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PubMed2001

Likelihood maximization for list-mode emission tomographic image reconstruction.

The maximum a posteriori (MAP) Bayesian iterative algorithm using priors that are gamma distributed, due to Lange, Bahn and Little, is extended to include parameter choices that fall outside the gamma distribution model. Special cases of the resulting iterative method include the expectation maximization maximum likelihood (EMML) method based on the Poisson model in emission tomography, as well as algorithms obtained by Parra and Barrett and by Huesman et al. that converge to maximum likelihood and maximum conditional likelihood estimates of radionuclide intensities for list-mode emission tomography. The approach taken here is optimization-theoretic and does not rely on the usual expectation maximization (EM) formalism. Block-iterative variants of the algorithms are presented. A self-contained, elementary proof of convergence of the algorithm is included.

Algorithms↗
PubMed2001

A Bayesian framework for the analysis of microarray expression data: regularized t -test and statistical inferences of gene changes.

MOTIVATION: DNA microarrays are now capable of providing genome-wide patterns of gene expression across many different conditions. The first level of analysis of these patterns requires determining whether observed differences in expression are significant or not. Current methods are unsatisfactory due to the lack of a systematic framework that can accommodate noise, variability, and low replication often typical of microarray data. RESULTS: We develop a Bayesian probabilistic framework for microarray data analysis. At the simplest level, we model log-expression values by independent normal distributions, parameterized by corresponding means and variances with hierarchical prior distributions. We derive point estimates for both parameters and hyperparameters, and regularized expressions for the variance of each gene by combining the empirical variance with a local background variance associated with neighboring genes. An additional hyperparameter, inversely related to the number of empirical observations, determines the strength of the background variance. Simulations show that these point estimates, combined with a t -test, provide a systematic inference approach that compares favorably with simple t -test or fold methods, and partly compensate for the lack of replication.

Bayes Theorem↗
PubMed2005

Spatiotemporal video segmentation based on graphical models.

This paper proposes a probabilistic framework for spatiotemporal segmentation of video sequences. Motion information, boundary information from intensity segmentation, and spatial connectivity of segmentation are unified in the video segmentation process by means of graphical models. A Bayesian network is presented to model interactions among the motion vector field, the intensity segmentation field, and the video segmentation field. The notion of the Markov random field is used to encourage the formation of continuous regions. Given consecutive frames, the conditional joint probability density of the three fields is maximized in an iterative way. To effectively utilize boundary information from the intensity segmentation, distance transformation is employed in local objective functions. Experimental results show that the method is robust and generates spatiotemporally coherent segmentation results. Moreover, the proposed video segmentation approach can be viewed as the compromise of previous motion based approaches and region merging approaches.

Algorithms↗
PubMed2006

Operon information improves gene expression estimation for cDNA microarrays.

BACKGROUND: In prokaryotic genomes, genes are organized in operons, and the genes within an operon tend to have similar levels of expression. Because of co-transcription of genes within an operon, borrowing information from other genes within the same operon can improve the estimation of relative transcript levels; the estimation of relative levels of transcript abundances is one of the most challenging tasks in experimental genomics due to the high noise level in microarray data. Therefore, techniques that can improve such estimations, and moreover are based on sound biological premises, are expected to benefit the field of microarray data analysis RESULTS: In this paper, we propose a hierarchical Bayesian model, which relies on borrowing information from other genes within the same operon, to improve the estimation of gene expression levels and, hence, the detection of differentially expressed genes. The simulation studies and the analysis of experiential data demonstrated that the proposed method outperformed other techniques that are routinely used to estimate transcript levels and detect differentially expressed genes, including the sample mean and SAM t statistics. The improvement became more significant as the noise level in microarray data increases. CONCLUSION: By borrowing information about transcriptional activity of genes within classified operons, we improved the estimation of gene expression levels and the detection of differentially expressed genes.

Animals↗
PubMed2004

Statistical modeling of complex backgrounds for foreground object detection.

This paper addresses the problem of background modeling for foreground object detection in complex environments. A Bayesian framework that incorporates spectral, spatial, and temporal features to characterize the background appearance is proposed. Under this framework, the background is represented by the most significant and frequent features, i.e., the principal features, at each pixel. A Bayes decision rule is derived for background and foreground classification based on the statistics of principal features. Principal feature representation for both the static and dynamic background pixels is investigated. A novel learning method is proposed to adapt to both gradual and sudden "once-off" background changes. The convergence of the learning process is analyzed and a formula to select a proper learning rate is derived. Under the proposed framework, a novel algorithm for detecting foreground objects from complex environments is then established. It consists of change detection, change classification, foreground segmentation, and background maintenance. Experiments were conducted on image sequences containing targets of interest in a variety of environments, e.g., offices, public buildings, subway stations, campuses, parking lots, airports, and sidewalks. Good results of foreground detection were obtained. Quantitative evaluation and comparison with the existing method show that the proposed method provides much improved results.

Algorithms↗
PubMed2006

Model-based hand tracking using a hierarchical Bayesian filter.

This paper sets out a tracking framework, which is applied to the recovery of three-dimensional hand motion from an image sequence. The method handles the issues of initialization, tracking, and recovery in a unified way. In a single input image with no prior information of the hand pose, the algorithm is equivalent to a hierarchical detection scheme, where unlikely pose candidates are rapidly discarded. In image sequences, a dynamic model is used to guide the search and approximate the optimal filtering equations. A dynamic model is given by transition probabilities between regions in parameter space and is learned from training data obtained by capturing articulated motion. The algorithm is evaluated on a number of image sequences, which include hand motion with self-occlusion in front of a cluttered background.

Algorithms↗
PubMed1998

Population pharmacokinetics of gentamicin in horses.

OBJECTIVE: To develop and validate a population pharmacokinetic model for gentamicin in horses, using retrospective clinical data. ANIMALS: 62 horses that had been treated IV with multiple doses of gentamicin at our veterinary teaching hospital between 1987 and 1996. Procedure-46 horses were assigned to the study group, and 16 to the validation group. Detailed history of dosage, sample collection times, and selected pathophysiologic variables were recorded for each patient. Samples were analyzed by use of a fluorescence polarization immunoassay method. Pharmacostatistical analysis was conducted, using computer software. The predictive model correlates pharmacokinetic parameters to concomitant pathophysiologic variables and estimates the inter- and intraindividual variability in disposition. RESULTS: A two-compartment model best described the data. Clearance (CI) was linearly correlated to body weight and serum creatinine concentration. Volume of the central compartment (Vd(c)) was linearly related to body weight. Interindividual coefficients of variability for CI and Vd(c) were 24 and 16%, respectively. The residual variability (intraindividual) was 13%; mean prediction error percent (bias) was 2%; and mean absolute prediction error percent (precision) was 29%. CONCLUSIONS: Population pharmacokinetic analysis allows study of the basic features of gentamicin disposition in horses with sparse data per individual. A considerable proportion of the pharmacokinetic variability of gentamicin in our study population was explained by differences in body weight and serum creatinine concentration. CLINICAL RELEVANCE: Population pharmacokinetics can be used to design first-dosage regimens according to the clinical characteristics of individual animals. Population pharmacokinetic models could also be included in Bayesian forecasting strategies to improve plasma concentration predictions in individual patients.

Age Factors↗
PubMed2006

Assessing site-interdependent phylogenetic models of sequence evolution.

In recent works, methods have been proposed for applying phylogenetic models that allow for a general interdependence between the amino acid positions of a protein. As of yet, such models have focused on site interdependencies resulting from sequence-structure compatibility constraints, using simplified structural representations in combination with a set of statistical potentials. This structural compatibility criterion is meant as a proxy for sequence fitness, and the methods developed thus far can incorporate different site-interdependent fitness proxies based on other measurements. However, no methods have been proposed for comparing and evaluating the adequacy of alternative fitness proxies in this context, or for more general comparisons with canonical models of protein evolution. In the present work, we apply Bayesian methods of model selection-based on numerical calculations of marginal likelihoods and posterior predictive checks-to evaluate models encompassing the site-interdependent framework. Our application of these methods indicates that considering site-interdependencies, as done here, leads to an improved model fit for all data sets studied. Yet, we find that the use of pairwise contact potentials alone does not suitably account for across-site rate heterogeneity or amino acid exchange propensities; for such complexities, site-independent treatments are still called for. The most favored models combine the use of statistical potentials with a suitably rich site-independent model. Altogether, the methodology employed here should allow for a more rigorous and systematic exploration of different ways of modeling explicit structural constraints, or any other site-interdependent criterion, while best exploiting the richness of previously proposed models.

Bayes Theorem↗
PubMed2005

Bayesian parameter estimates of nelfinavir and its active metabolite, hydroxy-tert-butylamide, in infants perinatally infected with human immunodeficiency virus type 1.

The objective of the present study was to develop a population pharmacokinetic model for nelfinavir mesylate (NFV) and nelfinavir hydroxy-tert-butylamide (M8), the most abundant metabolite of NFV, in infants vertically infected with human immunodeficiency virus type 1 and participating in the Paediatric European Network for Treatment of AIDS 7 study. Plasma NFV concentrations were determined during repeated NFV administrations (two to three times a day). Eighteen infants younger that age 2 years participated in this study. The doses administered ranged from 71 to 203 mg/kg of body weight/day. Pharmacokinetic parameter estimates were obtained by a compartmental approach by using a kinetic model to simultaneously fit NFV and M8 (active metabolite) concentrations. M8 was shown to be formation rate limited and was characterized by first-order rate constants of formation and elimination. Body weight was found to be a more appropriate predictor than age of the changes in (i) the rate of metabolism, (ii) the elimination rate constant of NFV, and (iii) NFV clearance. Population parameters were computed to account for the relationship between the rate of metabolism and body weight. The estimated NFV and M8 elimination half-lives were 4.3 and 2.04 h, respectively. The estimated NFV clearance was 2.13 liters/h/kg. The M8 concentration-to-NFV concentration ratio was 0.64 +/- 0.44. In conclusion, the population pharmacokinetic model describing the dispositions of NFV and M8 should facilitate the design of future studies to elucidate the relative contributions of the parent compound and M8 to the pharmacological and toxic effects of NFV therapy.

Aging↗
PubMedDate not supplied

Analyzing gene expression time-courses.

Measuring gene expression over time can provide important insights into basic cellular processes. Identifying groups of genes with similar expression time-courses is a crucial first step in the analysis. As biologically relevant groups frequently overlap, due to genes having several distinct roles in those cellular processes, this is a difficult problem for classical clustering methods. We use a mixture model to circumvent this principal problem, with hidden Markov models (HMMs) as effective and flexible components. We show that the ensuing estimation problem can be addressed with additional labeled data-partially supervised learning of mixtures-through a modification of the Expectation-Maximization (EM) algorithm. Good starting points for the mixture estimation are obtained through a modification to Bayesian model merging, which allows us to learn a collection of initial HMMs. We infer groups from mixtures with a simple information-theoretic decoding heuristic, which quantifies the level of ambiguity in group assignment. The effectiveness is shown with high-quality annotation data. As the HMMs we propose capture asynchronous behavior by design, the groups we find are also asynchronous. Synchronous subgroups are obtained from a novel algorithm based on Viterbi paths. We show the suitability of our HMM mixture approach on biological and simulated data and through the favorable comparison with previous approaches. A software implementing the method is freely available under the GPL from http://ghmm.org/gql.

Algorithms↗
PubMed2005

Approximate Bayesian inference reveals evidence for a recent, severe bottleneck in a Netherlands population of Drosophila melanogaster.

Genome-wide nucleotide variation in non-African populations of Drosophila melanogaster is a subset of variation found in East sub-Saharan African populations, suggesting a bottleneck in the history of the former. We implement an approximate Bayesian approach to infer the timing, duration, and severity of this putative bottleneck and ask whether this inferred model is sufficient to account for patterns of variability observed at 115 loci scattered across the X chromosome. We estimate a recent bottleneck 0.006N(e) generations ago, somewhat further in the past than suggested by biogeographical evidence. Using various proposed statistical tests, we find that this bottleneck model is able to predict the majority of observed features of diversity and linkage disequilibrium in the data. Thus, while precise estimates of bottleneck parameters (like inferences of selection) are sensitive to model assumptions, our results imply that it may be unnecessary to invoke frequent selective sweeps associated with the dispersal of D. melanogaster from Africa to explain patterns of variability in non-African populations.

Animals↗
PubMed2006

Bayesian hierarchical model for correcting signal saturation in microarrays using pixel intensities.

Pixel saturation occurs when the pixel intensity exceeds the scanner upper threshold of detection and the recorded pixel intensity is then truncated at the threshold. Truncation of the pixel intensity causes the estimates of gene expression (i.e., intensity) to be biased. Microarray experiments are commonly affected by saturated pixels; as a result all higher level analyses are made on these biased gene expression estimates. In this paper, we propose a method for improving the quality of the signal for cDNA microarrays by making use of several scans at varying scanner sensitivities. For each spot, pixel level intensity readings are given as input to a Bayesian hierarchical model. The model uses the pixel intensities of the spot to provide a posterior distribution of the true expression level of the corresponding genes. The parameters of the hierarchical model are estimated jointly with these expression levels, thus performing an integrated analysis of the measurement data. The method improves in all ranges the accuracy with which intensities can be estimated and extends the dynamic range of measured gene expression at the high end. The method is generic and can be applied to data from any organism and for imaging with any scanner. Results from a real data set illustrate an improved precision in the estimation of the expression of genes compared to what can be achieved by applying standard methods and using only a single scan.

Bayes Theorem↗
PubMed2002

Combining location and expression data for principled discovery of genetic regulatory network models.

We develop principled methods for the automatic induction (discovery) of genetic regulatory network models from multiple data sources and data modalities. Models of regulatory networks are represented as Bayesian networks, allowing the models to compactly and robustly capture probabilistic multivariate statistical dependencies between the various cellular factors in these networks. We build on previous Bayesian network validation results by extending the validation framework to the context of model induction, leveraging heuristic simulated annealing search algorithms and posterior model averaging. Using expression data in isolation yields results inconsistent with location data so we incorporate genomic location data to guide the model induction process. We combine these two data modalities by allowing location data to influence the model prior and expression data to influence the model likelihood. We demonstrate the utility of this approach by discovering genetic regulatory models of thirty-three variables involved in S. cerevisiae pheromone response. The models we automatically generate are consistent with the current understanding regarding this regulatory network, but also suggest new directions for future experimental investigation.

Bayes Theorem↗
PubMed2006

In silico human and rat Vss quantitative structure-activity relationship models.

We present herein a QSAR tool enabling an entirely in silico prediction of human and rat steady-state volume of distribution (Vss), to be made prior to chemical synthesis, preceding detailed allometric or mechanistic assessment of Vss. Three different statistical methodologies, Bayesian neural networks (BNN), classification and regression trees (CART), and partial least squares (PLS) were employed to model human (N=199) and rat (N=2086) data sets. The results in prediction of an independent test set show the human model has an r2 of 0.60 and an rms error in prediction of 0.48. The corresponding rat model has an r2 of 0.53 and an rms error in prediction of 0.37, indicating both models could be very useful in the early stages of the drug discovery process. This is the first reported entirely in silico approach to the prediction of rat and human steady-state volume of distribution.

Animals↗
PubMed2003

Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks.

MOTIVATION: Bayesian networks have been applied to infer genetic regulatory interactions from microarray gene expression data. This inference problem is particularly hard in that interactions between hundreds of genes have to be learned from very small data sets, typically containing only a few dozen time points during a cell cycle. Most previous studies have assessed the inference results on real gene expression data by comparing predicted genetic regulatory interactions with those known from the biological literature. This approach is controversial due to the absence of known gold standards, which renders the estimation of the sensitivity and specificity, that is, the true and (complementary) false detection rate, unreliable and difficult. The objective of the present study is to test the viability of the Bayesian network paradigm in a realistic simulation study. First, gene expression data are simulated from a realistic biological network involving DNAs, mRNAs, inactive protein monomers and active protein dimers. Then, interaction networks are inferred from these data in a reverse engineering approach, using Bayesian networks and Bayesian learning with Markov chain Monte Carlo. RESULTS: The simulation results are presented as receiver operator characteristics curves. This allows estimating the proportion of spurious gene interactions incurred for a specified target proportion of recovered true interactions. The findings demonstrate how the network inference performance varies with the training set size, the degree of inadequacy of prior assumptions, the experimental sampling strategy and the inclusion of further, sequence-based information. AVAILABILITY: The programs and data used in the present study are available from http://www.bioss.sari.ac.uk/~dirk/Supplements

Bayes Theorem↗
PubMed1999

Prediction of the international normalized ratio and maintenance dose during the initiation of warfarin therapy.

AIMS: A pharmacokinetic/pharmacodynamic model, with Bayesian parameter estimation, was used to retrospectively predict the daily International Normalized Ratios (INRs) and the maintenance doses during the initiation of warfarin therapy in 74 inpatients. METHODS: INRs and maintenance doses predicted by the model were compared with the actual INRs and the eventual maintenance dose. Cases with drugs or medical conditions interacting with warfarin or receiving concurrent heparin therapy were not excluded. As the study was retrospective, model predictions of the maintenance dose were not those that were administered. Mean prediction error (MPE) and percentage absolute prediction errors (PAPE) were used to assess the model predictions. RESULTS: INR MPE ranged from -0.07 to 0.06 and median PAPE from 10% to 20%. Dose MPE ranged from -0.7 to 0.17 mg and median PAPE from 16.7% to 37.5%. Accurate and precise dose predictions were obtained after 3 or more INR feedback's. CONCLUSIONS: This study shows that the model can accurately predict daily INRs and the maintenance dose in this sample of cases. The model can be incorporated into computer decision-support systems for warfarin therapy and may lead to improvement in the initiation of warfarin therapy.

Adult↗
PubMed2003

Estimation of population growth or decline in genetically monitored populations.

This article introduces a new general method for genealogical inference that samples independent genealogical histories using importance sampling (IS) and then samples other parameters with Markov chain Monte Carlo (MCMC). It is then possible to more easily utilize the advantages of importance sampling in a fully Bayesian framework. The method is applied to the problem of estimating recent changes in effective population size from temporally spaced gene frequency data. The method gives the posterior distribution of effective population size at the time of the oldest sample and at the time of the most recent sample, assuming a model of exponential growth or decline during the interval. The effect of changes in number of alleles, number of loci, and sample size on the accuracy of the method is described using test simulations, and it is concluded that these have an approximately equivalent effect. The method is used on three example data sets and problems in interpreting the posterior densities are highlighted and discussed.

Alleles↗
PubMed2003

Gene networks inference using dynamic Bayesian networks.

This article deals with the identification of gene regulatory networks from experimental data using a statistical machine learning approach. A stochastic model of gene interactions capable of handling missing variables is proposed. It can be described as a dynamic Bayesian network particularly well suited to tackle the stochastic nature of gene regulation and gene expression measurement. Parameters of the model are learned through a penalized likelihood maximization implemented through an extended version of EM algorithm. Our approach is tested against experimental data relative to the S.O.S. DNA Repair network of the Escherichia coli bacterium. It appears to be able to extract the main regulations between the genes involved in this network. An added missing variable is found to model the main protein of the network. Good prediction abilities on unlearned data are observed. These first results are very promising: they show the power of the learning algorithm and the ability of the model to capture gene interactions.

Algorithms↗