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PubMed2003

Singularities in mixture models and upper bounds of stochastic complexity.

A learning machine which is a mixture of several distributions, for example, a gaussian mixture or a mixture of experts, has a wide range of applications. However, such a machine is a non-identifiable statistical model with a lot of singularities in the parameter space, hence its generalization property is left unknown. Recently an algebraic geometrical method has been developed which enables us to treat such learning machines mathematically. Based on this method, this paper rigorously proves that a mixture learning machine has the smaller Bayesian stochastic complexity than regular statistical models. Since the generalization error of a learning machine is equal to the increase of the stochastic complexity, the result of this paper shows that the mixture model can attain the more precise prediction than regular statistical models if Bayesian estimation is applied in statistical inference.

Bayes Theorem↗

PubMed2002

A unified approach to joint modeling of multiple quantitative and qualitative traits in gene mapping.

Using graph theory, we present a theoretical basis for mapping oligogenes in the joint presence of multiple phenotypic measurements of both quantitative and qualitative types. Various statistical models proposed earlier for several traits of solely single type are special cases of the unified approach given here. Our emphasis is on the generality of the framework, without specifying explicit assumptions about a sampling design. When information about environmental factors potentially affecting the traits is available, it can be incorporated into the genetic model. We adopt the Bayesian inferential machinery due to its firm theoretical basis and its capability of handling uncertain quantities; such as unobserved model parameters, missing marker data, and even different putative genetic models, probabilistically within a single framework. It is shown here that biological hypotheses about single gene affecting simultaneously multiple traits (pleiotropy) can be intuitively imposed as parameter constraints, leading to pleiotropic models for which posterior probabilities can be calculated. Outline of the possible implementation of the Bayesian method is described using the general reversible-jump Markov chain Monte Carlo algorithm. Some future challenges and extensions are also discussed.

Animals↗

PubMed2002

Pharmacokinetics of intravenous busulfan in children prior to stem cell transplantation.

AIMS: Intravenous formulations of busulfan have recently become available. Although busulfan is used frequently in children as part of a myeloablative regimen prior to bone marrow transplantation, pharmacokinetic data on intravenous busulfan in children are scarce. The aim was to investigate intravenous busulfan pharmacokinetics in children and to suggest a limited sampling strategy in order to determine busulfan systemic exposure with the minimum of inconvenience and risk for the patient. METHODS: Plasma pharmacokinetics after the first administration was investigated in six children using nonlinear mixed effect modelling. RESULTS: Pharmacokinetics showed little variability and were described adequately with a one-compartment model (population estimates CL,av=0.29 l h(-1) kg(-1); V,av=0.84 l kg(-1); t(1/2)=1.7-2.8 h). Combined with limited sampling and a Bayesian fitting procedure, the model can adequately estimate the systemic exposure to intravenous busulfan, which in children appears to be at the lower end of the adult range. CONCLUSIONS: Busulfan systemic exposure in children during intravenous administration can be estimated adequately with limited sampling and a Bayesian fitting procedure from a one-compartment model. Intravenous busulfan pharmacokinetics in children should be the subject of more research.

Adolescent↗

PubMed2006

Invariance priors for Bayesian feed-forward neural networks.

Neural networks (NN) are famous for their advantageous flexibility for problems when there is insufficient knowledge to set up a proper model. On the other hand, this flexibility can cause overfitting and can hamper the generalization of neural networks. Many approaches to regularizing NN have been suggested but most of them are based on ad hoc arguments. Employing the principle of transformation invariance, we derive a general prior in accordance with the Bayesian probability theory for feed-forward networks. An optimal network is determined by Bayesian model comparison, verifying the applicability of this approach. Additionally the prior presented affords cell pruning.

Algorithms↗

PubMed2000

Linkage problem, distribution estimation, and Bayesian networks.

This paper proposes an algorithm that uses an estimation of the joint distribution of promising solutions in order to generate new candidate solutions. The algorithm is settled into the context of genetic and evolutionary computation and the algorithms based on the estimation of distributions. The proposed algorithm is called the Bayesian Optimization Algorithm (BOA). To estimate the distribution of promising solutions, the techniques for modeling multivariate data by Bayesian networks are used. The BOA identifies, reproduces, and mixes building blocks up to a specified order. It is independent of the ordering of the variables in strings representing the solutions. Moreover, prior information about the problem can be incorporated into the algorithm, but it is not essential. First experiments were done with additively decomposable problems with both nonoverlapping as well as overlapping building blocks. The proposed algorithm is able to solve all but one of the tested problems in linear or close to linear time with respect to the problem size. Except for the maximal order of interactions to be covered, the algorithm does not use any prior knowledge about the problem. The BOA represents a step toward alleviating the problem of identifying and mixing building blocks correctly to obtain good solutions for problems with very limited domain information.

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↗

PubMed2003

Bubbles: a unifying framework for low-level statistical properties of natural image sequences.

Recently, different models of the statistical structure of natural images have been proposed. These models predict properties of biological visual systems and can be used as priors in Bayesian inference. The fundamental model is independent component analysis, which can be estimated by maximization of the sparsenesses of linear filter outputs. This leads to the emergence of principal simple cell properties. Alternatively, simple cell properties are obtained by maximizing the temporal coherence in natural image sequences. Taking account of the basic dependencies of linear filter outputs permit modeling of complex cells and topographic organization as well. We propose a unifying framework for these statistical properties, based on the concept of spatiotemporal activity "bubbles."A bubble means here an activation of simple cells (linear filters) that is contiguous both in space (the cortical surface) and in time.

Bayes Theorem↗

PubMed2004

A biological network describing infection with Mycoplasma hyopneumoniae in swine herds.

We have made a biological model based on a Bayesian network for risk factors for infection with Mycoplasma hyopneumoniae (Mycoplasma) in slaughter pigs; prevalence of infection is based on veterinary examinations. The model is a probabilistic/stochastic determination based on the inherent biological uncertainty of the severity of infection with Mycoplasma and the derived stochastic effects on productivity for the herd. The conditional probabilities in the Bayesian network are based on published studies and expert opinions. We used the model to calculate how the risk factors and our evidence about the herd influenced our view on the severity of Mycoplasma, and how our view changed when we had more veterinary evidence. We also show how one can use the model to deal with conflicting examinations.

Abattoirs↗

PubMed2000

Bayesian approach to control of amikacin serum concentrations in critically ill patients with sepsis.

OBJECTIVE: To compare the predictive performance of a Bayesian program incorporating a population model with and without severity of illness covariates in intensive care unit (ICU) patients with sepsis. DESIGN: The clinical, physiologic, and pharmacokinetic data of 62 patients with sepsis admitted to a tertiary-care center were analyzed retrospectively. The patients were randomly assigned to a active group and a validation group. The model was developed using a three-step approach involving Bayesian estimation of pharmacokinetic parameters, selection of covariates by principal component analysis, and final selection of covariates by stepwise multiple linear regression. The predictive performance of this model was tested in patients from the validation group and compared with that of a general population model without covariates. RESULTS: Regression analysis revealed that the Acute Physiologic and Chronic Health Evaluation (APACHE II) score was the most important determinant for amikacin volume of distribution (1.5 L/kg, APACHE II; r2 = 0.77). For amikacin clearance (CIamik), creatinine clearance (CIcr), positive end-expiratory pressure (PEEP), and use of catecholamines (CAT) were the most important predictors (CIamik = 44.5 + 0.67 CIcr - 1.29 PEEP - 8.34 CAT; r2 = 0.72). The relative mean error (deltaME) and root mean-square error (deltaRMSE) (95% CI) were -0.62 (-1.2 to 0.01) and 3.78 (2.3 to 4.8) mg/L, respectively. Since the 95% CI for deltaRMSE did not include zero, it appears that the model with covariates is significantly improved in terms of precision. CONCLUSIONS: Our results show that, in ICU patients treated with amikacin, it is relevant to consider covariates related to pathophysiologic status and therapeutic measures. Application of a Bayesian program allows improved control of the pharmacokinetic parameters in patients who exhibit rapidly changing physiologic conditions.

Amikacin↗

PubMed1997

Bayesian population pharmacokinetic and pharmacodynamic analyses using mixture models.

Population studies of the pharmacokinetics or pharmacodynamics of drugs help us, learn about the variability in drug disposition and effects, information that can be used to treat future patients at safe and effective doses. We present a new approach to population modeling based on a weighted mixture of normal distributions having random weights and means. This method allows estimation of underlying continuous population distributions without prespecifying the parametric form or shape of these probability distributions. Additionally, this method can carry out nonparametric regression of pharmacokinetic or dynamic parameters on patient covariates while estimating the underlying distributions. Two examples illustrate the method and its flexibility.

Bayes Theorem↗

PubMedDate not supplied

Bayesian estimation of the parameters of a nonlinear model. An application to human height.

The estimation of the parameters of a nonlinear model by means of the maximum likelihood procedure is widely used in the study of growth phenomena. The accuracy with which these parameters are calculated is a function of the number of measures taken and particularly, of their distribution across the growth period. If the growth curve is only partially known, the inaccuracy can increase considerably. However, if we have information on the distribution of the parameters of a model in the population, the empirical Bayes method should be used. In this paper, the principle of this approach for nonlinear modeling was recalled. The method was then applied on data of human height. Four nonlinear models are used and their performances are compared. The results show the importance of information on the quality of estimates of growth parameters and consequently on the prediction of adult height.

Adult↗

PubMed2001

Bayesian restoration of ion channel records using hidden Markov models.

Hidden Markov models have been used to restore recorded signals of single ion channels buried in background noise. Parameter estimation and signal restoration are usually carried out through likelihood maximization by using variants of the Baum-Welch forward-backward procedures. This paper presents an alternative approach for dealing with this inferential task. The inferences are made by using a combination of the framework provided by Bayesian statistics and numerical methods based on Markov chain Monte Carlo stochastic simulation. The reliability of this approach is tested by using synthetic signals of known characteristics. The expectations of the model parameters estimated here are close to those calculated using the Baum-Welch algorithm, but the present methods also yield estimates of their errors. Comparisons of the results of the Bayesian Markov Chain Monte Carlo approach with those obtained by filtering and thresholding demonstrate clearly the superiority of the new methods.

Bayes Theorem↗

PubMed1996

Population toxicokinetics of tetrachloroethylene.

In assessing the distribution and metabolism of toxic compounds in the body, measurements are not always feasible for ethical or technical reasons. Computer modeling offers a reasonable alternative, but the variability and complexity of biological systems pose unique challenges in model building and adjustment. Recent tools from population pharmacokinetics, Bayesian statistical inference, and physiological modeling can be brought together to solve these problems. As an example, we modeled the distribution and metabolism of tetrachloroethylene (PERC) in humans. We derive statistical distributions for the parameters of a physiological model of PERC, on the basis of data from Monster et al. (1979). The model adequately fits both prior physiological information and experimental data. An estimate of the relationship between PERC exposure and fraction metabolized is obtained. Our median population estimate for the fraction of inhaled tetrachloroethylene that is metabolized, at exposure levels exceeding current occupational standards, is 1.5% [95% confidence interval (0.52%, 4.1%)]. At levels approaching ambient inhalation exposure (0.001 ppm), the median estimate of the fraction metabolized is much higher, at 36% [95% confidence interval (15%, 58%)]. This disproportionality should be taken into account when deriving safe exposure limits for tetrachloroethylene and deserves to be verified by further experiments.

Administration, Inhalation↗

PubMed2005

Assessing uncertainty in simulation-based maritime risk assessment.

Recent work in the assessment of risk in maritime transportation systems has used simulation-based probabilistic risk assessment techniques. In the Prince William Sound and Washington State Ferries risk assessments, the studies' recommendations were backed up by estimates of their impact made using such techniques and all recommendations were implemented. However, the level of uncertainty about these estimates was not available, leaving the decisionmakers unsure whether the evidence was sufficient to assess specific risks and benefits. The first step toward assessing the impact of uncertainty in maritime risk assessments is to model the uncertainty in the simulation models used. In this article, a study of the impact of proposed ferry service expansions in San Francisco Bay is used as a case study to demonstrate the use of Bayesian simulation techniques to propagate uncertainty throughout the analysis. The conclusions drawn in the original study are shown, in this case, to be robust to the inherent uncertainties. The main intellectual merit of this work is the development of Bayesian simulation technique to model uncertainty in the assessment of maritime risk. However, Bayesian simulations have been implemented only as theoretical demonstrations. Their use in a large, complex system may be considered state of the art in the field of computational sciences.

Journal Article↗

PubMed2004

An integrated comprehensive workbench for inferring genetic networks: voyagene.

We propose an integrated, comprehensive network-inferring system for genetic interactions, named VoyaGene, which can analyze experimentally observed expression profiles by using and combining the following five independent inferring models: Clustering, Threshold-Test, Bayesian, multi-level digraph and S-system models. Since VoyaGene also has effective tools for visualizing the inferred results, researchers may evaluate the combination of appropriate inferring models, and can construct a genetic network to an accuracy that is beyond the reach of a single inferring model. Through the use of VoyaGene, the present study demonstrates the effectiveness of combining different inferring models.

Algorithms↗

PubMed1996

Population toxicokinetics of benzene.

In assessing the distribution and metabolism of toxic compounds in the body, measurements are not always feasible for ethical or technical reasons. Computer modeling offers a reasonable alternative, but the variability and complexity of biological systems pose unique challenges in model building and adjustment. Recent tools from population pharmacokinetics, Bayesian statistical inference, and physiological modeling can be brought together to solve these problems. As an example, we modeled the distribution and metabolism of benzene in humans. We derive statistical distributions for the parameters of a physiological model of benzene, on the basis of existing data. The model adequately fits both prior physiological information and experimental data. An estimate of the relationship between benzene exposure (up to 10 ppm) and fraction metabolized in the bone marrow is obtained and is shown to be linear for the subjects studied. Our median population estimate for the fraction of benzene metabolized, independent of exposure levels, is 52% (90% confidence interval, 47-67%). At levels approaching occupational inhalation exposure (continuous 1 ppm exposure), the estimated quantity metabolized in the bone marrow ranges from 2 to 40 mg/day.

Bayes Theorem↗

PubMed2005

Locally adaptive function estimation for binary regression models.

In this paper we present a nonparametric Bayesian approach for fitting unsmooth or highly oscillating functions in regression models with binary responses. The approach extends previous work by Lang et al. for Gaussian responses. Nonlinear functions are modelled by first or second order random walk priors with locally varying variances or smoothing parameters. Estimation is fully Bayesian and uses latent utility representations of binary regression models for efficient block sampling from the full conditionals of nonlinear functions.

Bayes Theorem↗

PubMed1999

Threshold-linear versus linear-linear analysis of birth weight and calving ease using an animal model: I. Variance component estimation.

Birth weight and calving difficulty were analyzed with Bayesian methodology using univariate linear models, a bivariate linear model, a threshold model for calving difficulty, and a joint threshold-linear model using a probit approach. Field data included 26,006 records of Gelbvieh cattle. Simulated populations were generated using parameters estimated from the field data. The Gibbs sampler was used to obtain estimates of the marginal posterior mean and standard deviation of the (co)variance components, heritabilities, and correlations. In the univariate analyses, the posterior mean of direct heritability for calving difficulty was .23 with the threshold model and .18 with the linear model. Maternal heritabilities were .10 and .08, respectively. In the bivariate analysis, posterior means of direct heritability for calving difficulty were .21 and .18 for the bivariate linear-threshold and linear-linear model, respectively. Maternal heritabilities were .09 and .06, respectively. Direct heritability for birth weight was .25 for the univariate model and .26 for bivariate models. Maternal heritability was .05 for the linear-threshold model and the univariate model and .06 for the bivariate linear model. Genetic correlation between direct genetic effects in both traits was .81 for the linear-threshold model and .79 for the bivariate linear. Residual correlation was .35 for the bivariate linear model and .50 for the bivariate linear-threshold. A simulation study confirmed that the posterior mean of the marginal distribution was suitable as a point estimate for univariate threshold and bivariate linear-threshold models.

Animals↗