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PubMed2002

A Bayesian network model for protein fold and remote homologue recognition.

MOTIVATION: The Bayesian network approach is a framework which combines graphical representation and probability theory, which includes, as a special case, hidden Markov models. Hidden Markov models trained on amino acid sequence or secondary structure data alone have been shown to have potential for addressing the problem of protein fold and superfamily classification. RESULTS: This paper describes a novel implementation of a Bayesian network which simultaneously learns amino acid sequence, secondary structure and residue accessibility for proteins of known three-dimensional structure. An awareness of the errors inherent in predicted secondary structure may be incorporated into the model by means of a confusion matrix. Training and validation data have been derived for a number of protein superfamilies from the Structural Classification of Proteins (SCOP) database. Cross validation results using posterior probability classification demonstrate that the Bayesian network performs better in classifying proteins of known structural superfamily than a hidden Markov model trained on amino acid sequences alone.

Amino Acid Sequence↗

PubMed1999

A hierarchical Bayesian model to predict the duration of immunity to Haemophilus influenzae type b.

A hierarchical Bayesian regression model is fitted to longitudinal data on Haemophilus influenzae type b (Hib) serum antibodies. To estimate the decline rate of the antibody concentration, the model accommodates the possibility of unobserved subclinical infections with Hib bacteria that cause increasing concentrations during the study period. The computations rely on Markov chain Monte Carlo simulation of the joint posterior distribution of the model parameters. The model is used to predict the duration of immunity to subclinical Hib infection and to a serious invasive Hib disease.

Antibodies, Bacterial↗

PubMed1980

Numerical evaluation of cytologic data. V. Bivariate distributions and the Bayesian decision Boundary.

The evaluation of cytologic data often involves the classification of observations into alternative categories (data sets). Plotting the elliptical contours of bivariate distributions provides immediate insight into the structure of data sets and their mutual relations. In this paper, the computation of tolerance ellipses and confidence ellipses for bivariate distribution is demonstrated, and the finding of a Bayesian decision boundary between two bivariate distributions is illustrated.

Bayes Theorem↗

PubMed1997

A population approach to initial dose selection.

Before a drug can be marketed, an initial dose must be established. Sheiner et al. argue that a population approach leads to the most informed and rational decision making. We discuss the choice of an initial dose from both a predictive and estimative viewpoint. Our criteria are based upon evaluating the probabilities that a patient from the specified population obtains a response that is at least of a specified size. We demonstrate the approach using a simulation study and compare estimation of population parameters and initial dose using Bayesian and likelihood-based methods.

Bayes Theorem↗

PubMed2001

Algebraic geometrical methods for hierarchical learning machines.

Hierarchical learning machines such as layered perceptrons, radial basis functions, Gaussian mixtures are non-identifiable learning machines, whose Fisher information matrices are not positive definite. This fact shows that conventional statistical asymptotic theory cannot be applied to neural network learning theory, for example either the Bayesian a posteriori probability distribution does not converge to the Gaussian distribution, or the generalization error is not in proportion to the number of parameters. The purpose of this paper is to overcome this problem and to clarify the relation between the learning curve of a hierarchical learning machine and the algebraic geometrical structure of the parameter space. We establish an algorithm to calculate the Bayesian stochastic complexity based on blowing-up technology in algebraic geometry and prove that the Bayesian generalization error of a hierarchical learning machine is smaller than that of a regular statistical model, even if the true distribution is not contained in the parametric model.

Algorithms↗

PubMed1997

Bayesian color constancy.

The problem of color constancy may be solved if we can recover the physical properties of illuminants and surfaces from photosensor responses. We consider this problem within the framework of Bayesian decision theory. First, we model the relation among illuminants, surfaces, and photosensor responses. Second, we construct prior distributions that describe the probability that particular illuminants and surfaces exist in the world. Given a set of photosensor responses, we can then use Bayes's rule to compute the posterior distribution for the illuminants and the surfaces in the scene. There are two widely used methods for obtaining a single best estimate from a posterior distribution. These are maximum a posteriori (MAP) and minimum mean-square-error (MMSE) estimation. We argue that neither is appropriate for perception problems. We describe a new estimator, which we call the maximum local mass (MLM) estimate, that integrates local probability density. The new method uses an optimality criterion that is appropriate for perception tasks: It finds the most probable approximately correct answer. For the case of low observation noise, we provide an efficient approximation. We develop the MLM estimator for the color-constancy problem in which flat matte surfaces are uniformly illuminated. In simulations we show that the MLM method performs better than the MAP estimator and better than a number of standard color-constancy algorithms. We note conditions under which even the optimal estimator produces poor estimates: when the spectral properties of the surfaces in the scene are biased.

Color Perception↗

PubMed1995

Adaptive control of therapeutic drug regimens relations between clinical situations: outcomes and simulations using nonlinear dynamic models.

With Bayesian modeling and adaptive control of drug dosage regimens, serum and peripheral drug concentrations can be predicted in clinical situations using linear pharmacokinetic compartmental models (PK). Recently, several pathophysiologic and pharmacodynamic nonlinear models (PD) have been developed. The present report illustrates both their utility and limits for the computation of effects in clinical situations in the setting of actual routine and acute patient care. Patients who received therapy with aminoglycosides or/and vancomycin were selected. For each patient, after estimation of individual pharmacokinetic parameters, the computed outputs of the linear compartmental pharmacokinetic model were used as inputs for 2 different a priori nonlinear dynamic models: 1) the EFFECT modeling program, using a Hill model, and 2) the BACTCIDE program, which is a combination of a simple growth model for the organism and a Hill effect model considering both the microorganism, the antibiotic, and the patient's minimal inhibitory concentration (MIC). The programs (1) and (2) can use as inputs the computed concentrations from any of three compartments: central, peripheral, or a spherical diffusion compartment to compute drug diffusion into endocardial vegetations or abscesses. The EFFECT program can be used alone for the evaluation of drug effects. The BACTCIDE program illustrates differences in activity between concentration-dependent and time-dependent antibiotics. Such nonlinear programs are very sensitive to the MIC values.

Aged↗

PubMed2002

Probabilistic Boolean Networks: a rule-based uncertainty model for gene regulatory networks.

MOTIVATION: Our goal is to construct a model for genetic regulatory networks such that the model class: (i) incorporates rule-based dependencies between genes; (ii) allows the systematic study of global network dynamics; (iii) is able to cope with uncertainty, both in the data and the model selection; and (iv) permits the quantification of the relative influence and sensitivity of genes in their interactions with other genes. RESULTS: We introduce Probabilistic Boolean Networks (PBN) that share the appealing rule-based properties of Boolean networks, but are robust in the face of uncertainty. We show how the dynamics of these networks can be studied in the probabilistic context of Markov chains, with standard Boolean networks being special cases. Then, we discuss the relationship between PBNs and Bayesian networks--a family of graphical models that explicitly represent probabilistic relationships between variables. We show how probabilistic dependencies between a gene and its parent genes, constituting the basic building blocks of Bayesian networks, can be obtained from PBNs. Finally, we present methods for quantifying the influence of genes on other genes, within the context of PBNs. Examples illustrating the above concepts are presented throughout the paper.

Cell Cycle↗

PubMed1992

Predictive performance of Bayesian and nonlinear least-squares regression programs for lidocaine.

The predictive performance of two computer programs for lidocaine dosing were evaluated. Two-compartment Bayesian and nonlinear least-squares regression programs were used in two groups of patients (15 acute arrhythmia patients and 14 chronic arrhythmia patients). Lidocaine was given as a 1.5 mg/kg bolus and a 2.8 mg/min infusion for 48 h. A second bolus (0.5 mg/kg) was given 10 min after the first bolus over 2 min. Serum samples of the patients receiving lidocaine were drawn at 2, 15, 30 min and 1, 2, and 4 h and were used in forecasting the serum concentrations at 6, 8, 12, and 48 h. Predictive performance was assessed by mean error and mean-squared error. The results (mean +/- 95% confidence intervals) demonstrated the Bayesian program predicted a significant (p less than 0.05) difference at 12 h between the two arrhythmia groups (acute 0.52 [-0.95; -0.09] and chronic 0.28 [0.12; 0.44]). The results also demonstrated the Bayesian method was significantly more precise compared to the nonlinear least-squares regression program at 8, 12, and 48 h for the acute group. While caution is warranted, this study demonstrated that the predictive performance by a two-compartment Bayesian model is more accurate in predicting future lidocaine serum concentrations than that by nonlinear least-squares regression.

Acute Disease↗

PubMed1994

Pharmacokinetics and dosage regimens of amikacin in intensive care unit patients.

The pharmacokinetics of amikacin have been studied in 40 intensive care unit (ICU) patients using a two-compartment model and the Bayesian estimation method implemented in the USC PC-PACK program of Jelliffe et al. The volume of the central compartment was significantly higher in these patients (0.36 l.kg-1) than in the reference population (0.20 l.kg-1). A method has been designed to compute dosage regimens in order to maintain a constant steady-state average plasma concentration of 8 mg.l-1 for repeated i.v. infusions. The regimen calculated for the 'average' ICU patient varies between 11 mg.kg-1 three times per day for the patient with normal renal function and 6 mg.kg-1 every 2 days for the anuric patient. This regimen is intended to begin amikacin therapy in an ICU patient, while the population pharmacokinetic parameters would allow the individualization of the regimen by means of the Bayesian method.

Amikacin↗

PubMed1994

Application of USC*PACK clinical programs to vancomycin in neutropenic patients.

The pharmacokinetics of vancomycin were studied in 10 neutropenic patients (4 male, 6 female) using the USC*PACK Clinical Programs. The experimental data was determined after the first administration of 1000 mg injected as a 1-h infusion. Eight blood samples were collected between 15 min and 11 h after the end of the infusion. Plasma vancomycin concentrations were measured by immunoassay procedure. Creatinine clearance and urine flow were also measured. Pharmacokinetic parameters were computed using a two-compartment model: Vc = 0.270665 +/- 0.161033 (l.kg-1); Kcp = 0.732927 +/- 0.464449 (h-1); Ks = 0.004952 +/- 0.00272 (min.ml-1.h-1); Kpc = 0.470243 +/- 0.194677 (h-1); Ki = 0.011675 +/- 0.004086 (h-1); Ke = 0.644415 +/- 0.239376 (h-1). When we compared this population to the general population of the program, Ke was increased. Elimination constant Ke was not correlated to either creatinine clearance or urine flow. Evaluation of the predictive performance of the Bayesian PC Program for adaptive control of vancomycin therapy in neutropenic patients is the next step of this study.

Adolescent↗

PubMed2001

Bayesian 2-D deconvolution: effect of using spatially invariant ultrasound point spread functions.

Observed ultrasound images are degraded representations of the-true tissue reflectance. The specular reflections at boundaries between regions of different tissue types are blurred, and the diffuse scattering within homogenous regions causes speckle because of the oscillating nature of the transmitted pulse. To reduce both blur and speckle, we have developed algorithms for the restoration of simulated and real ultrasound images based on Markov random field models and Bayesian statistical methods. The algorithm is summarized here, although a more detailed description can be found in our companion paper [1]. Because the point spread function (psf) is unknown, we investigate the effects of using incorrect frequencies and sizes for the model psf during the restoration process. First, we degrade the images either with a known simulated psf or a measured psf. Then, we use different psf shapes during restoration to study the robustness of the method. We found that small variations in the parameters characterizing the psf, less than +/- 25% change in frequency, width, or length, still yielded satisfactory results. When altering the psf more than this, the restorations were not acceptable. The restorations were particularly sensitive to large increases in the restoring psf frequency. Thus, 2-D Bayesian restoration using a fixed psf may yield acceptable results as long as the true variant psfs have not varied too much during imaging.

Bayes Theorem↗

PubMed2001

Bayesian regression methodology for estimating a receiver operating characteristic curve with two radiologic applications: prostate biopsy and spiral CT of ureteral stones.

RATIONALE AND OBJECTIVES: The authors evaluated two Bayesian regression models for receiver operating characteristic (ROC) curve analysis of continuous diagnostic outcome data with covariates. MATERIALS AND METHODS: Full and partial Bayesian regression models were applied to data from two studies (n = 180 and 100, respectively): (a) The diagnostic value of prostate-specific antigen (PSA) levels (outcome variable) for predicting disease after radical prostatectomy (gold standard) was evaluated for three risk groups (covariates) based on Gleason scores. (b) Spiral computed tomography was performed on patients with proved obstructing ureteral stones. The predictive value of stone size (outcome) was evaluated along with two treatment options (gold standard), as well as stone location (in or not in the ureterovesical junction [UVJ]) and patient age (covariates). Summary ROC measures were reported, and various prior distributions of the regression coefficients were investigated. RESULTS: (a) In the PSA example, the ROC areas under the full model were 0.667, 0.769, and 0.703, respectively, for the low-, intermediate-, and high-risk groups. Under the partial model, the area beneath the ROC curve was 0.706. (b) The ROC areas for patients with ureteral stones in the UVJ decreased dramatically with age but otherwise were close to that under the partial model (ie, 0.774). The prior distribution had greater influence in the second example. CONCLUSION: The diagnostic tests were accurate in both examples. PSA levels were most accurate for staging prostate cancer among intermediate-risk patients. Stone size was predictive of treatment option for all patients other than those 40 years or older and with a stone in the UVJ.

Adult↗

PubMed1999

Bayesian inference on biopolymer models.

MOTIVATION: Most existing bioinformatics methods are limited to making point estimates of one variable, e.g. the optimal alignment, with fixed input values for all other variables, e.g. gap penalties and scoring matrices. While the requirement to specify parameters remains one of the more vexing issues in bioinformatics, it is a reflection of a larger issue: the need to broaden the view on statistical inference in bioinformatics. RESULTS: The assignment of probabilities for all possible values of all unknown variables in a problem in the form of a posterior distribution is the goal of Bayesian inference. Here we show how this goal can be achieved for most bioinformatics methods that use dynamic programming. Specifically, a tutorial style description of a Bayesian inference procedure for segmentation of a sequence based on the heterogeneity in its composition is given. In addition, full Bayesian inference algorithms for sequence alignment are described. AVAILABILITY: Software and a set of transparencies for a tutorial describing these ideas are available at http://www.wadsworth.org/res&res/bioinfo/

Bayes Theorem↗

PubMed1995

Bayesian estimation of p-aminohippurate clearance by a limited sampling strategy.

This study describes a methodology to calculated p-aminohippurate (PAH) clearance (CL) and volume of distribution (V) with both the population parameters and one or two samples taken during the disposition and the elimination phase after a single intravenous infusion. The computer program P-PHARM was used, and a log-normal distribution and a heteroscedastic residual error distribution were assumed. Ninety-six patients with and without renal insufficiency were available for analysis, and a two-compartment model was used for data modeling. Population parameters were evaluated for 70 patients (mean number of observed concentration per individual, 6) by a three-step approach. In step 1, the computer program was used to estimate the average pharmacokinetic parameters without taking into account the demographic and/or biological factors. In step 2, the relationship between the posterior individual estimates and the covariables was investigated with multiple linear stepwise algorithm. In step 3, the population parameters were re-estimated considering the relationship with the covariables. From the regression performed in step 2, the following covariables were included: serum creatinine, body surface area, and body weight. The population averages of CL and V were 30.7 +/- 2.36 L/h and 10.6 +/- 1.29 L, respectively. To evaluate the predictive performance of the population parameters, the remaining 26 patients were used. The population parameters combined with one or two individual PAH plasma concentrations led to a bayesian estimation of individual CL and V. This estimation was compared with the classical procedure of parameter estimation (individual fitting from multiple blood samples).(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗

PubMed2002

Finding and fixing systems weaknesses: probabilistic methods and applications of engineering risk analysis.

Methods of engineering risk analysis are based on a functional analysis of systems and on the probabilities (generally Bayesian) of the events and random variables that affect their performances. These methods allow identification of a system's failure modes, computation of its probability of failure or performance deterioration per time unit or operation, and of the contribution of each component to the probabilities and consequences of failures. The model has been extended to include the human decisions and actions that affect components' performances, and the management factors that affect behaviors and can thus be root causes of system failures. By computing the risk with and without proposed measures, one can then set priorities among different risk management options under resource constraints. In this article, I present briefly the engineering risk analysis method, then several illustrations of risk computations that can be used to identify a system's weaknesses and the most cost-effective way to fix them. The first example concerns the heat shield of the space shuttle orbiter and shows the relative risk contribution of the tiles in different areas of the orbiter's surface. The second application is to patient risk in anesthesia and demonstrates how the engineering risk analysis method can be used in the medical domain to rank the benefits of risk mitigation measures, in that case, mostly organizational. The third application is a model of seismic risk analysis and mitigation, with application to the San Francisco Bay area for the assessment of the costs and benefits of different seismic provisions of building codes. In all three cases, some aspects of the results were not intuitively obvious. The probabilistic risk analysis (PRA) method allowed identifying system weaknesses and the most cost-effective way to fix them.

Journal Article↗

PubMed1990

Classification of audiograms by sequential testing using a dynamic Bayesian procedure.

A new method for estimating audiograms using behavioral responses is presented. The method is based upon a modification of the Bayesian probability formula in which an outcome is predicted from a static set of events. In the new method, classification of audiograms by sequential testing (CAST), the probabilities of occurrence of audiogram patterns are dynamically updated according to the outcome of each test trial. Computer simulation using an infant response model suggests that the procedure is efficient, sensitive, and specific.

Algorithms↗

PubMed2025

The signed two-space proximity model for learning representations in protein-protein interaction networks.

MOTIVATION: Accurately predicting complex protein-protein interactions (PPIs) is crucial for decoding biological processes, from cellular functioning to disease mechanisms. However, experimental methods for determining PPIs are computationally expensive. Thus, attention has been recently drawn to machine learning approaches. Furthermore, insufficient effort has been made toward analyzing signed PPI networks, which capture both activating (positive) and inhibitory (negative) interactions. To accurately represent biological relationships, we present the Signed Two-Space Proximity Model (S2-SPM) for signed PPI networks, which explicitly incorporates both types of interactions, reflecting the complex regulatory mechanisms within biological systems. This is achieved by leveraging two independent latent spaces to differentiate between positive and negative interactions while representing protein similarity through proximity in these spaces. Our approach also enables the identification of archetypes representing extreme protein profiles. RESULTS: S2-SPM's superior performance in predicting the presence and sign of interactions in SPPI networks is demonstrated in link prediction tasks against relevant baseline methods. Additionally, the biological prevalence of the identified archetypes is confirmed by an enrichment analysis of Gene Ontology (GO) terms, which reveals that distinct biological tasks are associated with archetypal groups formed by both interactions. This study is also validated regarding statistical significance and sensitivity analysis, providing insights into the functional roles of different interaction types. Finally, the robustness and consistency of the extracted archetype structures are confirmed using the Bayesian Normalized Mutual Information (BNMI) metric, proving the model's reliability in capturing meaningful SPPI patterns. AVAILABILITY: S2-SPM is implemented and freely available under the MIT license at https://github.com/Nicknakis/S2SPM.

Protein Interaction Mapping↗