[A Markov chain model for comparison of the incidence of miscarriage in various partial samples of a pregnancy follow-up study].
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Female↗
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A non-homogeneous Markov chain model for follow-up studies with application to epilepsy.
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Adolescent↗
S-SPatt: simple statistics for patterns on Markov chains.
SUMMARY: S-SPatt allows the counting of patterns occurrences in text files and, assuming these texts are generated from a random Markovian source, the computation of the P-value of a given observation using a simple binomial approximation.
Algorithms↗
Frequency and Markov chain analysis of amino-acid sequences of human glutathione reductase.
The amino-acid sequence of human glutathione reductase was measured according to two- and three-amino-acid sequences. The measured frequency and probability were compared with predicted frequency and probability. Of 477 two-amino-acid sequences in human glutathione reductase, 176 (36.897%) and 90 (18.868%) sequences can be explained by the predicted frequency and the predicted probability according to a purely random mechanism. Of 477 measured first Markov transition probabilities for the second amino acid in two-amino-acid sequences, 1 (0.210%) measured first Markov transition probability matches the predicted conditional probability and can therefore be explained by a purely random mechanism. No more than two-amino-acid sequences can be explained by a purely random mechanism.
Amino Acid Sequence↗
[Statistical characteristics in primary structures of functional regions of Escherichia coli genome. II. Non-stationary Markov chains].
We introduced non-stationary Marcov chains for statistical description of the DNA E. coli structural domains. The values of all needed parameters for those chains was determined by the preliminary statistical processing of a wide set of the E. coli coding regions. It was shown that non-stationary models predict frequencies of occurrences of various combinations of nucleotides within the coding fragments of DNA, better than stationary ones. In particular non-stationary models give good approximation for short and long distance arrangement of nucleotides in the coding regions. The correlation parameters for neighbour codons and for neighbour amino acid residuals in E. coli protein's primary structure was determined from the non-stationary model of the second order. With the aid of the statistical criteria it was found that neighbour residuals in polypeptide chains can't be considered as independent. The new model of the DNA structural domain may be used in computer algorithms for recognition and classification of DNA functional regions.
Base Sequence↗
Frequency and markov chain analysis of amino-acid sequences of human tumour necrosis factor.
The amino-acid sequence of human tumour necrosis factor was measured according to two- and three-amino-acid sequences. The measured frequency and probability were compared with predicted frequency and probability. Of 232 two-amino-acid sequences in human tumour necrosis factor, 64 (27.586%) and 24 (10.345%) sequences can be explained by the predicted frequency and the predicted probability according to a purely random mechanism. Of 243 non-appeared two-amino-acid sequences in human tumour necrosis factor, 176 (72. 428%) and 42 (17.284%) sequences can be explained by the predicted frequency and the predicted probability according to a purely random mechanism. No measured Markov transition probability matches the predicted conditional probability. No more-than-two-amino-acid sequences can be explained by a purely random mechanism.
Amino Acid Sequence↗
Frequency and Markov chain analysis of the amino-acid sequence of human alcohol dehydrogenase alpha-chain.
The amino-acid sequences of human alcohol dehydrogenase alpha-chain (ADH1) were analysed according to two-, three- and four-amino-acid sequences. The measured frequencies and probabilities were compared with the predicted frequencies and probabilities. Of 373 two-amino-acid sequences in the ADH1, 92 (24.665%) and 32 (8.579%) sequences can be explained by the predicted frequencies and probabilities according to a purely random mechanism. Of 191 non-appearing two-amino-acid sequences in the ADH1, 119 (62.304%) and 52 (27.225%) sequences can be explained by the predicted frequencies and probabilities according to a purely random mechanism. Of 373 measured first-order Markov transition probabilities for the second amino acid in two-amino-acid sequences, three (0.804%) probabilities match the predicted conditional probabilities and therefore can be explained by a purely random mechanism. No more-than-two-amino-acid sequences can be explained by a purely random mechanism.
Alcohol Dehydrogenase↗
Prediction of protein subcellular locations using Markov chain models.
A novel method was introduced to predict protein subcellular locations from sequences. Using sequence data, this method achieved a prediction accuracy higher than previous methods based on the amino acid composition. For three subcellular locations in a prokaryotic organism, the overall prediction accuracy reached 89.1%. For eukaryotic proteins, prediction accuracies of 73.0% and 78.7% were attained within four and three location categories, respectively. These results demonstrate the applicability of this relative simple method and possible improvement of prediction for the protein subcellular location.
Markov Chains↗
On the Metropolis-Hastings acceptance probability to add or drop a quantitative trait locus in Markov chain Monte Carlo-based Bayesian analyses.
The Metropolis-Hastings algorithm used in analyses that estimate the number of QTL segregating in a mapping population requires the calculation of an acceptance probability to add or drop a QTL from the model. Expressions for this acceptance probability need to recognize that sets of QTL are unordered such that the number of equivalent sets increases with the factorial of the QTL number. Here, we show how accounting for this fact affects the acceptance probability and review expressions found in the literature.
Algorithms↗
Linkage analysis of a complex pedigree with severe bipolar disorder, using a Markov chain Monte Carlo method.
Recently developed algorithms permit nonparametric linkage analysis of large, complex pedigrees with multiple inbreeding loops. We have used one such algorithm, implemented in the package SimWalk2, to reanalyze previously published genome-screen data from a Costa Rican kindred segregating for severe bipolar disorder. Our results are consistent with previous linkage findings on chromosome 18 and suggest a new locus on chromosome 5 that was not identified using traditional linkage analysis.
Algorithms↗
Frequency and Markov chain analysis of amino acid sequences of mouse p53.
The amino acid sequence of mouse p53 was measured according to two- and three-amino-acid sequences. The measured frequency and probability were compared with predicted frequency and probability. Of 389 two-amino-acid sequences in mouse p53,85 (21.851%) and 27 (6.941%) sequences can be explained by the predicted frequency and probability according to a purelyrandom mechanism. Of 188 non-appearing two-amino-acid sequences in mouse p53, 86 (45.745%) and 32 (17.021%) can be explained by the predicted frequency and probability according to a purely random mechanism; no more than two-amino-acid sequences in mouse p53 can be explained by a purely random mechanism.
Amino Acid Sequence↗
Application of Markov chains to linked genes with interference. II. Genotypic selection.
The case of a selfing population and three diallelic loci under genotypic selection is considered. Expressions are obtained for the mean number of times that a process passes through a transient state, for the mean number of generations needed to reach an absorbing state, and for other interesting parameters. The variates under analysis are the coefficient of coincidence, the probabilities of recombination, and the genotypic fitness. The expressions obtained allow the direct computation of the entries of the inverse matrices, avoiding the inverting routines that could present problems of ill-conditioning. Three types of inheritance for fitness are considered in a numerical application: no dominance, complete dominance, and overdominance. Finally, the possible existence of interaction between coincidence and dominance for fitness is analyzed.
Genes, Dominant↗
A Markov chain Monte Carlo EM algorithm for analyzing interval-censored data under the Cox proportional hazards model.
This paper proposes a Monte Carlo EM (MCEM) algorithm for fitting the proportional hazards model for interval-censored failure-time data. The algorithm generates orderings of the failures from their probability distribution under the model. We maximize the average of the log-likelihoods from these completed data sets to obtain updated parameter estimates. As with the standard Cox model, this algorithm does not require the estimation of the baseline hazard function. The performance of the algorithm is evaluated using simulations, and the method is applied to data from AIDS and cancer studies. Our results indicate that our method produced more precise and unbiased estimates than methods of right and midpoint imputation.
Acquired Immunodeficiency Syndrome↗
Random evolutions, markov chains, and systems of partial differential equations.
Several authors have considered Markov processes defined by the motion of a particle on a fixed line with a random velocity(1, 6, 8, 10) or a random diffusivity.(5, 12) A "random evolution" is a natural but apparently new generalization of this notion. In this note we hope to show that this concept leads to simple and powerful applications of probabilistic tools to initial-value problems of both parabolic and hyperbolic type. We obtain existence theorems, representation theorems, and asymptotic formulas, both old and new.
Journal Article↗
A markov chain approach to calculate r(0) in stochastic epidemic models.
R(0) has been defined as "The expected number of secondary infections originated by a "typical" infective individual when introduced into a population of susceptibles", and it is perhaps the single most important parameter in epidemic models. A general framework to calculate R(0) that can be applied to complicated stochastic epidemic models that may include demography, several strains, latent or carrier-like states, with or without density-dependent parameters is introduced. This framework helps us to understand the concept of a "typical" infective individual used in the deterministic definition of R(0). The method is illustrated with applications to several epidemic models, including some in which it has been found that the disease may persist even if R(0)<1. It is shown that although the probability of extinction is difficult to calculate in these latter cases, it is possible to give general conditions on the parameters under which eventual extinction is certain.
Algorithms↗
Reconstruction of extended cortical sources for EEG and MEG based on a Monte-Carlo-Markov-chain estimator.
A new procedure to model extended cortical sources from EEG and MEG recordings based on a probabilistic approach is presented. The method (SPMECS) was implemented within the framework of maximum likelihood estimators. Neuronal activity generating EEG or MEG signals was characterized by the number of sources and their location and extension. Based on the noise distribution of the measured data, source configurations were associated with the according value of the likelihood function. To find the most likely source, i.e., the maximum likelihood estimator, and its level of confidence, a stochastic solver (Metropolis algorithm) was applied. The method presented supports the incorporation of virtually any constraint, e.g., based on physiological and anatomical a priori knowledge. Thus, ambiguity of the ill-posed inverse problem was reduced considerably by confining sources to the cortical surface extracted from individual MR images. The influence of different levels and types of noise on the outcome was investigated by means of simulations. Somatosensory evoked magnetic fields analyzed by the method presented suggest that larger extended cortical areas are involved in the processing of combined finger stimulation as compared to single finger stimulation.
Algorithms↗
Maximum-likelihood and markov chain monte carlo approaches to estimate inbreeding and effective size from allele frequency changes.
Maximum-likelihood and Bayesian (MCMC algorithm) estimates of the increase of the Wright-Malécot inbreeding coefficient, F(t), between two temporally spaced samples, were developed from the Dirichlet approximation of allelic frequency distribution (model MD) and from the admixture of the Dirichlet approximation and the probabilities of fixation and loss of alleles (model MDL). Their accuracy was tested using computer simulations in which F(t) = 10% or less. The maximum-likelihood method based on the model MDL was found to be the best estimate of F(t) provided that initial frequencies are known exactly. When founder frequencies are estimated from a limited set of founder animals, only the estimates based on the model MD can be used for the moment. In this case no method was found to be the best in all situations investigated. The likelihood and Bayesian approaches give better results than the classical F-statistics when markers exhibiting a low polymorphism (such as the SNP markers) are used. Concerning the estimations of the effective population size all the new estimates presented here were found to be better than the F-statistics classically used.
Gene Frequency↗
Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient.
Many well-established statistical methods in genetics were developed in a climate of severe constraints on computational power. Recent advances in simulation methodology now bring modern, flexible statistical methods within the reach of scientists having access to a desktop workstation. We illustrate the potential advantages now available by considering the problem of assessing departures from Hardy-Weinberg (HW) equilibrium. Several hypothesis tests of HW have been established, as well as a variety of point estimation methods for the parameter which measures departures from HW under the inbreeding model. We propose a computational, Bayesian method for assessing departures from HW, which has a number of important advantages over existing approaches. The method incorporates the effects-of uncertainty about the nuisance parameters--the allele frequencies--as well as the boundary constraints on f (which are functions of the nuisance parameters). Results are naturally presented visually, exploiting the graphics capabilities of modern computer environments to allow straightforward interpretation. Perhaps most importantly, the method is founded on a flexible, likelihood-based modelling framework, which can incorporate the inbreeding model if appropriate, but also allows the assumptions of the model to he investigated and, if necessary, relaxed. Under appropriate conditions, information can be shared across loci and, possibly, across populations, leading to more precise estimation. The advantages of the method are illustrated by application both to simulated data and to data analysed by alternative methods in the recent literature.
Algorithms↗