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Results for “Monte Carlo Method”

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PubMedDate not supplied

[Numerical help to bacterial identification: definition of a first kind error risk].

The numerical method commonly used as an help to the bacterian identification appears quite efficient in its first role, i.e. to propose the name of the plausible bacteria, but it fails to define a confidence level to be assiociated to the final decision. To correct this, this paper propose to calculate the response probability distribution for each possible bacteria. The calculation uses the so-called "Monte-Carlo" method and has to be performed once for all on a given set of biochemical tests. For each calculated ditribution, it is easy to find a first kind error risk, or alpha-error risk. The proposed theoretical approach moreover avoid the comparison of "identification scores", which is always questionable so far the various bacteria present very different sensitivities to the biochemical tests.

Bacteria↗

PubMed2002

Reservoir boundaries in Brownian dynamics simulations of ion channels.

Brownian dynamics (BD) simulations provide a practical method for the calculation of ion channel conductance from a given structure. There has been much debate about the implementation of reservoir boundaries in BD simulations in recent years, with claims that the use of improper boundaries could have large effects on the calculated conductance values. Here we compare the simple stochastic boundary that we have been using in our BD simulations with the recently proposed grand canonical Monte Carlo method. We also compare different methods of creating transmembrane potentials. Our results confirm that the treatment of the reservoir boundaries is mostly irrelevant to the conductance properties of an ion channel as long as the reservoirs are large enough.

Biophysical Phenomena↗

PubMed2004

Maximum likelihood analysis of a general latent variable model with hierarchically mixed data.

A general two-level latent variable model is developed to provide a comprehensive framework for model comparison of various submodels. Nonlinear relationships among the latent variables in the structural equations at both levels, as well as the effects of fixed covariates in the measurement and structural equations at both levels, can be analyzed within the framework. Moreover, the methodology can be applied to hierarchically mixed continuous, dichotomous, and polytomous data. A Monte Carlo EM algorithm is implemented to produce the maximum likelihood estimate. The E-step is completed by approximating the conditional expectations through observations that are simulated by Markov chain Monte Carlo methods, while the M-step is completed by conditional maximization. A procedure is proposed for computing the complicated observed-data log likelihood and the BIC for model comparison. The methods are illustrated by using a real data set.

Acquired Immunodeficiency Syndrome↗

PubMed1981

Monte Carlo simulation studies of backscatter factors in mammography.

Experimentally determined backscatter factors in mammography can contain significant systematic errors due to the energy response, dimensions, and location of the dosimeter used. In this study, the Monte Carlo method was applied to simulate photon-scattering in tissue-equivalent media and to determine backscatter factors without the interference of a detector. The physical processes of measuring backscatter factors with a lithium fluoride thermoluminescent dosimeter (TLD) and an "ideal" tissue-equivalent detector were also simulated. Computed results were compared with the "true" backscatter factors and with measured values reported by other investigators. It was found that the TLD method underestimated backscatter factors in mammography by as much as 10% at high energies with TLD-100 (3.2- x 3.2- x 0.89-mm3) crystals.

Mammography↗

PubMed1999

Monte Carlo estimation of extrapolation of quality-adjusted survival for follow-up studies.

The expected quality-adjusted survival (QAS) for an index population with a specific disease can be estimated by summing the product of the survival function and the mean quality of life function of the population. In many follow-up studies with heavy censoring, the expected QAS may not be well estimated due to the lack of data beyond the close of follow-up. In this paper, we first created a reference population from the life tables of the general population according to the Monte Carlo method. Secondly, we fitted a simple linear regression line to the logit of the ratio of quality-adjusted survival functions for the index and reference populations up to the end of follow-up. Finally, combining information on the reference population with the fitted line, we predicted the expected quality-adjusted survival curve beyond the follow-up period for the index population. Simulation studies have shown that the simple Monte Carlo estimation procedure is a potential approach for estimating expected QAS and the survival function beyond the follow-up with a certain degree of accuracy.

Computer Simulation↗

PubMedDate not supplied

A convolution algorithm for brachytherapy dose computations in heterogeneous geometries.

Currently-available brachytherapy dose computation algorithms ignore heterogeneities such as tissue-air interfaces, shielded gynecological colpostats, and tissue-composition variations in 125I implants despite dose computation errors as large as 40%. To calculate dose in the presence of tissue and applicator heterogeneities, a computer code has been developed that describes scatter dose as a 3-D spatial integral which convolves primary photon fluence with a dose-spread array. The dose-spread array describes the distribution of dose due to multiple scattering about a single primary interaction site and is precomputed by the Monte Carlo method. To correct for heterogeneities traversed by the primary photons, the dose-spread array is renormalized to reflect the density and composition of the element, and the distance to the point of interest is scaled by the path-length of the intervening medium. Convolution calculations for 125I and 137Cs point sources in the presence of finite phantoms, air voids and high-density shields have been compared to the corresponding Monte Carlo calculations. The convolution code absolute and relative dose rate predictions are shown to agree with Monte Carlo calculations within 3%. Direct evaluation of the 3-D spatial convolution integral using 1-D adaptive integration reveals efficiency gains of 20-50 relative to Monte Carlo photon-transport calculations.

Algorithms↗

PubMed2000

A virtual source model for Monte Carlo modeling of arbitrary intensity distributions.

A photon virtual source model was developed for simulating arbitrary, external beam, intensity distributions using the Monte Carlo method. The source model consists of a photon fluence grid composed of a matrix of square elements, located 25-cm downstream from the linear accelerator target. Each particle originating from the fluence map is characterized by the seven phase space parameters, position (x, y, z), direction (u, v, w), and energy. The map was reconstructed from fluence and energy spectra acquired by modeling components of the linear accelerator treatment head using the Monte Carlo code MCNP4B. The effect of contaminant electrons is accounted for by the use of a sub-source derived from a phase-space simulation of a 25-MV linac treatment head using the code BEAM. The BEAM sub-source was incorporated into the MCNP4B phase-space model and is sampled using a field-size dependent sampling ratio. A Gaussian blurring kernel is convolved with the photon fluence map to account for the finite focal spot size and scattering effects from structures such as the flattening filter and MLC leaves. Depth dose and profile source calculations for 6-MV and 25-MV photon beams, for 5 x 5 cm2, 10 x 10 cm2, and 15 x 15 cm2 field sizes, are in good agreement with measurement and are well within acceptability criteria suggested by the AAPM Task Group Report No. 53. Irregular field calculations compared with film measurement and with a 3-D pencil beam algorithm show that the source model is capable of accurately simulating arbitrary MLC fields.

Biophysical Phenomena↗

PubMed1995

Estimating effective population size and mutation rate from sequence data using Metropolis-Hastings sampling.

We present a new way to make a maximum likelihood estimate of the parameter 4N mu (effective population size times mutation rate per site, or theta) based on a population sample of molecular sequences. We use a Metropolis-Hastings Markov chain Monte Carlo method to sample genealogies in proportion to the product of their likelihood with respect to the data and their prior probability with respect to a coalescent distribution. A specific value of theta must be chosen to generate the coalescent distribution, but the resulting trees can be used to evaluate the likelihood at other values of theta, generating a likelihood curve. This procedure concentrates sampling on those genealogies that contribute most of the likelihood, allowing estimation of meaningful likelihood curves based on relatively small samples. The method can potentially be extended to cases involving varying population size, recombination, and migration.

Base Sequence↗

PubMed2005

Monte Carlo simulation of a mammographic test phantom.

A test phantom, including a wide range of mammographic tissue equivalent materials and test details, was imaged on a digital mammographic system. In order to quantify the effect of scatter on the contrast obtained for the test details, calculations of the scatter-to-primary ratio (S/P) have been made using a Monte Carlo simulation of the digital mammographic imaging chain, grid and test phantom. The results show that the S/P values corresponding to the imaging conditions used were in the range 0.084-0.126. Calculated and measured pixel values in different regions of the image were compared as a validation of the model and showed excellent agreement. The results indicate the potential of Monte Carlo methods in the image quality-patient dose process optimisation, especially in the assessment of imaging conditions not available on standard mammographic units.

Adipose Tissue↗

PubMed2006

Proceedings of the SMBE Tri-National Young Investigators' Workshop 2005. Coalescent-based estimation of population parameters when the number of demes changes over time.

We expand a coalescent-based method that uses serially sampled genetic data from a subdivided population to incorporate changes to the number of demes and patterns of colonization. Often, when estimating population parameters or other parameters of interest from genetic data, the demographic structure and parameters are not constant over evolutionary time. In this paper, we develop a Bayesian Markov chain Monte Carlo method that allows for step changes in mutation, migration, and population sizes, as well as changing numbers of demes, where the times of these changes are also estimated. We show that in parameter ranges of interest, reliable estimates can often be obtained, including the historical times of parameter changes. However, posterior densities of migration rates can be quite diffuse and estimators somewhat biased, as reported by other authors.

Bayes Theorem↗

PubMed1994

Optimization of a polarized source for in vivo x-ray fluorescence analysis of platinum and other heavy metals.

The Monte Carlo method was used to optimize a polarized photon source for the x-ray fluorescence analysis of platinum and other heavy metals in vivo. The source consisted of a 140 kVp, 25 mA x-ray tube with the photons plane-polarized by 90 degrees scattering. The use of plane-polarized photons results in a significant reduction in background when the fluorescent radiation is measured along the direction of polarization. A Monte Carlo computer programme was written to simulate the production and interaction of polarized photons in order to determine the optimal polarizing material and dimensions, together with beam width and geometrical arrangement of source, polarizer and beam collimators. Calculated photon energy distributions are compared with experimental data to test the validity of the model. The best configuration of the polarization system for the in vivo analysis of platinum consisted of a 20 mm Cu polarizing block with a secondary collimator subtending a 0.1 radian angle at the polarizer.

Humans↗

PubMed1997

Estimating the age of the common ancestor of a sample of DNA sequences.

We present a simple Monte Carlo method for estimating the age of the most recent common ancestor (MRCA) of a sample of DNA sequences. We show that Templeton's (1993) estimator of the age of the MRCA based on the maximum number of nucleotide differences between two sequences in a sample is inaccurate, and we demonstrate the new method by reanalyzing a sample of DNA sequences from human Y chromosomes and a sample of human Alu sequences.

Animals↗

PubMedDate not supplied

Parameter estimation in distributed models of blood-tissue exchange: a Monte Carlo strategy to assess precision.

Distributed parameter models of blood-tissue exchange are increasingly used to interpret multiple tracer dilution data in regional kinetic studies. To derive a measure of the precision with which the model parameters are estimated is therefore of paramount importance. The standard approach to deriving precision of estimates does not take into account the fact that some of the model parameters are fixed. Thus, the precision of parameter estimates is not realistic and, in all likelihood, it is overestimated. The aim of this study is to describe a Monte Carlo method devised to obtain a theoretically sound measure of the precision of estimates, which takes into account both measurement error and the uncertainty associated with the fixed parameters. The fixed parameter values are taken from a probability distribution. By letting the fixed parameters vary according to their distribution, a large number of synthetic datasets is generated. Noise is then added. Estimating the parameters in each of these synthetic datasets allows the derivation of a Monte Carlo mean and standard deviation, which provides a realistic measure of precision. The methodology is illustrated for a simulated data case study dealing with the estimation of the capillary permeability-surface area product in a two tracer experiment.

Animals↗

PubMed2005

Bayesian inference for recurrent events data using time-dependent frailty.

In medical studies, we commonly encounter multiple events data such as recurrent infection or attack times in patients suffering from a given disease. A number of statistical procedures for the analysis of such data use the Cox proportional hazards model, modified to include a random effect term called frailty which summarizes the dependence of recurrent times within a subject. These unobserved random frailty effects capture subject effects that are not explained by the known covariates. They are typically modelled constant over time and are assumed to be independently and identically distributed across subjects. However, in some situations, the subject-specific random frailty may change over time in the same manner as time-dependent covariate effects. This paper presents a time-dependent frailty model for recurrent failure time data in the Bayesian context and estimates it using a Markov chain Monte Carlo method. Our approach is illustrated by a data set relating to patients with chronic granulomatous disease and it is compared to the constant frailty model using the deviance information criterion.

Bayes Theorem↗

PubMed2005

A Monte Carlo algorithm for computing the IBD matrices using incomplete marker information.

Identity-By-Descent (IBD) is a general measurement of the relationship between two groups of genes. If the two groups consist of two homologous genes, one from each individual, the IBD is called the coancestry between the two individuals. Coancestry is an important concept in both population and quantitative genetics. It is the probability that both genes are copies of the same gene in the genealogy. The average coancestry value at a random locus in a population reflects the level of population diversity, effective population size, the level of inbreeding and other attributes. Coancestry is also the building block for the covariance structure used to estimate the additive genetic variance component for a quantitative trait. There are many other types of IBD matrices, depending on the natures of the genes included in each group, and these IBD matrices vary from locus to locus. Molecular markers distributed along the genome provide information that can be used to infer these locus-specific IBD matrices. As a result, we can estimate and test the variance components of a quantitative trait contributed by these loci using the inferred IBD matrices. In this study, we develop the concept of locus-specific epistatic IBD matrices and a Monte Carlo method to infer these IBD matrices. The method is suitable for large pedigrees with arbitrary complexity and various levels of missing marker information. With these locus-specific IBD matrices, we are ready to search for quantitative trait loci along the genome in complicated pedigrees.

Algorithms↗

PubMed2005

A correlated frailty model for analysing risk factors in bilateral corneal graft rejection for Keratoconus: a Bayesian approach.

There are many unknown causes that increase the rate of corneal graft rejection. In bilateral cases, some of these unknown causes are common, and some are individual factors. In this paper, we use a correlated frailty model to analyse risk factors for bilateral corneal graft in Keratoconus. Applying the piecewise constant baseline hazard model, we have performed a Bayesian analysis of the correlated frailty model using the Markov chain Monte Carlo method. The correlated frailty model and the shared frailty model are compared by deviance information criterion. The results show more accurate and better fit for the correlated frailty model.

Bayes Theorem↗

PubMed2007

Bayesian analysis of non-homogeneous Markov chains: application to mental health data.

In this paper we present a formal treatment of non-homogeneous Markov chains by introducing a hierarchical Bayesian framework. Our work is motivated by the analysis of correlated categorical data which arise in assessment of psychiatric treatment programs. In our development, we introduce a Markovian structure to describe the non-homogeneity of transition patterns. In doing so, we introduce a logistic regression set-up for Markov chains and incorporate covariates in our model. We present a Bayesian model using Markov chain Monte Carlo methods and develop inference procedures to address issues encountered in the analyses of data from psychiatric treatment programs. Our model and inference procedures are implemented to some real data from a psychiatric treatment study.

Adolescent↗

PubMed2001

A Bayesian method for finding regulatory segments in DNA.

A goal of the human genome project is to determine the entire sequence of DNA (3 x 10(9) base pairs) found in chromosomes. The massive amounts of data produced by this project require interpretation. A Bayesian model is developed for locating regulatory regions in a DNA sequence. Regulatory regions are areas of DNA to which specific proteins bind and control whether or not a gene is transcribed to produce templates for protein synthesis. Each human cell contains the same DNA sequence. Thus the particular function of different cells is determined by the genes that are transcribed in that cell. A Hidden Markov chain is used to model whether a small interval of the DNA is in a regulatory region or not. This can be regarded as a changepoint problem where the changepoints are the start of a regulatory or nonregulatory region. The data consists of protein-binding elements, which are short subsequences, or "words," in the DNA sequence. Although these words can occur anywhere in the sequence, a larger number are expected in regulatory regions. Therefore, regulatory regions are detected by locating clusters of words. For a particular DNA sequence, the model automatically selects those words that best predict regions of interest. Markov chain Monte Carlo methods are used to explore the posterior distribution of the Hidden Markov chain. The model is tested by means of simulations, and applied to several DNA sequences.

Bayes Theorem↗