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At least 181 records · Page 10Linked to original sources
PubMed1998

A two-state Markov chain for heterogeneous transitional data: a quasi-likelihood approach.

Many chronic diseases are measured by repeated binary data where the scientific interest is on the transition process between two states of disease activity. Examples include: depression; schizophrenia; multiple sclerosis, and respiratory illness. The course for many of these diseases is inherently heterogeneous, making it difficult to make inference on the transition process. This paper presents a model that incorporates heterogeneity by allowing the transition probabilities to vary randomly across subjects. In the proposed quasi-likelihood formulation for a two-state Markov chain, only the first two moments of the bivariate distribution on the transition probabilities are specified, and we develop a generalized estimating equations (GEE) approach for estimating the mean and variance of this distribution. In addition to estimating the model parameters, we discuss the estimation of derived quantities of the transition matrix such as estimating the expected first passage times and we discuss how we can introduce covariate dependence into the model. We use this methodology to summarize the transitioning pattern of respiratory illness in a group of children with intra-uteral growth retardation, and we conduct a simulation to investigate the finite sample properties of our procedure and to demonstrate marked bias if heterogeneity is ignored.

Chronic Disease↗
PubMed2006

Markov chain approach to analyze the dynamics of pathogen fecal shedding--example of Listeria monocytogenes shedding in a herd of dairy cattle.

Fecal shedding is an important mechanism of spreading of a number of human and animal pathogens. Understanding of the dynamics of pathogen fecal shedding is critical to be able to control or prevent the spread of diseases caused by these pathogens. The objective of this study was to develop a model for analysis of the dynamics of pathogen fecal shedding. Fecal shedding of Listeria monocytogenes in dairy cattle was used as a model system. A Markov chain model (MCM) with two states, shedding and non-shedding, has been developed for overall L. monocytogenes fecal shedding (all L. monocytogenes subtypes) and fecal shedding of three L. monocytogenes subtypes (ribotypes 1058A, 1039E and 1042B) using data from one study farm. The matrices of conditional probabilities of transition between shedding and non-shedding states for different sets of covariates have been estimated by application of logistic regression. The covariate-specific matrices of conditional probabilities, describing the presence of different risk factors, were used to estimate (i) the stationary prevalence of dairy cows that shed any L. monocytogenes subtype or ribotypes 1058A, 1039E, and 1042B, (ii) the duration of overall and subtype specific fecal shedding, and (iii) the duration of periods without shedding. A non-homogeneous MCM was constructed to study how the prevalence of fecal shedders changes over time. The model was validated with data from the study farm and published literature. The results of our modeling work indicated that (i) the prevalence of L. monocytogenes fecal shedders varies over time and can be higher than 90%, (ii) L. monocytogenes subtypes exhibit different dynamics of fecal shedding, (iii) the dynamics of L. monocytogenes fecal shedding are highly associated with contamination of silage (fermented feed) and cows' exposure to stress, and (iv) the developed approach can be readily used to study the dynamics of fecal shedding in other pathogen-host-environment systems.

Animals↗
PubMed1998

The pharmacokinetics of saquinavir: a Markov chain Monte Carlo population analysis.

Saquinavir is an HIV proteinase inhibitor marketed as a treatment for HIV infection. The drug has potent (Ki approximately 0.1 nM) antiviral activity and acts by inhibiting the processing of gag and gag-pol polyproteins, thus blocking the maturation of replicated viral particles. By assuming standard two-compartment disposition kinetics in combination with a variety of absorption processes we have identified two structural models that perform well with respect to describing the pharmacokinetic behavior of saquinavir when administered to healthy human volunteers from various Phase I studies. These structural models have been implemented for population analysis of these Phase I data via the Bayesian Markov chain Monte Carlo approach. We conclude that saquinavir exhibits complex and highly variable behavior, but can be modeled adequately using a two-compartment zero-order absorption model. There is also an indication that saquinavir kinetics may be time-dependent.

Adolescent↗
PubMed2003

An application of reversible-jump Markov chain Monte Carlo to spike classification of multi-unit extracellular recordings.

Multi-electrode recordings in neural tissue contain the action potential waveforms of many closely spaced neurons. While we can observe the action potential waveforms, we cannot observe which neuron is the source for which waveform nor how many source neurons are being recorded. Current spike-sorting algorithms solve this problem by assuming a fixed number of source neurons and assigning the action potentials given this fixed number. We model the spike waveforms as an anisotropic Gaussian mixture model and present, as an alternative, a reversible-jump Markov chain Monte Carlo (MCMC) algorithm to simultaneously estimate the number of source neurons and to assign each action potential to a source. We derive this MCMC algorithm and illustrate its application using simulated three-dimensional data and real four-dimensional feature vectors extracted from tetrode recordings of rat entorhinal cortex neurons. In the analysis of the simulated data our algorithm finds the correct number of mixture components (sources) and classifies the action potential waveforms with minimal error. In the analysis of real data, our algorithm identifies clusters closely resembling those previously identified by a user-dependent graphical clustering procedure. Our findings suggest that a reversible-jump MCMC algorithm could offer a new strategy for designing automated spike-sorting algorithms.

Action Potentials↗
PubMed2003

Ideal-observer computation in medical imaging with use of Markov-chain Monte Carlo techniques.

The ideal observer sets an upper limit on the performance of an observer on a detection or classification task. The performance of the ideal observer can be used to optimize hardware components of imaging systems and also to determine another observer's relative performance in comparison with the best possible observer. The ideal observer employs complete knowledge of the statistics of the imaging system, including the noise and object variability. Thus computing the ideal observer for images (large-dimensional vectors) is burdensome without severely restricting the randomness in the imaging system, e.g., assuming a flat object. We present a method for computing the ideal-observer test statistic and performance by using Markov-chain Monte Carlo techniques when we have a well-characterized imaging system, knowledge of the noise statistics, and a stochastic object model. We demonstrate the method by comparing three different parallel-hole collimator imaging systems in simulation.

Diagnostic Imaging↗
PubMed2002

Futile cycles revisited: a markov chain model of simultaneous glycolysis and gluconeogenesis.

We have used a random walk model of glycolysis and gluconeogenesis to investigate the bioenergetic implications of considering the cell cytoplasm to be a uniform well-mixed compartment. Radiotracer studies conducted on hepatocytes harvested from fasted rats and incubated with 40 mM glucose and 10 mM lactate demonstrated simultaneous glycolysis and gluconeogenesis, with net glycolysis. Tracer introduced as glycerol was incorporated both into glucose (via gluconeogenesis) and into pyruvate (via glycolysis). The data allow us to place a lower bound on the energetic cost of futile cycles involving adenosine triphosphate (ATP) hydrolysis in the early phosphorylation steps of glycolysis. Applying the Markov Chain model for glucose undergoing metabolism to pyruvate, the expected number of ATP molecules hydrolysed is not less than 15 ATP molecules per glucose molecule. The data suggest that, in hepatocytes under the circumstances of this experiment, either glycolysis is a net consumer of ATP, or glycolysis and gluconeogenesis are compartmentalized to a greater extent than is generally supposed.

Animals↗
PubMed2006

Predicting protein subcellular locations using hierarchical ensemble of Bayesian classifiers based on Markov chains.

BACKGROUND: The subcellular location of a protein is closely related to its function. It would be worthwhile to develop a method to predict the subcellular location for a given protein when only the amino acid sequence of the protein is known. Although many efforts have been made to predict subcellular location from sequence information only, there is the need for further research to improve the accuracy of prediction. RESULTS: A novel method called HensBC is introduced to predict protein subcellular location. HensBC is a recursive algorithm which constructs a hierarchical ensemble of classifiers. The classifiers used are Bayesian classifiers based on Markov chain models. We tested our method on six various datasets; among them are Gram-negative bacteria dataset, data for discriminating outer membrane proteins and apoptosis proteins dataset. We observed that our method can predict the subcellular location with high accuracy. Another advantage of the proposed method is that it can improve the accuracy of the prediction of some classes with few sequences in training and is therefore useful for datasets with imbalanced distribution of classes. CONCLUSION: This study introduces an algorithm which uses only the primary sequence of a protein to predict its subcellular location. The proposed recursive scheme represents an interesting methodology for learning and combining classifiers. The method is computationally efficient and competitive with the previously reported approaches in terms of prediction accuracies as empirical results indicate. The code for the software is available upon request.

Amino Acid Sequence↗
PubMedDate not supplied

Modeling population kinetics of free fatty acids in isolated rat hepatocytes using Markov Chain Monte Carlo.

The aim of this study is the characterization, by means of mathematical models, of the activity of isolated hepatic rat cells as regards the conversion of free fatty acids (FFA) to ketone bodies (KB). A new physiologically based compartmental model of FFA metabolism is used within a context of population pharmacokinetics. This analysis is based on a hierarchical model, that differs from standard model formulations, to account for the fact that some data sets belong to the same animal but have been collected under different experimental conditions. The statistical inference problem has been addressed within a Bayesian context and solved by using Markov Chain Monte Carlo (MCMC) simulation. The results obtained in this study indicate that, although hormones epinephrine and insulin are important metabolic regulatory factors in vivo, the conversion of FFA to KB by isolated hepatic rat cells is not significantly affected by epinephrine and only little influenced by insulin. So we conclude that in vivo, the interaction of these two hormones with other compounds not considered in this study plays a fundamental role in ketogenesis. From this study it appears that mathematical models of metabolic processes can be successfully employed in population kinetic studies using MCMC methods.

Animals↗
PubMed2004

The use of Markov chain Monte Carlo for analysis of correlated binary data: patterns of somatic cells in milk and the risk of clinical mastitis in dairy cows.

Two analytical approaches were used to investigate the relationship between somatic cell concentrations in monthly quarter milk samples and subsequent, naturally occurring clinical mastitis in three dairy herds. Firstly, cows with clinical mastitis were selected and a conventional matched analysis was used to compare affected and unaffected quarters of the same cow. The second analysis included all cows, and in order to overcome potential bias associated with the correlation structure, a hierarchical Bayesian generalised linear mixed model was specified. A Markov chain Monte Carlo (MCMC) approach, that is Gibbs sampling, was used to estimate parameters. The results of both the matched analysis and the hierarchical modelling suggested that quarters with a somatic cell count (SCC) in the range 41,000-100,000 cells/ml had a lower risk of clinical mastitis during the next month than quarters <41,000 cell/ml. Quarters with an SCC >200,000 cells/ml were at the greatest risk of clinical mastitis in the next month. There was a reduced risk of clinical mastitis between 1 and 2 months later in quarters with an SCC of 81,000-150,000 cells/ml compared with quarters below this level. The hierarchical modelling analysis identified a further reduced risk of clinical mastitis between 2 and 3 months later in quarters with an SCC 61,000-150,000 cells/ml, compared to other quarters. We conclude that low concentrations of somatic cells in milk are associated with increased risk of clinical mastitis, and that high concentrations are indicative of pre-existing immunological mobilisation against infection. The variation in risk between quarters of affected cows suggests that local quarter immunological events, rather than solely whole cow factors, have an important influence on the risk of clinical mastitis. MCMC proved a useful tool for estimating parameters in a hierarchical Bernoulli model. Model construction and an approach to assessing goodness of model fit are described.

Animals↗
PubMed2005

A novel Markov chain monte carlo approach for constructing accurate meiotic maps.

Mapping markers from linkage data continues to be a task performed in many genetic epidemiological studies. Data collected in a study may be used to refine published map estimates and a study may use markers that do not appear in any published map. Furthermore, inaccuracies in meiotic maps can seriously bias linkage findings. To make best use of the available marker information, multilocus linkage analyses are performed. However, two computational issues greatly limit the number of markers currently mapped jointly; the number of candidate marker orders increases exponentially with marker number and computing exact multilocus likelihoods on general pedigrees is computationally demanding. In this article, a new Markov chain Monte Carlo (MCMC) approach that solves both these computational problems is presented. The MCMC approach allows many markers to be mapped jointly, using data observed on general pedigrees with unobserved individuals. The performance of the new mapping procedure is demonstrated through the analysis of simulated and real data. The MCMC procedure performs extremely well, even when there are millions of candidate orders, and gives results superior to those of CRI-MAP.

Bayes Theorem↗
PubMed2004

Markov chain Monte Carlo techniques and spatial-temporal modelling for medical EIT.

Many imaging problems such as imaging with electrical impedance tomography (EIT) can be shown to be inverse problems: that is either there is no unique solution or the solution does not depend continuously on the data. As a consequence solution of inverse problems based on measured data alone is unstable, particularly if the mapping between the solution distribution and the measurements is also nonlinear as in EIT. To deliver a practical stable solution, it is necessary to make considerable use of prior information or regularization techniques. The role of a Bayesian approach is therefore of fundamental importance, especially when coupled with Markov chain Monte Carlo (MCMC) sampling to provide information about solution behaviour. Spatial smoothing is a commonly used approach to regularization. In the human thorax EIT example considered here nonlinearity increases the difficulty of imaging, using only boundary data, leading to reconstructions which are often rather too smooth. In particular, in medical imaging the resistivity distribution usually contains substantial jumps at the boundaries of different anatomical regions. With spatial smoothing these boundaries can be masked by blurring. This paper focuses on the medical application of EIT to monitor lung and cardiac function and uses explicit geometric information regarding anatomical structure and incorporates temporal correlation. Some simple properties are assumed known, or at least reliably estimated from separate studies, whereas others are estimated from the voltage measurements. This structural formulation will also allow direct estimation of clinically important quantities, such as ejection fraction and residual capacity, along with assessment of precision.

Algorithms↗
PubMed1996

Interpretation of pooling experiments using the Markov chain Monte Carlo method.

This paper describes an effective method for extracting as much information as possible from pooling experiments for library screening. Pools are collections of clones, and screening a pool with a probe determines whether any of these clones are positive for the probe. The results of the pool screenings are interpreted, or decoded, to infer which clones are candidates to be positive. These candidate positives are subjected to confirmatory testing. Decoding the pool screening results is complicated by the presence of errors, which typically lead to ambiguities in the inference of positive clones. However, in many applications there are reasonable models for the prior distributions for positives and for errors, and Bayes inference is the preferred method for ranking candidate positives. Because of the combinatoric complexity of the Bayes formulation, we implemented a decoding algorithm using a Markov chain Monte Carlo method. The algorithm was used in screening a library with 1298 clones using 47 pools. We corroborated the posterior probabilities for positives with results from confirmatory screening. We also simulated the screening of a 10-fold coverage library of 33,000 clones using 253 pools. The use of our algorithm, effective under conditions where combinatorial decoding techniques are imprudent, allows the use of fewer pools and also introduces needed robustness.

Algorithms↗
PubMed2007

Predicting costs over time using Bayesian Markov chain Monte Carlo methods: an application to early inflammatory polyarthritis.

This article focuses on the modelling and prediction of costs due to disease accrued over time, to inform the planning of future services and budgets. It is well documented that the modelling of cost data is often problematic due to the distribution of such data; for example, strongly right skewed with a significant percentage of zero-cost observations. An additional problem associated with modelling costs over time is that cost observations measured on the same individual at different time points will usually be correlated. In this study we compare the performance of four different multilevel/hierarchical models (which allow for both the within-subject and between-subject variability) for analysing healthcare costs in a cohort of individuals with early inflammatory polyarthritis (IP) who were followed-up annually over a 5-year time period from 1990/1991. The hierarchical models fitted included linear regression models and two-part models with log-transformed costs, and two-part model with gamma regression and a log link. The cohort was split into a learning sample, to fit the different models, and a test sample to assess the predictive ability of these models. To obtain predicted costs on the original cost scale (rather than the log-cost scale) two different retransformation factors were applied. All analyses were carried out using Bayesian Markov chain Monte Carlo (MCMC) simulation methods.

Adult↗
PubMed2005

Inference on microsatellite mutation processes in the invasive mite, Varroa destructor, using reversible jump Markov chain Monte Carlo.

Varroa destructor is a parasitic mite of the Eastern honeybee Apis cerana. Fifty years ago, two distinct evolutionary lineages (Korean and Japanese) invaded the Western honeybee Apis mellifera. This haplo-diploid parasite species reproduces mainly through brother-sister matings, a system which largely favors the fixation of new mutations. In a worldwide sample of 225 individuals from 21 locations collected on Western honeybees and analyzed at 19 microsatellite loci, a series of de novo mutations was observed. Using historical data concerning the invasion, this original biological system has been exploited to compare three mutation models with allele size constraints for microsatellite markers: stepwise (SMM) and generalized (GSM) mutation models, and a model with mutation rate increasing exponentially with microsatellite length (ESM). Posterior probabilities of the three models have been estimated for each locus individually using reversible jump Markov Chain Monte Carlo. The relative support of each model varies widely among loci, but the GSM is the only model that always receives at least 9% support, whatever the locus. The analysis also provides robust estimates of mutation parameters for each locus and of the divergence time of the two invasive lineages (67,000 generations with a 90% credibility interval of 35,000-174,000). With an average of 10 generations per year, this divergence time fits with the last post-glacial Korea-Japan land separation.

Animals↗
PubMed1998

Estimation for restriction sites observed by optical mapping using reversible-jump Markov Chain Monte Carlo.

A fundamentally new molecular-biology approach in constructing restriction maps, Optical Mapping, has been developed by Schwartz et al. (1993). Using this method restriction maps are constructed by measuring the relevant fluorescence intensity and length measurements. However, it is difficult to directly estimate the restriction site locations of single DNA molecules based on these optical mapping data because of the precision of length measurements and the unknown number of true restriction sites in the data. We propose the use of a hierarchical Bayes model based on a mixture model with normals and random noise. In this model we explicitly consider the missing observation structure of the data, such as the orientations of molecules, the allocations of cutting sites to restriction sites, and the indicator variables of whether observed cut sites are true or false. Because of the complexity of the model, the large number of missing data, and the unknown number of restriction sites, we use Reversible-Jump Markov Chain Monte Carlo (MCMC) to estimate the number and the locations of the restriction sites. Since there exists a high multimodality due to unknown orientations of molecules, we also use a combination of our MCMC approach and the flipping algorithm suggested by Dancík and Waterman (1997). The study is highly computer-intensive and the development of an efficient algorithm is required.

Algorithms↗
PubMed2006

[Markov Chain Monte Carlo scheme for parameter uncertainty analysis in water quality model].

Parameter identification plays an important role in environmental model application. Markov Chain Monte Carlo method was introduced to estimate parameter uncertainty, since usual Bayes discrete methods were not applicable to produce posterior distribution of complicated environmental model due to the limit of computation. In order to study the performance and efficiency of MCMC, two case studies were used. Results indicate that, either sampling performance or sampling efficiency, MCMC method both has its special advantages in producing posterior distribution. Moreover, results of Gelman convergence diagnostics indicate that sampling sequence can converge to a stationary distribution. A key finding was that the MCMC scheme presented herein provided a powerful means of parameter identification and uncertainty analysis.

Models, Theoretical↗
PubMedDate not supplied

Modeling turbulent diffusion and advection of indoor air contaminants by Markov chains.

Turbulent eddy diffusion models are used to describe a continuous concentration gradient with distance from an in-room contaminant emission source. A refined diffusion model termed the Drivas model also accounts for contaminant reflection by wall surfaces and partially accounts for removal by exhaust air. This article develops two models based on Markov chains to describe indoor air contaminant dispersion by turbulent diffusion and advection, and removal by the exhaust airflow. Markov model I is equivalent to the Drivas model and is computationally simple. Markov model II can provide more realism by accounting for the locations of air inlets and outlets, advective flow patterns, in-room reflective surfaces, and contaminant removal mechanisms at specific room positions. The price paid for this greater realism is greater computational complexity. Both Markov models are explicitly probabilistic and estimate the expected concentration values at given room positions.

Air Pollution, Indoor↗