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PubMed2003

Predicting interresidue contacts using templates and pathways.

We present a novel method, HMMSTR-CM, for protein contact map predictions. Contact potentials were calculated by using HMMSTR, a hidden Markov model for local sequence structure correlations. Targets were aligned against protein templates using a Bayesian method, and contact maps were generated by using these alignments. Contact potentials then were used to evaluate these templates. An ab initio method based on the target contact potentials using a rule-based strategy to model the protein-folding pathway was developed. Fold recognition and ab initio methods were combined to produce accurate, protein-like contact maps. Pathways sometimes led to an unambiguous prediction of topology, even without using templates. The results on CASP5 targets are discussed. Also included is a brief update on the quality of fully automated ab initio predictions using the I-sites server.

Algorithms↗
PubMed2003

Joint Bayesian estimation of mutation location and age using linkage disequilibrium.

Associations between disease and marker alleles on chromosomes in populations can arise as a consequence of historical forces such as mutation, selection and genetic drift, and is referred to as "linkage disequilibrium" (LD). LD can be used to estimate the map position of a disease mutation relative to a set of linked markers, as well as to estimate other parameters of interest, such as mutation age. Parametric methods for estimating the location of a disease mutation using marker linkage disequilibrium in a sample of normal and affected individuals require a detailed knowledge of population demography, and in particular require users to specify the postulated age of a mutation and past population growth rates. A new Bayesian method is presented for jointly estimating the position of a disease mutation and its age. The method is illustrated using haplotype data for the cystic fibrosis deltaF508 mutation in Europe and the DTD mutation in Finland. It is shown that, for these datasets, the posterior probability distribution of disease mutation location is insensitive to the population growth rate when the model is averaged over possible mutation ages using a prior probability distribution for the mutation age based on the population frequency of the disease mutation. Fewer assumptions are therefore needed for parametric LD mapping.

Bayes Theorem↗
PubMedDate not supplied

Predicting survival in malignant skin melanoma using Bayesian networks automatically induced by genetic algorithms. An empirical comparison between different approaches.

In this work we introduce a methodology based on genetic algorithms for the automatic induction of Bayesian networks from a file containing cases and variables related to the problem. The structure is learned by applying three different methods: The Cooper and Herskovits metric for a general Bayesian network, the Markov blanket approach and the relaxed Markov blanket method. The methodologies are applied to the problem of predicting survival of people after 1, 3 and 5 years of being diagnosed as having malignant skin melanoma. The accuracy of the obtained models, measured in terms of the percentage of well-classified subjects, is compared to that obtained by the so-called Naive-Bayes. In the four approaches, the estimation of the model accuracy is obtained from the 10-fold cross-validation method.

Algorithms↗
PubMed2006

A sequential injection electronic tongue employing the transient response from potentiometric sensors for anion multidetermination.

Intelligent and automatic systems based on arrays of non-specific-response chemical sensors were recently developed in our laboratory. For multidetermination applications, the normal choice is an array of potentiometric sensors to generate the signal, and an artificial neural network (ANN) correctly trained to obtain the calibration model. As a great amount of information is required for the proper modelling, we proposed its automated generation by using the sequential injection analysis (SIA) technique. First signals used were steady-state: the equilibrium signal after a step-change in concentration. We have now adapted our procedures to record the transient response corresponding to a sample step. The novelty in this approach is therefore the use of the dynamic components of the signal in order to better discriminate or differentiate a sample. In the developed electronic tongue systems, detection is carried out by using a sensor array formed by five potentiometric sensors based on PVC membranes. For the developed application we employed two different chloride-selective sensors, two nitrate-selective sensors and one generic response sensor. As the amount of raw data (fivefold recordings corresponding to the five sensors) is excessive for an ANN, some feature extraction step prior to the modelling was needed. In order to attain substantial data reduction and noise filtering, the data obtained were fitted with orthonormal Legendre polynomials. In this case, a third-degree Legendre polynomial was shown to be sufficient to fit the data. The coefficients of these polynomials were the input information fed into the ANN used to model the concentrations of the determined species (Cl-, NO3- and HCO3-). Best results were obtained by using a backpropagation neural network trained with the Bayesian regularisation algorithm; the net had a single hidden layer containing three neurons with the tansig transfer function. The results obtained from the time-dependent response were compared with those obtained from steady-state conditions, showing the former superior performance. Finally, the method was applied for determining anions in synthetic samples and real water samples, where a satisfactory comparison was also achieved.

Algorithms↗
PubMedDate not supplied

Optimisation of the predictive ability of artificial neural network (ANN) models: a comparison of three ANN programs and four classes of training algorithm.

The purpose of this study was to determine whether artificial neural network (ANN) programs implementing different backpropagation algorithms and default settings are capable of generating equivalent highly predictive models. Three ANN packages were used: INForm, CAD/Chem and MATLAB. Twenty variants of gradient descent, conjugate gradient, quasi-Newton and Bayesian regularization algorithms were used to train networks containing a single hidden layer of 3-12 nodes. All INForm and CAD/Chem models trained satisfactorily for tensile strength, disintegration time and percentage dissolution at 15, 30, 45 and 60 min. Similarly, acceptable training was obtained for MATLAB models using Bayesian regularization. Training of MATLAB models with other algorithms was erratic. This effect was attributed to a tendency for the MATLAB implementation of the algorithms to attenuate training in local minima of the error surface. Predictive models for tablet capping and friability could not be generated. The most predictive models from each ANN package varied with respect to the optimum network architecture and training algorithm. No significant differences were found in the predictive ability of these models. It is concluded that comparable models are obtainable from different ANN programs provided that both the network architecture and training algorithm are optimised. A broad strategy for optimisation of the predictive ability of an ANN model is proposed.

Algorithms↗
PubMed2006

Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical gaussian models and bayesian networks.

MOTIVATION: An important problem in systems biology is the inference of biochemical pathways and regulatory networks from postgenomic data. Various reverse engineering methods have been proposed in the literature, and it is important to understand their relative merits and shortcomings. In the present paper, we compare the accuracy of reconstructing gene regulatory networks with three different modelling and inference paradigms: (1) Relevance networks (RNs): pairwise association scores independent of the remaining network; (2) graphical Gaussian models (GGMs): undirected graphical models with constraint-based inference, and (3) Bayesian networks (BNs): directed graphical models with score-based inference. The evaluation is carried out on the Raf pathway, a cellular signalling network describing the interaction of 11 phosphorylated proteins and phospholipids in human immune system cells. We use both laboratory data from cytometry experiments as well as data simulated from the gold-standard network. We also compare passive observations with active interventions. RESULTS: On Gaussian observational data, BNs and GGMs were found to outperform RNs. The difference in performance was not significant for the non-linear simulated data and the cytoflow data, though. Also, we did not observe a significant difference between BNs and GGMs on observational data in general. However, for interventional data, BNs outperform GGMs and RNs, especially when taking the edge directions rather than just the skeletons of the graphs into account. This suggests that the higher computational costs of inference with BNs over GGMs and RNs are not justified when using only passive observations, but that active interventions in the form of gene knockouts and over-expressions are required to exploit the full potential of BNs. AVAILABILITY: Data, software and supplementary material are available from http://www.bioss.sari.ac.uk/staff/adriano/research.html

Algorithms↗
PubMed2004

Dose-finding based on efficacy-toxicity trade-offs.

We present an adaptive Bayesian method for dose-finding in phase I/II clinical trials based on trade-offs between the probabilities of treatment efficacy and toxicity. The method accommodates either trinary or bivariate binary outcomes, as well as efficacy probabilities that possibly are nonmonotone in dose. Doses are selected for successive patient cohorts based on a set of efficacy-toxicity trade-off contours that partition the two-dimensional outcome probability domain. Priors are established by solving for hyperparameters that optimize the fit of the model to elicited mean outcome probabilities. For trinary outcomes, the new algorithm is compared to the method of Thall and Russell (1998, Biometrics 54, 251-264) by application to a trial of rapid treatment for ischemic stroke. The bivariate binary outcome case is illustrated by a trial of graft-versus-host disease treatment in allogeneic bone marrow transplantation. Computer simulations show that, under a wide rage of dose-outcome scenarios, the new method has high probabilities of making correct decisions and treats most patients at doses with desirable efficacy-toxicity trade-offs.

Abciximab↗
PubMed2006

A multiscale method for disease mapping in spatial epidemiology.

The effects of spatial scale in disease mapping are well-recognized, in that the information conveyed by such maps varies with scale. Here we provide an inferential framework, in the context of tract count data, for describing the distribution of relative risk simultaneously across a hierarchy of multiple scales. In particular, we offer a multiscale extension of the canonical standardized mortality ratio (SMR), consisting of Bayesian posterior-based strategies for both estimation and characterization of uncertainty. As a result, a hierarchy of informative disease and confidence maps can be produced, without the need to first try to identify a single appropriate scale of analysis. We explore the behaviour of the proposed methodology in a small simulation study, and we illustrate its usage through an application to data on gastric cancer in Tuscany.

Bayes Theorem↗
PubMed2005

Proceedings of the SMBE Tri-National Young Investigators' Workshop 2005. Improved consensus network techniques for genome-scale phylogeny.

Although recent studies indicate that estimating phylogenies from alignments of concatenated genes greatly reduces the stochastic error, the potential for systematic error still remains, heightening the need for reliable methods to analyze multigene data sets. Consensus methods provide an alternative, more inclusive, approach for analyzing collections of trees arising from multiple genes. We extend a previously described consensus network method for genome-scale phylogeny (Holland, B. R., K. T. Huber, V. Moulton, and P. J. Lockhart. 2004. Using consensus networks to visualize contradictory evidence for species phylogeny. Mol. Biol. Evol. 21:1459-1461) to incorporate additional information. This additional information could come from bootstrap analysis, Bayesian analysis, or various methods to find confidence sets of trees. The new methods can be extended to include edge weights representing genetic distance. We use three data sets to illustrate the approach: 61 genes from 14 angiosperm taxa and one gymnosperm, 106 genes from eight yeast taxa, and 46 members of a gene family from 15 vertebrate taxa.

Animals↗
PubMed2006

Bayesian model averaging of naive Bayes for clustering.

This paper considers a Bayesian model-averaging (MA) approach to learn an unsupervised naive Bayes classification model. By using the expectation model-averaging (EMA) algorithm, which is proposed in this paper, a unique naive Bayes model that approximates an MA over selective naive Bayes structures is obtained. This algorithm allows to obtain the parameters for the approximate MA clustering model in the same time complexity needed to learn the maximum-likelihood model with the expectation-maximization algorithm. On the other hand, the proposed method can also be regarded as an approach to an unsupervised feature subset selection due to the fact that the model obtained by the EMA algorithm incorporates information on how dependent every predictive variable is on the cluster variable.

Algorithms↗
PubMed2005

Incorporating organ movements in inverse planning: assessing dose uncertainties by Bayesian inference.

We present a method to calculate dose uncertainties due to inter-fraction organ movements in fractionated radiotherapy, i.e. in addition to the expectation value of the dose distribution a variance distribution is calculated. To calculate the expectation value of the dose distribution in the presence of organ movements, one estimates a probability distribution of possible patient geometries. The respective variance of the expected dose distribution arises for two reasons: first, the patient is irradiated with a finite number of fractions only and second, the probability distribution of patient geometries has to be estimated from a small number of images and is therefore not exactly known. To quantify the total dose variance, we propose a method that is based on the principle of Bayesian inference. The method is of particular interest when organ motion is incorporated in inverse IMRT planning by means of inverse planning performed on a probability distribution of patient geometries. In order to make this a robust approach, it turns out that the dose variance should be considered (and minimized) in the optimization process. As an application of the presented concept of Bayesian inference, we compare three approaches to inverse planning based on probability distributions that account for an increasing degree of uncertainty. The Bayes theorem further provides a concept to interpolate between patient specific data and population-based knowledge on organ motion which is relevant since the number of CT images of a patient is typically small.

Algorithms↗
PubMed2005

Children can solve Bayesian problems: the role of representation in mental computation.

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth, fifth, and sixth graders in terms of probabilities, their ability to estimate the Bayesian posterior probability was zero. Yet when the same information was presented in natural frequencies, Bayesian reasoning showed a steady increase from fourth to sixth grade, reaching an average level of 19, 39, and 53%, respectively, in two studies. Sixth graders' performance with natural frequencies matched the performance of adults with probabilities. But this general increase was accompanied by striking individual differences. More than half of the sixth graders solved most or all problems, whereas one third could not solve a single one. An analysis of the children's responses provides evidence for the use of three non-Bayesian strategies. These follow an overlapping wave model of development and continue to be observed in the minds of adults. More so than adults' probabilistic reasoning, children's reasoning depends on a proper representation of information.

Adult↗
PubMed2003

Estimating gene networks from gene expression data by combining Bayesian network model with promoter element detection.

We present a statistical method for estimating gene networks and detecting promoter elements simultaneously. When estimating a network from gene expression data alone, a common problem is that the number of microarrays is limited compared to the number of variables in the network model, making accurate estimation a difficult task. Our method overcomes this problem by integrating the microarray gene expression data and the DNA sequence information into a Bayesian network model. The basic idea of our method is that, if a parent gene is a transcription factor, its children may share a consensus motif in their promoter regions of the DNA sequences. Our method detects consensus motifs based on the structure of the estimated network, then re-estimates the network using the result of the motif detection. We continue this iteration until the network becomes stable. To show the effectiveness of our method, we conducted Monte Carlo simulations and applied our method to Saccharomyces cerevisiae data as a real application.

Bayes Theorem↗
PubMed1997

An up-down Bayesian, defibrillation efficacy estimator.

In both the clinic and the laboratory, efficacy estimators are used to estimate the shock strength required to achieve a given defibrillation success rate. In the clinic, efficacy estimators are used to estimate highly effective doses (i.e., the shock strength that defibrillates 95% of the time), in order to choose the setting for an ICD. Efficacy estimators are used in the laboratory to compare defibrillation techniques and configurations. Current efficacy estimators are inadequate because they are either difficult to use, can only estimate the shock strength that defibrillates 50% of the time, or do not yield desirable accuracy (low RMS error). This article presents a Bayesian estimation technique that forces the difference between successive test shock strengths (step-size) to be a fixed value after each measurement. Constraining the difference dramatically reduces the computational complexity of the up-down Bayesian method. This new, up-down Bayesian protocol can be used with up to 15 measurements to estimate the shock strength for any given success rate. Simulations show that the added constraint (fixed step-size) only slightly increases the rms error, as compared to the optimum Bayesian protocol. Our simulations also show that protocols can be generated for shock strengths rounded to the nearest 1, 10, or 50 V. without a great increase in RMS error. Experimental results from a subset of all the simulations are reported from six animals, showing a < -2.4% difference between the simulated and measured errors.

Animals↗
PubMed2006

A future for models and data in environmental science.

Together, graphical models and the Bayesian paradigm provide powerful new tools that promise to change the way that environmental science is done. The capacity to merge theory with mechanistic understanding and empirical evidence, to assimilate diverse sources of information and to accommodate complexity will transform the collection and interpretation of data. As we discuss here, we specifically expect a shift from a focus on simple experiments with inflexible design and selection among models that embrace parts of processes to a synthesis of integrated process models. With this potential come new challenges, including some that are specific and technical and others that are general and will involve reexamination of the role of inference and prediction.

Animals↗
PubMedDate not supplied

Bias reduction in skewed binary classification with Bayesian neural networks.

The Bayesian evidence framework has become a standard of good practice for neural network estimation of class conditional probabilities. In this approach the conditional probability is marginalised over the distribution of network weights, which is usually approximated by an analytical expression that moderates the network output towards the midrange. In this paper, it is shown that the network calibration is considerably improved by marginalising to the prior distribution. Moreover, marginalisation to the midrange can seriously bias the estimates of the conditional probabilities calculated from the evidence framework. This is especially the case in the modelling of censored data.

Bayes Theorem↗
PubMed2001

Properties of phylogenetic trees generated by Yule-type speciation models.

We investigate some discrete structural properties of evolutionary trees generated under simple null models of speciation, such as the Yule model. These models have been used as priors in Bayesian approaches to phylogenetic analysis, and also to test hypotheses concerning the speciation process. In this paper we describe new results for three properties of trees generated under such models. Firstly, for a rooted tree generated by the Yule model we describe the probability distribution on the depth (number of edges from the root) of the most recent common ancestor of a random subset of k species. Next we show that, for trees generated under the Yule model, the approximate position of the root can be estimated from the associated unrooted tree, even for trees with a large number of leaves. Finally, we analyse a biologically motivated extension of the Yule model and describe its distribution on tree shapes when speciation occurs in rapid bursts.

Animals↗
PubMed2006

Dragon Promoter Mapper (DPM): a Bayesian framework for modelling promoter structures.

UNLABELLED: Dragon Promoter Mapper (DPM) is a tool to model promoter structure of co-regulated genes using methodology of Bayesian networks. DPM exploits an exhaustive set of motif features (such as motif, its strand, the order of motif occurrence and mutual distance between the adjacent motifs) and generates models from the target promoter sequences, which may be used to (1) detect regions in a genomic sequence which are similar to the target promoters or (2) to classify other promoters as similar or not to the target promoter group. DPM can also be used for modelling of enhancers and silencers. AVAILABILITY: http://defiant.i2r.a-star.edu.sg/projects/BayesPromoter/ CONTACT: vlad@sanbi.ac.za SUPPLEMENTARY INFORMATION: Manual for using DPM web server is provided at http://defiant.i2r.a-star.edu.sg/projects/BayesPromoter/html/manual/manual.htm.

Algorithms↗