed positions and was applied to simulated data of a standard granddaughter design. The results showed a smooth mixing of QTL position after implementation of the simulated tempering sampler. In this implementation, map distance between QTL and its flanking markers was artificially stretched to reduce the dependence of markers and covariance. The method generalizes easily to more complicated applications and can ultimately contribute to QTL mapping in complex, heterogeneous, human, animal or plant populations.

Animals↗
PubMed2006

Fitting genetic models using Markov Chain Monte Carlo algorithms with BUGS.

Maximum likelihood estimation techniques are widely used in twin and family studies, but soon reach computational boundaries when applied to highly complex models (e.g., models including gene-by-environment interaction and gene-environment correlation, item response theory measurement models, repeated measures, longitudinal structures, extended pedigrees). Markov Chain Monte Carlo (MCMC) algorithms are very well suited to fit complex models with hierarchically structured data. This article introduces the key concepts of Bayesian inference and MCMC parameter estimation and provides a number of scripts describing relatively simple models to be estimated by the freely obtainable BUGS software. In addition, inference using BUGS is illustrated using a data set on follicle-stimulating hormone and luteinizing hormone levels with repeated measures. The examples provided can serve as stepping stones for more complicated models, tailored to the specific needs of the individual researcher.

Algorithms↗
PubMed1993

On the irreducibility of a Markov chain defined on a space of genotype configurations by a sampling scheme.

Techniques from image processing are now being considered for use in pedigree analysis. Although the method that we develop here was motivated by considering it as an analogue to the Gibbs sampler, we justify it independently using the ergodic theorem for aperiodic, irreducible, finite Markov chains. While it is trivial to show that aperiodicity holds, irreducibility is a more interesting condition. Proofs of irreducibility are provided for some special cases and counterexamples are provided for others. Where irreducibility does not hold, an alternative method using relaxed genetic parameters and rejection is recommended and justified.

Alleles↗
PubMedDate not supplied

Cluster modelling of disease incidence via RJMCMC methods: a comparative evaluation. Reversible jump Markov chain Monte Carlo.

The spatial modelling of small area health data has, for some time, included spatial autocorrelation as a random effect. This effect is non-specific and global and does not address the location of clusters of disease (a specific task). This paper addresses the need for specific and non-specific random effects within spatial epidemiology. In addition, individual frailty is also considered important and a computational algorithm based on reversible jump Markov chain Monte Carlo (RJMCMC) methods is described.

Algorithms↗
PubMed2005

Stochastic dietary restriction using a Markov-chain feeding protocol elicits complex, life history response in medflies.

Lifespan in individually housed medflies (virgins of both sexes) and daily reproduction for females were studied following one of 12 dietary restriction (DR) treatments in which the availability of high-quality food (yeast-sugar mixture) for each fly was based on a Markov chain feeding scheme--a stochastic dietary regime which specifies that the future dietary state depends only on the present dietary state and not on the path by which the present state was achieved. The stochastic treatments consisted of a combination of one of four values of a 'discovery' parameter and one of three values of a 'persistence' parameter. The results supported the hypotheses that: (i) longevity is extended in most medfly cohorts subject to stochastic DR; and (ii) longevity is more affected by the patch discovery than the patch persistence parameter. One of the main conclusions of the study is that, in combination with the results of earlier dietary restriction studies on the medfly, the results reinforce the concept that the details of the dietary restriction protocols have a profound impact on the sign and magnitude of the longevity extension relative to ad libitum cohorts and that a deeper understanding of the effect of food restriction on longevity is not possible without an understanding of its effect on reproduction.

Age Factors↗
PubMedDate not supplied

Conditional rate derivation in the presence of intervening variables using a Markov chain.

When conducting inferential and epidemiologic studies, researchers are often interested in the distribution of time until the occurrence of some specified event, a form of incidence calculation. Furthermore, this interest often extends to the effects of intervening factors on this distribution. In this paper we impose the assumption that the phenomena being investigated are governed by a stationary Markov chain and review how one may estimate the above distribution. We then introduce and relate two different methods of investigating the effects of intervening factors. In particular, we show how an investigator may evaluate the effect of potential intervention programs. Finally, we demonstrate the proposed methodology using data from a population study.

Abortion, Induced↗
PubMed2005

[Markov Chain Monte Carlo Method of multiple imputation for longitudinal data with missing values in the survey of maternal and children health].

OBJECTIVE: To deal with arbitrary missing pattern in longitudinal data of the Survey of Maternal and Child Health and make the most appropriate inferences with multiple imputation (MI) for further analysis. METHODS: SAS 9.0 was used for Markov Chain Monte Carlo (MCMC) method of MI procedure to impute missing values and combine inferences. RESULTS: The result is acceptable as the data set was imputed 5 times. CONCLUSION: MI is able to solve a variety of problems in missing data sets and to improve the statistical power, especially with the use of MCMC method, for complicated missing data sets.

Bias↗
PubMed2004

Bayesian Markov chain Monte Carlo sequence analysis reveals varying neutral substitution patterns in mammalian evolution.

We describe a model of neutral DNA evolution that allows substitution rates at a site to depend on the two flanking nucleotides ("context"), the branch of the phylogenetic tree, and position within the sequence and implement it by using a flexible and computationally efficient Bayesian Markov chain Monte Carlo approach. We then apply this approach to characterize phylogenetic variation in context-dependent substitution patterns in a 1.7-megabase genomic region in 19 mammalian species. In contrast to other substitution types, CpG transition substitutions have accumulated in a relatively clock-like fashion. More broadly, our results support the notion that context-dependent DNA replication errors, cytosine deamination, and biased gene conversion are major sources of naturally occurring mutations whose relative contributions have varied in mammalian evolution as a result of changes in generation times, effective population sizes, and recombination rates.

Animals↗
PubMed1995

Estimation of mean sojourn time in breast cancer screening using a Markov chain model of both entry to and exit from the preclinical detectable phase.

The sojourn time, time spent in the preclinical detectable phase (PCDP) for chronic diseases, for example, breast cancer, plays an important role in the design and assessment of screening programmes. Traditional methods to estimate it usually assume a uniform incidence rate of preclinical disease from a randomized control group or historical data. In this paper, a two-parameter Markov chain model is proposed and developed to explicitly estimate the preclinical incidence rate (lambda 1) and the rate of transition from preclinical to clinical state (lambda 2, equivalent to the inverse of mean sojourn time) without using control data. A new estimate of sensitivity is proposed, based on the estimated parameters of the Markov process. When this method is applied to the data from the Swedish two-county study of breast cancer screening in the age group 70-74, the estimate of MST is 2.3 with 95 per cent CI ranging from 2.1 to 2.5, which is close to the result based on the traditional method but the 95 per cent CI is narrower using the Markov model. The reason for the greater precision of the latter is the fuller use of all temporal data, since the continuous exact times to events are used in our method instead of grouping them as in the traditional method. Ongoing and future researches should extend this model to include, for example, the tumour size, nodal status and malignancy grade, along with methods of simultaneously estimating sensitivity and the transition rates in the Markov process.

Adult↗
PubMed2001

Estimating statistics of neuronal dynamics via Markov chains.

We present an efficient computational method for estimating the mean and variance of interspike intervals defined by the timing of spikes in typical orbits of one-dimensional neuronal maps. This is equivalent to finding the mean and variance of return times of orbits to particular regions of phase space. Rather than computing estimates directly from time series, the system is modelled as a finite state Markov chain to extract stationary behaviour in the form of invariant measures and average absorption times. Ergodic-theoretic formulae are then applied to produce the estimates without the need to generate orbits directly. The approach may be applied to both deterministic and randomly forced systems.

Action Potentials↗
PubMed1997

Analysis of aerial survey data on Florida manatee using Markov chain Monte Carlo.

We assess population trends of the Atlantic coast population of Florida manatee, Trichechus manatus latirostris, by reanalyzing aerial survey data collected between 1982 and 1992. To do so, we develop an explicit biological model that accounts for the method by which the manatees are counted, the mammals' movement between surveys, and the behavior of the population total over time. Bayesian inference, enabled by Markov chain Monte Carlo, is used to combine the survey data with the biological model. We compute marginal posterior distributions for all model parameters and predictive distributions for future counts. Several conclusions, such as a decreasing population growth rate and low sighting probabilities, are consistent across different prior specifications.

Animals↗
PubMedDate not supplied

An overview on the distribution of word counts in Markov chains.

In this paper, we give an overview about the different results existing on the statistical distribution of word counts in a Markovian sequence of letters. Results concerning the number of overlapping occurrences, the number of renewals and the number of clumps will be presented. Counts of single words and also multiple words are considered. Most of the results are approximations as the length of the sequence tends to infinity. We will see that Gaussian approximations switch to (compound) Poisson approximations for rare words. Modeling DNA sequences or proteins by stationary Markov chains, these results can be used to study the statistical frequency of motifs in a given sequence.

Biometry↗
PubMed2000

The first, second, third and fourth order Markov chain analysis on the amino-acid sequence of human dopamine beta-hydroxylase.

The repeated amino-acid sequences in human dopamine beta-hydroxylase (DBH) may be indispensable for DBH activity, because such repetitions cannot be simply attributed to random chance. The amino acid sequence of human DBH was analysed according to two-, three-, four- and five-amino-acid sequences and their probabilities in human DBH were calculated. The first, second, third and fourth order Markov chain was used to calculate the transition probability for two-, three-, four- and five-amino-acid sequences. The longest repeated sequence is glycine-isoleucine-leucine-glutamic acid-glutamic acid, which appears twice in DBH. The results suggest that the amino acids with a high Markov transition probability may serve as the potential targets of new drugs, because they are unlikely to change into other amino acids.

Amino Acid Sequence↗
PubMed2006

The use of Markov chain Monte Carlo uncertainty analysis to support a Public Health Goal for perchloroethylene.

The current Public Health Goal (PHG) for perchloroethylene (PCE) was derived using upper-bound estimates of fractional PCE metabolism in humans. These estimates were in part obtained from a published evaluation of the uncertainty and variability in human PCE metabolism conducted using a physiologically-based pharmacokinetic (PBPK) model in a Markov chain Monte Carlo (MCMC) analysis; however, the data used in that analysis were limited to post-exposure PCE blood and exhaled air concentrations from a single study. A more recent study [Volkel, W., Friedewald, M., Lederer, E., Pahler, A., Parker, J., Dekant, W., 1998. Biotransformation of perchloroethene: dose-dependent excretion of trichloroacetic acid, dichloroacetic acid, and N-acetyl-S-(trichlorovinyl)-l-cysteine in rats and humans after inhalation. Toxicol. Appl. Pharmacol. 153(1), 20-27.] provides data on blood concentrations of PCE and its major metabolite, trichloroacetic acid (TCA), and urinary excretion of TCA following exposure of human subjects to lower concentrations of PCE (10-40ppm) than in previous studies. In the present effort, a new MCMC analysis was performed that focused on data from this study along with two others [Fernandez, J., Guberan, E., Caperos, J., 1976. Experimental human exposures to tetrachloroethylene vapor and elimination in breath after inhalation. Am. Ind. Hyg. Assoc. J. 37, 143-150; Monster, A., Boersma, G., Steenweg, H., 1979. Kinetics of tetrachloroethylene in volunteers; influence of exposure concentration and work load. Int. Arch. Occup. Environ. Health 42, 303-309.] providing data on PCE blood concentrations and urinary excretion of TCA. To provide an accurate prediction of TCA kinetics, the PBPK model used here includes a description of the metabolism of PCE to TCA in both the liver and kidney. The resulting upper 95th percentile estimates of fraction of PCE metabolized by inhalation and oral routes were 2.1 and 5.2%, respectively, compared to 58 and 79% used in the derivation of the PHG.

Carcinogens, Environmental↗
PubMed1995

Exceptional motifs in different Markov chain models for a statistical analysis of DNA sequences.

Identifying exceptional motifs is often used for extracting information from long DNA sequences. The two difficulties of the method are the choice of the model that defines the expected frequencies of words and the approximation of the variance of the difference T(W) between the number of occurrences of a word W and its estimation. We consider here different Markov chain models, either with stationary or periodic transition probabilities. We estimate the variance of the difference T(W) by the conditional variance of the number of occurrences of W given the oligonucleotides counts that define the model. Two applications show how to use asymptotically standard normal statistics associated with the counts to describe a given sequence in terms of its outlying words. Sequences of Escherichia coli and of Bacillus subtilis are compared with respect to their exceptional tri- and tetranucleotides. For both bacteria, exceptional 3-words are mainly found in the coding frame. E. coli palindrome counts are analyzed in different models, showing that many overabundant words are one-letter mutations of avoided palindromes.

Bacillus subtilis↗
PubMedDate not supplied

Use of Bayesian Markov Chain Monte Carlo methods to model cost-of-illness data.

It is well known that the modeling of cost data is often problematic due to the distribution of such data. Commonly observed problems include 1) a strongly right-skewed data distribution and 2) a significant percentage of zero-cost observations. This article demonstrates how a hurdle model can be implemented from a Bayesian perspective by means of Markov Chain Monte Carlo simulation methods using the freely available software WinBUGS. Assessment of model fit is addressed through the implementation of two cross-validation methods. The relative merits of this Bayesian approach compared to the classical equivalent are discussed in detail. To illustrate the methods described, patient-specific non-health-care resource-use data from a prospective longitudinal study and the Norfolk Arthritis Register (NOAR) are utilized for 218 individuals with early inflammatory polyarthritis (IP). The NOAR database also includes information on various patient-level covariates.

Arthritis↗
PubMed2001

Genomewide multipoint linkage analysis of seven extended Palauan pedigrees with schizophrenia, by a Markov-chain Monte Carlo method.

Palauans are an isolated population in Micronesia with lifetime prevalence of schizophrenia (SCZD) of 2%, compared to the world rate of approximately 1%. The possible enrichment for SCZD genes, in conjunction with the potential for reduced etiological heterogeneity and the opportunity to ascertain statistically powerful extended pedigrees, makes Palauans a population of choice for the mapping of SCZD genes. We have used a Markov-chain Monte Carlo method to perform a genomewide multipoint analysis in seven extended pedigrees from Palau. Robust multipoint parametric and nonparametric linkage (NPL) analyses were performed under three nested diagnostic classifications-core, spectrum, and broad. We observed four regions of interest across the genome. Two of these regions-on chromosomes 2p13-14 (for which, under core diagnostic classification, NPL=6.5 and parametric LOD=4.8) and 13q12-22 (for which, under broad diagnostic classification, parametric LOD=3.6, and, under spectrum diagnostic classification, parametric LOD=3.5)-had evidence for linkage with genomewide significance, after correction for multiple testing; with the current pedigree resource and genotyping, these regions are estimated to be 4.3 cM and 19.75 cM in size, respectively. A third region, with intermediate evidence for linkage, was identified on chromosome 5q22-qter (for which, under broad diagnostic classification, parametric LOD=2.5). The fourth region of interest had only borderline suggestive evidence for linkage (on 3q24-28; for this region, under broad diagnostic classification, parametric LOD=2.0). All regions exhibited evidence for genetic heterogeneity. Our findings provide significant evidence for susceptibility loci on chromosomes 2p13-14 and 13q12-22 and support both a model of genetic heterogeneity and the utility of a broader set of diagnostic classifications in the population from Palau.

Chromosome Mapping↗