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At least 1,297 records · Page 72Linked to original sources
PubMed2005

On the relationship between deterministic and probabilistic directed Graphical models: from Bayesian networks to recursive neural networks.

Machine learning methods that can handle variable-size structured data such as sequences and graphs include Bayesian networks (BNs) and Recursive Neural Networks (RNNs). In both classes of models, the data is modeled using a set of observed and hidden variables associated with the nodes of a directed acyclic graph. In BNs, the conditional relationships between parent and child variables are probabilistic, whereas in RNNs they are deterministic and parameterized by neural networks. Here, we study the formal relationship between both classes of models and show that when the source nodes variables are observed, RNNs can be viewed as limits, both in distribution and probability, of BNs with local conditional distributions that have vanishing covariance matrices and converge to delta functions. Conditions for uniform convergence are also given together with an analysis of the behavior and exactness of Belief Propagation (BP) in 'deterministic' BNs. Implications for the design of mixed architectures and the corresponding inference algorithms are briefly discussed.

Bayes Theorem↗
PubMed2006

A regularized discriminative model for the prediction of protein-peptide interactions.

MOTIVATION: Short well-defined domains known as peptide recognition modules (PRMs) regulate many important protein-protein interactions involved in the formation of macromolecular complexes and biochemical pathways. Since high-throughput experiments like yeast two-hybrid and phage display are expensive and intrinsically noisy, it would be desirable to more specifically target or partially bypass them with complementary in silico approaches. In the present paper, we present a probabilistic discriminative approach to predicting PRM-mediated protein-protein interactions from sequence data. The model is motivated by the discriminative model of Segal and Sharan as an alternative to the generative approach of Reiss and Schwikowski. In our evaluation, we focus on predicting the interaction network. As proposed by Williams, we overcome the problem of susceptibility to over-fitting by adopting a Bayesian a posteriori approach based on a Laplacian prior in parameter space. RESULTS: The proposed method was tested on two datasets of protein-protein interactions involving 28 SH3 domain proteins in Saccharmomyces cerevisiae, where the datasets were obtained with different experimental techniques. The predictions were evaluated with out-of-sample receiver operator characteristic (ROC) curves. In both cases, Laplacian regularization turned out to be crucial for achieving a reasonable generalization performance. The Laplacian-regularized discriminative model outperformed the generative model of Reiss and Schwikowski in terms of the area under the ROC curve on both datasets. The performance was further improved with a hybrid approach, in which our model was initialized with the motifs obtained with the method of Reiss and Schwikowski. AVAILABILITY: Software and supplementary material is available from http://lehrach.com/wolfgang/dmf.

Algorithms↗
PubMed1999

Optimal sampling times for Bayesian estimation of the pharmacokinetic parameters of nortriptyline during therapeutic drug monitoring.

Sampling times for Bayesian estimation of the pharmacokinetic parameters of an antidepressant drug, nortriptyline, during its therapeutic drug monitoring were optimized. Our attention was focused on designs including a limited number of measurements: one, two, and three sample designs in which sampling times had to be chosen between 0 and 24 hr after the last intake of a test-dose study. The optimization was conducted in four groups of patients defined by their gender and the administration or not of concomitant drugs inhibiting the metabolism of nortriptyline. The Bayesian design criterion was defined as the expected information provided by an experiment. A stochastic approximation algorithm, the Kiefer-Wolfowitz algorithm, was used for the criterion maximization under experimental constraints. Results showed that optimal Bayesian sampling times differ between patients in monotherapy and polytherapy. For one-sample designs the measurements have to be performed either at the lower (0 hr) or at the upper (24 hr) bound of the admissible interval. Replications were often found for 2- and 3-point designs. Other sampling designs can lead to criterion close to the optimum and can therefore be performed without great loss of information. In contrast, we found that several designs lead to low values of the information criterion, which justifies the approach.

Absorption↗
PubMed1982

OPT: a package of computer programs for parameter optimisation in clinical pharmacokinetics.

1 OPT is a series of computer programs designed to assist dose optimisation for individual patients. It is based on Bayesian Statistical Theory and Maximum Likelihood Estimation. 2 OPT uses prior information on the distribution of population pharmacokinetic parameters and plasma drug concentration measurements to obtain the "most likely' set of parameters for the individual. 3 Complex dosage regimes and non-steady state conditions can be handled. 4 OPT is designed for use in a Clinical Pharmacokinetics Laboratory where informed interpretation of results is essential. 5 The drugs for which the system is currently available include theophylline, digoxin, lignocaine, disopyramide, gentamicin and phenytoin (steady state data only).

Administration, Oral↗
PubMed1993

A graphical user interface to facilitate patient-specific drug dosing.

This paper describes the development of a graphical user-interface (GUI) designed to facilitate the process of generating patient-specific drug doses using bayesian modelling software. The graphical user interface was developed in Visual Basic (Microsoft, Inc.) and runs under the Windows 3.1 (Microsoft, Inc.) operating system. Patient demographic data are stored in a relational database (Access, Microsoft, Inc.). The GUI and the database communicate via dynamic data exchange links. The largely object-oriented nature of the language allowed us to change the entire look and feel of the system with a few simple changes to the underlying code. Use of the relational database to store patient demographic information allows greater flexibility in searching for and displaying patient specific information. The GUI reduces the time required to enter data. The prototype has allowed us to experiment with different presentation methods, greatly improving the clinical acceptance of the dosing programs.

Computer Simulation↗
PubMed2005

An application of Bayesian statistical methods to adaptive radiotherapy.

In adaptive radiotherapy, measured patient-specific setup variations are used to modify the patient setup and treatment plan, potentially many times during the treatment course. To estimate the setup adjustments and re-plan the treatment, the measured data are usually processed using Kalman filtering or by computing running averages. We propose, as an alternative, the use of Bayesian statistical methods, which combine a population (prior) distribution of systematic and random setup errors with the measurements to determine a patient-specific (posterior) probability distribution. The posterior distribution can either be used directly in the re-planning of the treatment or in the generation of statistics needed for adjustments. Based on the assumption that day-to-day setup variations are independent and identically distributed Normal distributions, we can efficiently compute parameters of the posterior distribution from parameters of the prior distribution and statistics of the measurements. We illustrate a simple procedure to apply the method in practice to adaptive radiotherapy, allowing for multiple adjustments of treatment parameters during the course of treatment.

Algorithms↗
PubMed2001

Application of Bayesian inference to characterize risks associated with low doses of low-LET radiation.

Improved risk characterization for stochastic biological effects of low doses of low-LET radiation is important for protecting nuclear workers and the public from harm from radiation exposure. Here we present a Bayesian approach to characterize risks of stochastic effects from low doses of low-LET radiation. The stochastic effect considered is neoplastic transformation of cells because it relates closely to cancer induction. We have used a published model of neoplastic transformation called NEOTRANS1. It is based on two different classes of cellular sensitivity for asynchronous, exponentially growing populations (in vitro). One sensitivity class is the hypersensitive cell; the other is the resistant cell. NEOTRANS1 includes the effects of genomic damage accumulation, DNA repair during cell cycle arrest, and DNA misrepair (non-lethal repair errors). The model-associated differential equations are solved for conditions of in vitro irradiation at a fixed rate. Previously published solutions apply only to high dose rates and were incorrectly assumed to apply to only high-LET radiation. Solutions provided here apply to any fixed dose rate and to both high- and low-LET radiations. Markov chain Monte Carlo methods are used to carry out the Bayesian inference of the low-dose risk for neoplastic transformation of aneuploid C3H 10T1/2 cells for X-ray doses from 0 to 1000 mGy. We have assumed that for this low-dose range only the hypersensitive fraction of the cells are affected. Our results indicate that the initial slope of the risk vs dose relationship for neoplastic transformation is as follows: (1) directly proportional to the fraction, f1, of hypersensitive cells; (2) directly proportional to the radiosensitivity of the genomic target; and (3) inversely proportional to the rate at which hypersensitive cells with radiation-induced damage are committed to undergo correct repair of genomic damage. Further, our results indicate that very fast molecular events are associated with the commitment of cells to the correct repair pathway. Results also indicate a relatively large probability for misrepair that leads to genomic instability. Our results are consistent with the view that for very low doses, dose rate is not an important variable for characterizing low-LET radiation risks so long as age-related changes in sensitivity do not occur during irradiation.

Animals↗
PubMed2003

Clustering ensembles of neural network models.

We show that large ensembles of (neural network) models, obtained e.g. in bootstrapping or sampling from (Bayesian) probability distributions, can be effectively summarized by a relatively small number of representative models. In some cases this summary may even yield better function estimates. We present a method to find representative models through clustering based on the models' outputs on a data set. We apply the method on an ensemble of neural network models obtained from bootstrapping on the Boston housing data, and use the results to discuss bootstrapping in terms of bias and variance. A parallel application is the prediction of newspaper sales, where we learn a series of parallel tasks. The results indicate that it is not necessary to store all samples in the ensembles: a small number of representative models generally matches, or even surpasses, the performance of the full ensemble. The clustered representation of the ensemble obtained thus is much better suitable for qualitative analysis, and will be shown to yield new insights into the data.

Algorithms↗
PubMed2006

Enabling a powerful marine and offshore decision-support solution through Bayesian network technique.

A powerful practical solution is by far the most desired output when making decisions under the realm of uncertainty on any safety-critical marine or offshore units and their systems. With data and information typically being obtained incrementally, adopting Bayesian network (BN) is shown to realistically deal with the random uncertainties while at the same time making risk assessments easier to build and to check. A well-matched methodology is proposed to formalize the reasoning in which the focal mechanism of inference processing relies on the sound Bayes's rule/theorem that permits the logic. Expanding one or more influencing nodal parameters with decision and utility node(s) also yields an influence diagram (ID). BN and ID feasibility is shown in a marine evacuation scenario and that of authorized vessels to floating, production, storage, and offloading collision, developed via a commercial computer tool. Sensitivity analysis and validation of the produced results are also presented.

Accidents, Occupational↗
PubMed2006

How accurately can the parameters from a model of anisotropic 3He gas diffusion in lung acinar airways be estimated? Bayesian view.

In the framework of a recently proposed method for in vivo lung morphometry, acinar lung airways are considered as a set of randomly oriented cylinders covered by alveolar sleeves. Diffusion of (3)He in each airway is anisotropic and can be described by distinct longitudinal and transverse diffusion coefficients. This macroscopically isotropic but microscopically anisotropic model allows estimation of these diffusion coefficients from multi b-value MR experiments despite the airways being too small to be resolved by direct imaging. Herein a Bayesian approach is used for analyzing the uncertainties in the model parameter estimates. The approach allows evaluation of relative errors of the parameter estimates as functions of the "true" values of the parameters, the signal-to-noise ratio, the maximum b-value and the total number of b-values used in the experiment. For a given set of the "true" diffusion parameters, the uncertainty in the estimated diffusion coefficients has a minimum as a function of maximum b-value and total number of data points. Choosing the MR pulse sequence parameters corresponding to this minimum optimizes the diffusion MR experiment and gives the best possible estimates of the diffusion coefficients. The mathematical approach presented can be generalized for models containing arbitrary numbers of estimated parameters.

Anisotropy↗
PubMed1997

[Bayesian estimation of pharmacokinetic parameters of etoposide].

Studies of the relationships between the pharmacokinetics of a drug and its pharmacodynamics could significantly improve chemotherapy efficacy. However, despite their proven value, pharmacokinetic studies sometimes appear as cumbersome and difficult procedures. The bayesian approach associated with an optimal sampling time strategy (OST) allows the determination of the pharmacokinetic parameters of a drug with a smaller number of blood samples compared with that required by the classic maximum likelihood estimation (MLE). Therefore, the bayesian approach may lead to a less discomfort to the patients and less work for the medical staff. Such a method was developed to determine the individual pharmacokinetic parameters of etoposide (VP16). First, the statistical characteristics of the pharmacokinetic parameters were evaluated in 14 courses from 14 patients. Then, based on these results, a three-sample strategy was developed. Validation of this methodology was performed in 7 new patients and evaluated by computing bias and precision. The performance of the developed methodology shows that it could successfully be applied for the determination of VP16 pharmacokinetic parameters.

Adult↗
PubMed2000

Bayesian construction of geometrically based cortical thickness metrics.

This paper describes the construction of cortical metrics quantifying the probabilistic occurrence of gray matter, white matter, and cerebrospinal fluid compartments in their correlation to the geometry of the neocortex as measured in 0.5-1.0 mm magnetic resonance imagery. These cortical profiles represent the density of the tissue types as a function of distance to the cortical surface. These metrics are consistent when generated across multiple brains indicating a fundamental property of the neocortex. Methods are proposed for incorporating such metrics into automated Bayes segmentation.

Anthropometry↗
PubMed2004

Population pharmacokinetics of melphalan, infused over a 24-hour period, in patients with advanced malignancies.

PURPOSE: The objective of the present study was to characterize the population pharmacokinetics of melphalan infused over a 24-h period in patients with advanced malignancies. METHODS: Enrolled in the study were 64 patients (144 courses). The population pharmacokinetic analysis was performed using NONMEM through the graphical interface Visual-NM. Population characteristics were computed from an initial group of 43 patients (99 courses), and 21 additional patients (45 courses) were used for model validation. With the use of a one-compartment model, the influence of demographic and biological characteristics was examined. The basic parameters were total clearance (CL) and volume of distribution (V). The interoccasion variability was taken into account in the model. The drug exposure was estimated for each patient and correlated with markers of efficacy and toxicity. RESULTS: Data analysis was performed using a three-step approach. In step 2, a close relationship was found between creatinine clearance, gender and melphalan CL. The inclusion of this second stage model significantly improved the fit. Melphalan CL was higher in male patients (14.3+/-4.5 l/h per m2) than in female patients (12.3+/-4.5 l/h per m2). CL was also reduced somewhat in patients with decreased creatinine clearance. Large interindividual variability in pharmacokinetic parameters occurred (CL varied from 4.4 to 30.6 l/h per m2). The percentage intrapatient variability in clearance between courses was 25.4%. For determining melphalan AUC in clinical routine from one sample drawn at steady state, Bayesian methodology allowed a more accurate estimation of CL than the classical formula. Neutropenia and thrombocytopenia were the main haematological toxicities encountered; grade 4 was observed in 34 and 22 courses over a total of 144 courses, respectively. No significant relationship between AUC and haematological toxicity was found. In patients with prostatic cancer a weak relationship was observed between the decrease in PSA levels and AUC (P=0.0457), while in patients with ovarian cancer no relationship was found between AUC and CA125 levels. CONCLUSION: The population pharmacokinetic approach developed in this study should allow dosage to be individualized in order to decrease toxicity while maintaining good efficacy.

Adult↗
PubMed1998

Bayesian optimal design in population models for haematologic data.

We introduce a population model to design optimal apheresis schedules to collect blood stem cells from cancer patients. Blood stem cells are collected prior to the patient undergoing high-dose chemoradiotherapy and are returned after this treatment to enable reconstitution of the white blood cell components. Maximizing the number of cells collected in as few apheresis as possible is desirable. We use a longitudinal data model with random effects to describe profiles of individual patients. A hierarchical prior model introduces common mean profiles for patients undergoing different treatments. We find the optimal apheresis schedule for a new patient by minimizing an expected loss over the posterior predictive distribution of the patient's predicted CD34 profile. We implement estimation of the model and solution of the optimal design problem by a simulation approach, which allows us to accommodate arbitrary shapes for the profiles and realistic loss functions that include relative penalties for the number of scheduled stem cell collections and for collecting fewer than a specified target quantity of total collected stem cells.

Antigens, CD34↗
PubMed2005

Monte Carlo calibration of avalanches described as Coulomb fluid flows.

The idea that snow avalanches might behave as granular flows, and thus be described as Coulomb fluid flows, came up very early in the scientific study of avalanches, but it is not until recently that field evidence has been provided that demonstrates the reliability of this idea. This paper aims to specify the bulk frictional behaviour of snow avalanches by seeking a universal friction law. Since the bulk friction coefficient cannot be measured directly in the field, the friction coefficient must be calibrated by adjusting the model outputs to closely match the recorded data. Field data are readily available but are of poor quality and accuracy. We used Bayesian inference techniques to specify the model uncertainty relative to data uncertainty and to robustly and efficiently solve the inverse problem. A sample of 173 events taken from seven paths in the French Alps was used. The first analysis showed that the friction coefficient behaved as a random variable with a smooth and bell-shaped empirical distribution function. Evidence was provided that the friction coefficient varied with the avalanche volume, but any attempt to adjust a one-to-one relationship relating friction to volume produced residual errors that could be as large as three times the maximum uncertainty of field data. A tentative universal friction law is proposed: the friction coefficient is a random variable, the distribution of which can be approximated by a normal distribution with a volume-dependent mean.

Complex Mixtures↗
PubMed2006

Modeling the health care costs of geriatric inpatients.

This paper extends a method for modeling the survival of patients in hospitals to allow the expected cost to be estimated for the patients' accumulated duration of time in care. An extension of Bayesian network (BN) theory has previously been developed to model patients' survival time in hospitals with respect to the graphical and probabilistic representation of the interrelationships between the patients' clinical variables. Unlike previous BN techniques, this extended model can accommodate continuous times that are skewed in nature. This paper presents the theory behind such an approach and extends it by attaching a cost variable to the survival times, enabling the costing and efficient management of groups of patients in hospitals. An application of the model is illustrated by considering a group of 4260 patients admitted into the geriatric department of a U.K. hospital between 1994-1997. Results are derived for the distribution for their length of stay in the hospital and associated costs. The model's practical use is highlighted by illustrating how hospital managers could benefit using such a method for investigating the influence of future decisions and policy changes on the hospital's expenditure.

Computer Simulation↗
PubMed2006

Modelling multivariate outcomes in hierarchical data, with application to cluster randomised trials.

In the cluster randomised study design, the data collected have a hierarchical structure and often include multivariate outcomes. We present a flexible modelling strategy that permits several normally distributed outcomes to be analysed simultaneously, in which intervention effects as well as individual-level and cluster-level between-outcome correlations are estimated. This is implemented in a Bayesian framework which has several advantages over a classical approach, for example in providing credible intervals for functions of model parameters and in allowing informative priors for the intracluster correlation coefficients. In order to declare such informative prior distributions, and fit models in which the between-outcome covariance matrices are constrained, priors on parameters within the covariance matrices are required. Careful specification is necessary however, in order to maintain non-negative definiteness and symmetry between the different outcomes. We propose a novel solution in the case of three multivariate outcomes, and present a modified existing approach and novel alternative for four or more outcomes. The methods are applied to an example of a cluster randomised trial in the prevention of coronary heart disease. The modelling strategy presented would also be useful in other situations involving hierarchical multivariate outcomes.

Artificial Intelligence↗
PubMed2005

Bayesian models and Markov chain Monte Carlo methods for protein motifs with the secondary characteristics.

Statistical methods have been developed for finding local patterns, also called motifs, in multiple protein sequences. The aligned segments may imply functional or structural core regions. However, the existing methods often have difficulties in aligning multiple proteins when sequence residue identities are low (e.g., less than 25%). In this article, we develop a Bayesian model and Markov chain Monte Carlo (MCMC) methods for identifying subtle motifs in protein sequences. Specifically, a motif is defined not only in terms of specific sites characterized by amino acid frequency vectors, but also as a combination of secondary characteristics such as hydrophobicity, polarity, etc. Markov chain Monte Carlo methods are proposed to search for a motif pattern with high posterior probability under the new model. A special MCMC algorithm is developed, involving transitions between state spaces of different dimensions. The proposed methods were supported by a simulated study. It was then tested by two real datasets, including a group of helix-turn-helix proteins, and one set from the CATH Protein Structure Classification Database. Statistical comparisons showed that the new approach worked better than a typical Gibbs sampling approach which is based only on an amino acid model.

Amino Acid Motifs↗