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At least 1,081 records · Page 60Linked to original sources
PubMed2005

Bayesian error-in-variable survival model for the analysis of GeneChip arrays.

DNA microarrays in conjunction with statistical models may help gain a deeper understanding of the molecular basis for specific diseases. An intense area of research is concerned with the identification of genes related to particular phenotypes. The technology, however, is subject to various sources of error that may lead to expression readings that are substantially different from the true transcript levels. Few methods for microarray data analysis have accounted for measurement error in a substantial way and that is the purpose of this investigation. We describe a Bayesian error-in-variable model for the analysis of microarray data from a clinical study of patients with acute lymphoblastic leukemia. We focus in particular on the problem of identifying genes whose expression patterns are associated with duration of remission. This is a question of great practical interest since relapse is a major concern in the treatment of this disease. We explore the effects of ignoring the uncertainty in the expression estimates on the selection and ranking of genes.

Bayes Theorem↗
PubMed1984

Alternative approaches to estimation of population pharmacokinetic parameters: comparison with the nonlinear mixed-effect model.

Individual pharmacokinetic parameters can be viewed as independent realizations of a random variable. The probability density function of the variable is assumed to be specified by its first two moments (mean vector and covariance matrix), and these moments then characterize the distribution of the parameters in the population. The following methods are presented for estimation of population characteristics from a set of pharmacokinetic measurements in a sample of subjects: The Global Two-Stage Approach (GTS) uses estimates (and their covariances) of individual parameters obtained after separate fitting of each individual's data. The Iterated Two-Stage Approach (ITS) makes the GTS procedure iterative, using refined bayesian estimates of individual parameters at each step. The Nonlinear Filtering Approach (NLF) also relies on individual parameter estimates produced by using an optimal filter on each subject's data. The three methods give exact results (maximum likelihood estimates), as does NONMEM (the Nonlinear Mixed-Effect Model Approach), when the individual pharmacokinetic model is linear with respect to the parameters and when the distributions of the pharmacokinetic parameters and of the measurement noise in the individual data are both multivariate normal. When the individual pharmacokinetic model is statistically nonlinear (the usual case), the methods differ with respect to: (1) their strategy for handling nonlinearity, (2) their ability to deal with any type of data (experimental and/or routine), and (3) their sensitivity to the amplitude of random effects. With regard to computational aspects, both the computer memory storage requirements and the amount of computation required for the GTS approach are much smaller than for the three other methods. Contrasting considerations as well as results of simulations suggest that GTS, ITS, and, in future, NLF may be valuable alternatives to NONMEM or modifications of it for estimation of population characteristics of pharmacokinetic parameters.

Humans↗
PubMed2004

A Bayesian network classification methodology for gene expression data.

We present new techniques for the application of a Bayesian network learning framework to the problem of classifying gene expression data. The focus on classification permits us to develop techniques that address in several ways the complexities of learning Bayesian nets. Our classification model reduces the Bayesian network learning problem to the problem of learning multiple subnetworks, each consisting of a class label node and its set of parent genes. We argue that this classification model is more appropriate for the gene expression domain than are other structurally similar Bayesian network classification models, such as Naive Bayes and Tree Augmented Naive Bayes (TAN), because our model is consistent with prior domain experience suggesting that a relatively small number of genes, taken in different combinations, is required to predict most clinical classes of interest. Within this framework, we consider two different approaches to identifying parent sets which are supported by the gene expression observations and any other currently available evidence. One approach employs a simple greedy algorithm to search the universe of all genes; the second approach develops and applies a gene selection algorithm whose results are incorporated as a prior to enable an exhaustive search for parent sets over a restricted universe of genes. Two other significant contributions are the construction of classifiers from multiple, competing Bayesian network hypotheses and algorithmic methods for normalizing and binning gene expression data in the absence of prior expert knowledge. Our classifiers are developed under a cross validation regimen and then validated on corresponding out-of-sample test sets. The classifiers attain a classification rate in excess of 90% on out-of-sample test sets for two publicly available datasets. We present an extensive compilation of results reported in the literature for other classification methods run against these same two datasets. Our results are comparable to, or better than, any we have found reported for these two sets, when a train-test protocol as stringent as ours is followed.

Bayes Theorem↗
PubMed2006

Fusion of Hidden Markov Random Field models and its Bayesian estimation.

In this paper, we present a Hidden Markov Random Field (HMRF) data-fusion model. The proposed model is applied to the segmentation of natural images based on the fusion of colors and textons into Julesz ensembles. The corresponding Exploration/ Selection/Estimation (ESE) procedure for the estimation of the parameters is presented. This method achieves the estimation of the parameters of the Gaussian kernels, the mixture proportions, the region labels, the number of regions, and the Markov hyper-parameter. Meanwhile, we present a new proof of the asymptotic convergence of the ESE procedure, based on original finite time bounds for the rate of convergence.

Algorithms↗
PubMed1993

Drug delivery optimization through Bayesian networks: an application to erythropoietin therapy in uremic anemia.

This paper describes how Bayesian networks can be used in combination with compartmental models to plan recombinant human erythropoietin delivery in the treatment of anemia of chronic uremic patients. Past measurements of hemoglobin concentration in a patient during the therapy can be exploited to adjust the parameters of a compartmental model of erythropoiesis. This adaptive process provides more accurate patient-specific predictions, and hence a more rational dosage planning. Inferences are performed by using a stochastic simulation algorithm called Gibbs sampling. We describe a drug delivery optimization protocol based on our approach. Some results obtained on real data are presented.

Adult↗
PubMed2006

A Bayesian approach for stochastic white matter tractography.

White matter fiber bundles in the human brain can be located by tracing the local water diffusion in diffusion weighted magnetic resonance imaging (MRI) images. In this paper, a novel Bayesian modeling approach for white matter tractography is presented. The uncertainty associated with estimated white matter fiber paths is investigated, and a method for calculating the probability of a connection between two areas in the brain is introduced. The main merits of the presented methodology are its simple implementation and its ability to handle noise in a theoretically justified way. Theory for estimating global connectivity is also presented, as well as a theorem that facilitates the estimation of the parameters in a constrained tensor model of the local water diffusion profile.

Algorithms↗
PubMed2005

A Bayesian framework for noise covariance estimation using the facet model.

In image processing literature, thus far, researchers have assumed the perturbation in the data to be white (or uncorrelated) having a covariance matrix sigma2I, i.e., assumption of equal variance for all the data samples and that no correlation exists between the data samples. However, there have been very few attempts to estimate noise characteristics under the assumption that there is a correlation between data samples. In this work, we propose a new and a novel approach for the simultaneous Bayesian estimation of the unknown colored or correlated noise (population) covariance matrix and the hyperparameters of the covariance model using the well-known facet model. We also estimate the facet model coefficients. We use the facet model because of its simple, yet elegant, mathematical formulation. We use the generalized inverted Wishart density as the prior model for the noise covariance matrix. We place a structure on the covariance matrix using the parameters of a correlation filter. These hyperparameters are estimated by a new extension of the expectation-maximization algorithm called the generalized constrained expectation maximization algorithm that we developed.

Algorithms↗
PubMed1986

A microcomputer program for individualizing factor VIII dosage in hemophilia patients undergoing major surgery.

A pharmacokinetic program that allows individualization of Factor VIII dosage regiments in hemophilia patients undergoing major surgery is described. The program, which is designed for the IBM PC microcomputer and compatible machines, is based upon the one-compartment open model with instantaneous input. In the framework of such a pharmacokinetic model, it is assumed that the elimination of Factor VIII is faster during the early post-operative period and that it decreases progressively over the following days. Since Factor VIII half-life is dependent on the time elapsed since the operation (short half-life values during the early post-operative period, longer half-life values thereafter), the pharmacokinetic model is a nonlinear one. A first-order 'variation' rate constant is used to describe the prolongation of Factor VIII half-life from the initial value immediately after surgery to the final value achieved several days later. Individualized estimation of the patient's kinetic parameters (initial half-life, 'variation' rate constant and volume of distribution) is performed through the Bayesian method. Therefore, for such estimation the program exploits the Factor VIII plasma levels measured in the individual patient as well as the population pharmacokinetic data of Factor VIII. After estimating the individual's Bayesian parameters, the program predicts the dosage regimen that will elicit the desired time-course of Factor VIII plasma levels. If requested, the program is able to calculate the least-squares estimates for the parameters of the pharmacokinetic model and dosage prediction can also be made on the basis of such estimates. The least-squares estimates are useful for calculating population pharmacokinetic parameters according to the Standard Two-Stage method. Some examples of clinical use of the program are presented.

Computers↗
PubMed1999

A novel Bayesian decision procedure for early-phase dose-finding studies.

Phase I first-in-man studies in normal, healthy volunteers are performed to define a maximum safe dose and to identify a range of acceptable doses for later drug development studies in patients. Analysis of pharmacokinetic and pharmacodynamic data using mixed-effects modeling can be used to fit an overall dose-response relationship. By expressing prior information as pseudodata, the same methodology can be used to perform a Bayesian analysis and to determine posterior modal estimates for the model parameters. Decision theory can then be applied to maximize a chosen gain function, utilizing real-time data capture for choosing safe doses in a way that will provide more informative responses, thus accelerating study completion. The methodology is introduced elsewhere (1). The purpose of this paper is to describe software currently in development and to illustrate the method using an example from a recent study.

Area Under Curve↗
PubMed2006

Identifying the environmental factors that determine the genetic structure of populations.

The study of population genetic structure is a fundamental problem in population biology because it helps us obtain a deeper understanding of the evolutionary process. One of the issues most assiduously studied in this context is the assessment of the relative importance of environmental factors (geographic distance, language, temperature, altitude, etc.) on the genetic structure of populations. The most widely used method to address this question is the multivariate Mantel test, a nonparametric method that calculates a correlation coefficient between a dependent matrix of pairwise population genetic distances and one or more independent matrices of environmental differences. Here we present a hierarchical Bayesian method that estimates F(ST) values for each local population and relates them to environmental factors using a generalized linear model. The method is demonstrated by applying it to two data sets, a data set for a population of the argan tree and a human data set comprising 51 populations distributed worldwide. We also carry out a simulation study to investigate the performance of the method and find that it can correctly identify the factors that play a role in the structuring of genetic diversity under a wide range of scenarios.

Africa, Eastern↗
PubMed2006

A Bayesian model for joint segmentation and registration.

A statistical model is presented that combines the registration of an atlas with the segmentation of magnetic resonance images. We use an Expectation Maximization-based algorithm to find a solution within the model, which simultaneously estimates image artifacts, anatomical labelmaps, and a structure-dependent hierarchical mapping from the atlas to the image space. The algorithm produces segmentations for brain tissues as well as their substructures. We demonstrate the approach on a set of 22 magnetic resonance images. On this set of images, the new approach performs significantly better than similar methods which sequentially apply registration and segmentation.

Artifacts↗
PubMed2002

Hierarchical Bayesian model for prevalence inferences and determination of a country's status for an animal pathogen.

Certification that a country, region or state is "free" from a pathogen or has a prevalence less than a threshold value has implications for trade in animals and animal products. We develop a Bayesian model for assessment of (i) the probability that a country is "free" of or has an animal pathogen, (ii) the proportion of infected herds in an infected country, and (iii) the within-herd prevalence in infected herds. The model uses test results from animals sampled in a two-stage cluster sample of herds within a country. Model parameters are estimated using modern Markov-chain Monte Carlo methods. We demonstrate our approach using published data from surveys of Newcastle disease and porcine reproductive and respiratory syndrome in Switzerland, and for three simulated data sets.

Animals↗
PubMedDate not supplied

Probabilistic small area risk assessment using GIS-based data: a case study on Finnish childhood diabetes. Geographic information systems.

A Bayesian hierarchical spatial model is constructed to describe the regional incidence of insulin dependent diabetes mellitus (IDDM) among the under 15-year-olds in Finland. The model exploits aggregated pixel-wise locations for both the cases and the population at risk. Typically such data arise from combining geographic information systems (GIS) with large databases. The dates of diagnosis and locations of the cases are observed from 1987 to 1996. The population at risk counts are available for every second year during the same period. A hierarchical model is suggested for the pixel wise case counts, including a population model to account for the uncertainty of the population at risk over the years. The model is applied in the construction of disease maps (aggregated 100 km(2) pixels), and spatial posterior predictive distributions are computed to study whether there can be found a statistically exceptional number of cases in a small area of interest.

Bayes Theorem↗
PubMed2005

Modeling individual differences in cognition.

Many evaluations of cognitive models rely on data that have been averaged or aggregated across all experimental subjects, and so fail to consider the possibility of important individual differences between subjects. Other evaluations are done at the single-subject level, and so fail to benefit from the reduction of noise that data averaging or aggregation potentially provides. To overcome these weaknesses, we have developed a general approach to modeling individual differences using families of cognitive models in which different groups of subjects are identified as having different psychological behavior. Separate models with separate parameterizations are applied to each group of subjects, and Bayesian model selection is used to determine the appropriate number of groups. We evaluate this individual differences approach in a simulation study and show that it is superior in terms of the key modeling goals of prediction and understanding. We also provide two practical demonstrations of the approach, one using the ALCOVE model of category learning with data from four previously analyzed category learning experiments, the other using multidimensional scaling representational models with previously analyzed similarity data for colors. In both demonstrations, meaningful individual differences are found and the psychological models are able to account for this variation through interpretable differences in parameterization. The results highlight the potential of extending cognitive models to consider individual differences.

Cognition↗
PubMed2002

Overcredibility of molecular phylogenies obtained by Bayesian phylogenetics.

Bayesian phylogenetics has recently been proposed as a powerful method for inferring molecular phylogenies, and it has been reported that the mammalian and some plant phylogenies were resolved by using this method. The statistical confidence of interior branches as judged by posterior probabilities in Bayesian analysis is generally higher than that as judged by bootstrap probabilities in maximum likelihood analysis, and this difference has been interpreted as an indication that bootstrap support may be too conservative. However, it is possible that the posterior probabilities are too high or too liberal instead. Here, we show by computer simulation that posterior probabilities in Bayesian analysis can be excessively liberal when concatenated gene sequences are used, whereas bootstrap probabilities in neighbor-joining and maximum likelihood analyses are generally slightly conservative. These results indicate that bootstrap probabilities are more suitable for assessing the reliability of phylogenetic trees than posterior probabilities and that the mammalian and plant phylogenies may not have been fully resolved.

Amino Acid Substitution↗
PubMed2006

Improving source detection and separation in a spatiotemporal Bayesian inference dipole analysis.

Most existing spatiotemporal multi-dipole approaches for MEG/EEG source localization assume that the dipoles are active for the full time range being analysed. If the actual time range of activity of sources is significantly shorter than the time range being analysed, the detectability, localization and time-course determination of such sources may be adversely affected, especially for weak sources. In order to improve detectability and reconstruction of such sources, it is natural to add active time range information (starting time point and ending time point of source activation) for each candidate source as unknown parameters in the analysis. However, this adds additional nonlinear free parameters that could burden the analysis and could be unfeasible for some methods. Recently, we described a spatiotemporal Bayesian inference multi-dipole analysis for the MEG/EEG inverse problem. This approach treated the number of dipoles as a free parameter, produced realistic uncertainty estimates using a Markov chain Monte Carlo numerical sampling of the posterior distribution and included a method to reduce the unwanted effects of local minima. In this paper, our spatiotemporal Bayesian inference multi-dipole analysis is extended to incorporate active time range parameters of starting and stopping time points. The properties of this analysis in comparison to the previous one without active time range parameters are demonstrated through extensive studies using both simulated and empirical MEG data.

Action Potentials↗
PubMedDate not supplied

Bayesian estimates of disease maps: how important are priors?

In the fully Bayesian (FB) approach to disease mapping the choice of the hyperprior distribution of the dispersion parameter is a key issue. In this context we investigated the sensitivity of the rate ratio estimates to the choice of the hyperprior via a simulation study. We also compared the performance of the FB approach to mapping disease risk to the conventional approach of mapping maximum likelihood (ML) estimates and p-values. The study was modelled on the incidence data of insulin dependent diabetes mellitus (IDDM) as observed in the communes of Sardinia.

Bayes Theorem↗
PubMed1994

Removing the assumption of conditional independence from Bayesian decision models by using artificial neural networks: some practical techniques and a case study.

The article describes how artificial neural networks with special designs can be applied to approximate a subjective Bayesian decision model without the assumption of conditional independence. New techniques are proposed to resolve some of the practical difficulties during the processes of problem structuring, knowledge elicitation, quantitative modeling, and model interpretation. A Bayesian model considering the conditional dependencies to predict a teenager's marijuana use was constructed by experts using these techniques, and compared to another conventional Bayesian model which assumed conditional independence. The new approach without the assumption of conditional independence had predictive power (r = 0.7) in the test of linearity compared to the conventional approach (r = 0.58) on a data set (n = 129). Its receiver operating characteristic curve dominated the alternative approach within the range (true positive fraction > 0.7) that we were interested in. The interpretations of the possible conditional dependencies provided by the artificial neural network after the training process were consistent with the expert's descriptions.

Adolescent↗