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PubMed1995

Applications of the Dirichlet distribution to forensic match probabilities.

The Dirichlet distribution provides a convenient conjugate prior for Bayesian analyses involving multinomial proportions. In particular, allele frequency estimation can be carried out with a Dirichlet prior. If data from several distinct populations are available, then the parameters characterizing the Dirichlet prior can be estimated by maximum likelihood and then used for allele frequency estimation in each of the separate populations. This empirical Bayes procedure tends to moderate extreme multinomial estimates based on sample proportions. The Dirichlet distribution can also be employed to model the contributions from different ancestral populations in computing forensic match probabilities. If the ancestral populations are in genetic equilibrium, then the product rule for computing match probabilities is valid conditional on the ancestral contributions to a typical person of the reference population. This fact facilitates computation of match probabilities and tight upper bounds to match probabilities.

Alleles↗
PubMed2005

Robust non-homomorphic approach for speckle reduction in medical ultrasound images.

Most existing wavelet-based image denoising techniques are developed for additive white Gaussian noise. In applications to speckle reduction in medical ultrasound (US) images, the traditional approach is first to perform the logarithmic transform (homomorphic processing) to convert the multiplicative speckle noise model to an additive one, and then the wavelet filtering is performed on the log-transformed image, followed by an exponential operation. However, this non-linear operation leads to biased estimation of the signal and increases the computational complexity of the filtering method. To overcome these drawbacks, an efficient, non-homomorphic technique for speckle reduction in medical US images is proposed. The method relies on the true characterisation of the marginal statistics of the signal and speckle wavelet coefficients. The speckle component was modelled using the generalised Nakagami distribution, which is versatile enough to model the speckle statistics under various scattering conditions of interest in medical US images. By combining this speckle model with the generalised Gaussian signal first, the Bayesian shrinkage functions were derived using the maximum a posteriori (MAP) criterion. The resulting Bayesian processor used the local image statistics to achieve soft-adaptation from homogeneous to highly heterogeneous areas. Finally, the results showed that the proposed method, named GNDShrink, yielded a signal-to-noise ratio (SNR) gain of 0.42dB over the best state-of-the-art despeckling method reported in the literature, 1.73dB over the Lee filter and 1.31dB over the Kaun filter at an input SNR of 12.0dB, when tested on a US image. Further, the visual comparison of despeckled US images indicated that the new method suppressed the speckle noise well, while preserving the texture and organ surfaces.

Algorithms↗
PubMed2005

Bayesian model selection for genome-wide epistatic quantitative trait loci analysis.

The problem of identifying complex epistatic quantitative trait loci (QTL) across the entire genome continues to be a formidable challenge for geneticists. The complexity of genome-wide epistatic analysis results mainly from the number of QTL being unknown and the number of possible epistatic effects being huge. In this article, we use a composite model space approach to develop a Bayesian model selection framework for identifying epistatic QTL for complex traits in experimental crosses from two inbred lines. By placing a liberal constraint on the upper bound of the number of detectable QTL we restrict attention to models of fixed dimension, greatly simplifying calculations. Indicators specify which main and epistatic effects of putative QTL are included. We detail how to use prior knowledge to bound the number of detectable QTL and to specify prior distributions for indicators of genetic effects. We develop a computationally efficient Markov chain Monte Carlo (MCMC) algorithm using the Gibbs sampler and Metropolis-Hastings algorithm to explore the posterior distribution. We illustrate the proposed method by detecting new epistatic QTL for obesity in a backcross of CAST/Ei mice onto M16i.

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PubMedDate not supplied

Bayesian QTL mapping using skewed Student-t distributions.

In most QTL mapping studies, phenotypes are assumed to follow normal distributions. Deviations from this assumption may lead to detection of false positive QTL. To improve the robustness of Bayesian QTL mapping methods, the normal distribution for residuals is replaced with a skewed Student-t distribution. The latter distribution is able to account for both heavy tails and skewness, and both components are each controlled by a single parameter. The Bayesian QTL mapping method using a skewed Student-t distribution is evaluated with simulated data sets under five different scenarios of residual error distributions and QTL effects.

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PubMed2006

Comparing likelihood and Bayesian coalescent estimation of population parameters.

We have developed a Bayesian version of our likelihood-based Markov chain Monte Carlo genealogy sampler LAMARC and compared the two versions for estimation of theta = 4N(e)mu, exponential growth rate, and recombination rate. We used simulated DNA data to assess accuracy of means and support or credibility intervals. In all cases the two methods had very similar results. Some parameter combinations led to overly narrow support or credibility intervals, excluding the truth more often than the desired percentage, for both methods. However, the Bayesian approach rejected the generative parameter values significantly less often than the likelihood approach, both in cases where the level of rejection was normal and in cases where it was too high.

Bayes Theorem↗
PubMed1997

Stability and performance of a population pharmacokinetic model.

This study aimed to determine the stability (in terms of covariate selection) of a population pharmacokinetic model and evaluate its performance in the absence of a test data set. Data from 88 full-term infants, 11 of whom were human immunodeficiency virus (HIV)-seropositive, taking an antiinfective agent were analyzed using exploratory data analysis methods and the nonlinear mixed-effects modeling (NONMEM) program to obtain the final population pharmacokinetic model. The stability of the population pharmacokinetic model was tested using the nonparametric bootstrap approach in four steps: 1) with the base pharmacokinetic model, 100 bootstrap replicates of the original data were generated by sampling with replacement; 2) ascertainment that each bootstrap data replicate was described by the basic structural model using the NONMEM objective function; 3) generalized additive modeling (GAM) applied to empiric Bayesian estimates for covariate selection at alpha = 0.05 and a frequency (f) cutoff value of 0.50; and 4) NONMEM population model building using covariates selected in the third step with alpha = 0.005. Performance of the population pharmacokinetic model was evaluated using 200 additional bootstrap replicates of the data by fitting the model obtained in step 4 to them. Parameters obtained were compared with those obtained in the model stability step, and improved prediction error, a measure of predictive accuracy as an index of internal validation, was computed. The reciprocal of serum creatinine (RSC; f = 0.73) and HIV (f = 0.70) were selected by GAM as predictors of clearance (Cl). The population pharmacokinetic model obtained without the determination of model stability included RSC as a predictor of Cl, but the final model from the model stability step included both HIV and RSC as predictors of Cl. Final population pharmacokinetic parameters were obtained with this model fitted to the original data; however, the 95% confidence interval on the HIV status regression coefficient included zero, indicating no significance. The mean parameter estimates obtained with the additional 200 bootstrap replicates of data were within 15% of those obtained with the final model at the regression stability step. Bootstrap resampling procedure is useful for evaluating the stability and performance of a population model by repeatedly fitting it to the bootstrap samples when there is no test data set.

Adolescent↗
PubMed2005

Bayesian sonar detection performance prediction in the presence of interference in uncertain environments.

The detection performance of sonar systems can be greatly limited by the presence of interference and environmental uncertainty. The classic sonar equation does not take into account these two limiting factors and is inaccurate in predicting sonar detection performance. Here we have developed closed-form receiver operating characteristic (ROC) performance expressions for the Bayesian detector in the presence of interference in uncertain environments. Various scenarios extended from a NRL benchmark shallow-water model were used to test the analytical ROC expressions and to analyze the effects of interference and environmental uncertainty on detection performance. The results show that (1) the degradation on detection performance due to interference is greatly magnified by the presence of environmental uncertainty; (2) Bayesian sonar detection performance depends on the following fundamental parameters: the signal-to-noise ratio, the rank of the signal matrix, and the signal-to-interference coefficient; (3) the proposed analytical ROC performance predictions can be computed much faster than performance evaluations with commonly used Monte Carlo techniques.

Journal Article↗
PubMed1998

Bayesian variable selection method for censored survival data.

A Bayesian variable selection method for censored data is proposed in this paper. Based on the sufficiency and asymptotic normality of the maximum partial likelihood estimator, we approximate the posterior distribution of the parameters in a proportional hazards model. We consider a parsimonious model as the full model with some covariates unobserved and replaced by their conditional expected values. A loss function based on the posterior expected estimation error of the log-risk for the proportional hazards model is used to select a parsimonious model. We derive computational expressions for this loss function for both continuous and binary covariates. This approach provides an extension of Lindley's (1968, Journal of the Royal Statistical Society, Series B 30, 31-66) variable selection criterion for the linear case. Data from a randomized clinical trial of patients with primary biliary cirrhosis of the liver (PBC) (Fleming and Harrington, 1991, Counting Processes and Survival Analysis) is used to illustrate the proposed method and a simulation study compares it with the backward elimination procedure.

Bayes Theorem↗
PubMed2006

Bayesian detection of periodic mRNA time profiles without use of training examples.

BACKGROUND: Detection of periodically expressed genes from microarray data without use of known periodic and non-periodic training examples is an important problem, e.g. for identifying genes regulated by the cell-cycle in poorly characterised organisms. Commonly the investigator is only interested in genes expressed at a particular frequency that characterizes the process under study but this frequency is seldom exactly known. Previously proposed detector designs require access to labelled training examples and do not allow systematic incorporation of diffuse prior knowledge available about the period time. RESULTS: A learning-free Bayesian detector that does not rely on labelled training examples and allows incorporation of prior knowledge about the period time is introduced. It is shown to outperform two recently proposed alternative learning-free detectors on simulated data generated with models that are different from the one used for detector design. Results from applying the detector to mRNA expression time profiles from S. cerevisiae showsthat the genes detected as periodically expressed only contain a small fraction of the cell-cycle genes inferred from mutant phenotype. For example, when the probability of false alarm was equal to 7%, only 12% of the cell-cycle genes were detected. The genes detected as periodically expressed were found to have a statistically significant overrepresentation of known cell-cycle regulated sequence motifs. One known sequence motif and 18 putative motifs, previously not associated with periodic expression, were also over represented. CONCLUSION: In comparison with recently proposed alternative learning-free detectors for periodic gene expression, Bayesian inference allows systematic incorporation of diffuse a priori knowledge about, e.g. the period time. This results in relative performance improvements due to increased robustness against errors in the underlying assumptions. Results from applying the detector to mRNA expression time profiles from S. cerevisiae include several new findings that deserve further experimental studies.

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PubMed2006

On Bayesian inference for the K function.

The K function is a summary of spatial dependence in spatial point processes. In practice one observes a realization of the spatial point process, called a spatial point pattern. Although the K function of a spatial point process is typically unknown, several estimators of the process K function have been put forth. These estimators, however, are based upon empirical averages; the complicated distributional properties of the estimators unfortunately complicates interval estimation. In this paper, we propose a Bayesian inferential framework, allowing inference for the K function of the spatial point process (including interval estimation). Of particular interest is the unique use of the posterior predictive distribution to (efficiently) enable such inferences. To demonstrate our technique, the well known Swedish pine sapling data (Strand, 1972) is analyzed, including a discussion on evaluating model fit.

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PubMed2003

Population pharmacokinetics and metabolism of midazolam in pediatric intensive care patients.

OBJECTIVE: To determine the pharmacokinetics and metabolism of midazolam in pediatric intensive care patients. DESIGN: Prospective population pharmacokinetic study. SETTING: Pediatric intensive care unit. PATIENTS: Twenty-one pediatric intensive care patients aged between 2 days and 17 yrs. INTERVENTIONS: The pharmacokinetics of midazolam and metabolites were determined during and after a continuous infusion of midazolam (0.05-0.4 mg/kg/hr) for 3.8 hrs to 25 days administered for conscious sedation. MEASUREMENTS AND MAIN RESULTS: Blood samples were taken at different times during and after midazolam infusion for determination of midazolam, 1-OH-midazolam, and 1-OH-midazolam-glucuronide concentrations via high-performance liquid chromatography-ultraviolet detection. A population analysis was conducted via a two-compartment pharmacokinetic model by the NPEM program. The final population model was used to generate individual Bayesian posterior pharmacokinetic parameter estimates. Total body clearance, apparent volume distribution in terminal phase, and plasma elimination half-life were (mean +/- sd, n = 18): 5.0 +/- 3.9 mL/kg/min, 1.7 +/- 1.1 L/kg, and 5.5 +/- 3.5 hrs, respectively. The mean 1-OH-midazolam/midazolam ratio and (1-OH-midazolam + 1-OH-midazolam-glucuronide)/midazolam ratio were 0.14 +/- 0.21 and 1.4 +/- 1.1, respectively. Data from three patients with renal failure, hepatic failure, and concomitant erythromycin-fentanyl therapy were excluded from the final pharmacokinetic analysis. CONCLUSIONS: We describe population and individual midazolam pharmacokinetic parameter estimates in pediatric intensive care patients by using a population modeling approach. Lower midazolam elimination was observed in comparison to other studies in pediatric intensive care patients, probably as a result of differences in study design and patient differences such as age and disease state. Covariates such as renal failure, hepatic failure, and concomitant administration of CYP3A inhibitors are important predictors of altered midazolam and metabolite pharmacokinetics in pediatric intensive care patients. The derived population model can be useful for future dose optimization and Bayesian individualization.

Adolescent↗
PubMed1994

Adaptive control of drug dosage regimens: basic foundations, relevant issues, and clinical examples.

In this paper we examine several of the fundamental foundations and relevant clinical issues in adaptive control of drug dosage regimens for patients. Truly individualized therapy with drugs having narrow margins of safety first requires a practical pharmacokinetic/dynamic model of the behavior of a drug. Past experience with a drug is stored in the form of a population model. Next, using the information in such a model and its relationship to the incidence of adverse reactions, a specific, explicit therapeutic goal must be selected by the responsible clinician, based on the patient's need for the drug and the risk of adverse reactions felt to be justified by each patient's need, small, moderate, or great. Individualized drug therapy thus begins with the selection of individualized therapeutic goals (low, moderate, or high) for each patient. Using subsequent feedback from the patient's serum drug levels, and using Bayesian fitting, the model is then linked to each patient as a patient-specific model. Control of the model by the dosage regimen increasingly controls the patient, to better obtain the desired explicit therapeutic goals. This process is essentially similar to that of a flight control or missile guidance system.

Bayes Theorem↗
PubMed2002

A limited-sampling strategy to estimate individual pharmacokinetic parameters of vinorelbine in elderly patients with advanced metastatic cancer.

The aim of this study was to characterize the population pharmacokinetic of vinorelbine in elderly patients and to propose a limited-sampling strategy to estimate individual pharmacokinetic parameters. Vinorelbine was administered by a 10-min continuous infusion at a dose of 20-30 mg/m2. The population parameters were computed, using a three-compartment model, from an initial group of 27 patients. Twelve additional courses were used for model validation and evaluation of eight different limited-sampling strategies. The inter-individual variability of CL was explained by a linear dependency with age. The population average parameters and the interindividual variabilities (CV%) were: CL=47.1 l/h (31.7%), V=16.6 l (64%), k21=0.776 h-1 (20%), k31=0.0346 h-1 (15.2%), alpha=0.431 h-1 (6.84%) and beta=0.0167 h-1 (25%). Bayesian estimation with three measured levels (end of infusion, and 6 and 48 h) can be selected, because it allows adequate estimation of CL, elimination half-life and vinorelbine concentrations with a non-significant bias. Moreover, the choice of these three sampling times presents practicality advantages for the patient's comfort. Vinorelbine clearance decreasing with age and AUC being a good predictor of several toxicity end points during vinorelbine treatment, the limited-sampling strategy developed in this paper may be clinically relevant.

Aged↗
PubMedDate not supplied

A neural network approach to approximating MAP in belief networks.

Bayesian belief networks (BBN) are a widely studied graphical model for representing uncertainty and probabilistic interdependence among variables. One of the factors that restricts the model's wide acceptance in practical applications is that the general inference with BBN is NP-hard. This is also true for the maximum a posteriori probability (MAP) problem, which is to find the most probable joint value assignment to all uninstantiated variables, given instantiation of some variables in a BBN. To circumvent the difficulty caused by MAP's computational complexity, we suggest in this paper a neural network approximation approach. With this approach, a BBN is treated as a neural network without any change or transformation of the network structure, and the node activation functions are derived based on an energy function defined over a given BBN. Three methods are developed. They are the hill-climbing style discrete method, the simulated annealing method, and the continuous method based on the mean field theory. All three methods are for BBN of general structures, with the restriction that nodes of BBN are binary variables. In addition, rules for applying these methods to noisy-or networks are also developed, which may lead to more efficient computation in some cases. These methods' convergence is analyzed, and their validity tested through a series of computer experiments with two BBN of moderate size and complexity. Although additional theoretical and empirical work is needed, the analysis and experiments suggest that this approach may lead to effective and accurate approximation for MAP problems.

Algorithms↗
PubMed2006

Linkage disequilibrium on chromosome 6 in Australian Holstein-Friesian cattle.

We analysed linkage disequilibrium (LD) in Australian Holstein-Friesian cattle by genotyping a sample of 45 bulls for 15 closely-spaced microsatellites on two regions of BTA6 reported to carry important QTL for dairy traits. The order and distance of markers were based on the USDA-MARC linkage map. Frequencies of haplotypes were estimated using the E-M approach and a more computationally-intensive Bayesian approach as implemented in PHASE. LD was then estimated using the Hedrick multiallelic extension of Lewontin normalised coefficient D'. Estimates of D' from the two approaches were in close agreement (r = 0.91). The mean estimates of D' for marker pairs with an inter-marker distance of less than 5 cM (n = 13) are 0.57 and 0.51, and for distances more than 20 cM (n = 44) are 0.29 and 0.17, estimated from the E-M and Bayesian approaches, respectively. The Malecot model was fitted for the exponential decline of LD with map distance between markers. The swept radii (the distance at which LD has declined to 1/e ( approximately 37%) of its initial value) are 11.6 and 13.7 cM for the above two methods, respectively. The Malecot model was also fitted using map distance in Mb from the bovine integrated map (bovine location database, bLDB) in addition to cM from the MARC map. Overall, the results indicate a high level of LD on chromosome 6 in Australian dairy cattle.

Animals↗
PubMed2004

Inference of gene regulatory networks by means of dynamic differential Bayesian networks and nonparametric regression.

We propose a dynamic differential Bayesian networks (DDBNs) and nonparametric regression model. This model is an extended model of traditional dynamic Bayesian networks (DBNs), which can incorporate temporal information in a natural way and directly handle real-valued data obtained from microarrays without any transformation. In addition, it can cope with differential information between gene expression levels, without any loss to the traditional advantage, i.e., the capability of estimating non-linear relationships between genes. We apply DDBNs to analyze simulated data and real data, i.e., Saccharomyces cerevisiae cell cycle gene expression data. We have confirmed the effectiveness of our approach in the sense that some edges have been successfully detected only by DDBNs, not by DBNs.

Algorithms↗
PubMed2005

Direct reconstruction of kinetic parameter images from dynamic PET data.

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

Algorithms↗
PubMed2004

Bayesian mixture model based clustering of replicated microarray data.

MOTIVATION: Identifying patterns of co-expression in microarray data by cluster analysis has been a productive approach to uncovering molecular mechanisms underlying biological processes under investigation. Using experimental replicates can generally improve the precision of the cluster analysis by reducing the experimental variability of measurements. In such situations, Bayesian mixtures allow for an efficient use of information by precisely modeling between-replicates variability. RESULTS: We developed different variants of Bayesian mixture based clustering procedures for clustering gene expression data with experimental replicates. In this approach, the statistical distribution of microarray data is described by a Bayesian mixture model. Clusters of co-expressed genes are created from the posterior distribution of clusterings, which is estimated by a Gibbs sampler. We define infinite and finite Bayesian mixture models with different between-replicates variance structures and investigate their utility by analyzing synthetic and the real-world datasets. Results of our analyses demonstrate that (1) improvements in precision achieved by performing only two experimental replicates can be dramatic when the between-replicates variability is high, (2) precise modeling of intra-gene variability is important for accurate identification of co-expressed genes and (3) the infinite mixture model with the 'elliptical' between-replicates variance structure performed overall better than any other method tested. We also introduce a heuristic modification to the Gibbs sampler based on the 'reverse annealing' principle. This modification effectively overcomes the tendency of the Gibbs sampler to converge to different modes of the posterior distribution when started from different initial positions. Finally, we demonstrate that the Bayesian infinite mixture model with 'elliptical' variance structure is capable of identifying the underlying structure of the data without knowing the 'correct' number of clusters. AVAILABILITY: The MS Windows based program named Gaussian Infinite Mixture Modeling (GIMM) implementing the Gibbs sampler and corresponding C++ code are available at http://homepages.uc.edu/~medvedm/GIMM.htm SUPPLEMENTAL INFORMATION: http://expression.microslu.washington.edu/expression/kayee/medvedovic2003/medvedovic_bioinf2003.html

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