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PubMed1998

Issues in Bayesian Analysis of Neural Network Models

Stemming from work by Buntine and Weigend (1991) and MacKay (1992), there is a growing interest in Bayesian analysis of neural network models. Although conceptually simple, this problem is computationally involved. We suggest a very efficient Markov chain Monte Carlo scheme for inference and prediction with fixed&hyphenarchitecture feedforward neural networks. The scheme is then extended to the variable architecture case, providing a data&hyphendriven procedure to identify sensible architectures.

Journal Article↗
PubMed2003

Numerical non-identifiability regions of the minimal model of glucose kinetics: superiority of Bayesian estimation.

The so-called minimal model (MM) of glucose kinetics is widely employed to estimate insulin sensitivity (S(I)) both in clinical and epidemiological studies. Usually, MM is numerically identified by resorting to Fisherian parameter estimation techniques, such as maximum likelihood (ML). However, unsatisfactory parameter estimates are sometimes obtained, e.g. S(I) estimates virtually zero or unrealistically high and affected by very large uncertainty, making the practical use of MM difficult. The first result of this paper concerns the mathematical demonstration that these estimation difficulties are inherent to MM structure which can expose S(I) estimation to the risk of numerical non-identifiability. The second result is based on simulation studies and shows that Bayesian parameter estimation techniques are less sensitive, in terms of both accuracy and precision, than the Fisherian ones with respect to these difficulties. In conclusion, Bayesian parameter estimation can successfully deal with difficulties of MM identification inherently due to its structure.

Bayes Theorem↗
PubMed2006

Bayesian analyses of multiple epistatic QTL models for body weight and body composition in mice.

To comprehensively investigate the genetic architecture of growth and obesity, we performed Bayesian analyses of multiple epistatic quantitative trait locus (QTL) models for body weights at five ages (12 days, 3, 6, 9 and 12 weeks) and body composition traits (weights of two fat pads and five organs) in mice produced from a cross of the F1 between M16i (selected for rapid growth rate) and CAST/Ei (wild-derived strain of small and lean mice) back to M16i. Bayesian model selection revealed a temporally regulated network of multiple QTL for body weight, involving both strong main effects and epistatic effects. No QTL had strong support for both early and late growth, although overlapping combinations of main and epistatic effects were observed at adjacent ages. Most main effects and epistatic interactions had an opposite effect on early and late growth. The contribution of epistasis was more pronounced for body weights at older ages. Body composition traits were also influenced by an interacting network of multiple QTLs. Several main and epistatic effects were shared by the body composition and body weight traits, suggesting that pleiotropy plays an important role in growth and obesity.

Animals↗
PubMed2002

Identifiability of parameters in MCMC Bayesian inference of phylogeny.

Methods for Bayesian inference of phylogeny using DNA sequences based on Markov chain Monte Carlo (MCMC) techniques allow the incorporation of arbitrarily complex models of the DNA substitution process, and other aspects of evolution. This has increased the realism of models, potentially improving the accuracy of the methods, and is largely responsible for their recent popularity. Another consequence of the increased complexity of models in Bayesian phylogenetics is that these models have, in several cases, become overparameterized. In such cases, some parameters of the model are not identifiable; different combinations of nonidentifiable parameters lead to the same likelihood, making it impossible to decide among the potential parameter values based on the data. Overparameterized models can also slow the rate of convergence of MCMC algorithms due to large negative correlations among parameters in the posterior probability distribution. Functions of parameters can sometimes be found, in overparameterized models, that are identifiable, and inferences based on these functions are legitimate. Examples are presented of overparameterized models that have been proposed in the context of several Bayesian methods for inferring the relative ages of nodes in a phylogeny when the substitution rate evolves over time.

Algorithms↗
PubMed2005

Surrogate docking: structure-based virtual screening at high throughput speed.

Structure-based screening using fully flexible docking is still too slow for large molecular libraries. High quality docking of a million molecule library can take days even on a cluster with hundreds of CPUs. This performance issue prohibits the use of fully flexible docking in the design of large combinatorial libraries. We have developed a fast structure-based screening method, which utilizes docking of a limited number of compounds to build a 2D QSAR model used to rapidly score the rest of the database. We compare here a model based on radial basis functions and a Bayesian categorization model. The number of compounds that need to be actually docked depends on the number of docking hits found. In our case studies reasonable quality models are built after docking of the number of molecules containing approximately 50 docking hits. The rest of the library is screened by the QSAR model. Optionally a fraction of the QSAR-prioritized library can be docked in order to find the true docking hits. The quality of the model only depends on the training set size - not on the size of the library to be screened. Therefore, for larger libraries the method yields higher gain in speed no change in performance. Prioritizing a large library with these models provides a significant enrichment with docking hits: it attains the values of approximately 13 and approximately 35 at the beginning of the score-sorted libraries in our two case studies: screening of the NCI collection and a combinatorial libraries on CDK2 kinase structure. With such enrichments, only a fraction of the database must actually be docked to find many of the true hits. The throughput of the method allows its use in screening of large compound collections and in the design of large combinatorial libraries. The strategy proposed has an important effect on efficiency but does not affect retrieval of actives, the latter being determined by the quality of the docking method itself.

Bayes Theorem↗
PubMed2005

Phylogeny of Arthropoda inferred from mitochondrial sequences: strategies for limiting the misleading effects of multiple changes in pattern and rates of substitution.

In this study, mitochondrial sequences were used to investigate the relationships among the major lineages of Arthropoda. The data matrix used for the analyses includes 84 taxa and 3918 nucleotides representing six mitochondrial protein-coding genes (atp6 and 8, cox1-3, and nad2). The analyses of nucleotide composition show that a reverse strand-bias, i.e., characterized by an excess of T relative to A nucleotides and of G relative to C nucleotides, was independently acquired in six different lineages of Arthropoda: (1) the honeybee mite (Varroa), (2) Opisthothelae spiders (Argiope, Habronattus, and Ornithoctonus), (3) scorpions (Euscorpius and Mesobuthus), (4) Hutchinsoniella (Cephalocarid), (5) Tigriopus (Copepod), and (6) whiteflies (Aleurodicus and Trialeurodes). Phylogenetic analyses confirm that these convergences in nucleotide composition can be particularly misleading for tree reconstruction, as unrelated taxa with reverse strand-bias tend to group together in MP, ML, and Bayesian analyses. However, the use of a specific model for minimizing effects of the bias, the "Neutral Transition Exclusion" (NTE) model, allows Bayesian analyses to rediscover most of the higher taxa of Arthropoda. Furthermore, the analyses of branch lengths suggest that three main factors explain accelerated rates of substitution: (1) genomic rearrangements, including duplication of the control region and gene translocation, (2) parasitic lifestyle, and (3) small body size. The comparisons of Bayesian Bootstrap percentages show that the support for many nodes increases when taxa with long branches are excluded from the analyses. It is therefore recommended to select taxa and genes of the mitochondrial genome for inferring phylogenetic relationships among arthropod lineages. The phylogenetic analyses support the existence of a major dichotomy within Arthropoda, separating Pancrustacea and Paradoxopoda. Basal relationships between Pancrustacean lineages are not robust, and the question of Hexapod monophyly or polyphyly cannot be answered with the available mitochondrial sequences. Within Paradoxopoda, Chelicerata and Myriapoda are each found to be monophyletic, and Endeis (Pycnogonida) is, surprisingly, associated with Acari.

Animals↗
PubMed1996

Validity of Bayesian forecasting programme in therapeutic drug monitoring of vancomycin in a surgical intensive care unit: a prospective evaluation.

The objectives of this study were: (a) to assess the predictive performance of a 2-compartment Bayesian vancomycin forecasting programme in critically ill patients in the surgical intensive care unit, and (b) to show the applicability of the programme, which is based on parameters derived from Western population, in our local Asian population. Twenty critically ill patients were enrolled into the study programme. All patients received multiple-dose vancomycin for infections due to methicillin-resistant staphylococcus aureus (MRSA). The patients dosage regimen were optimised by entering a set of peak and trough vancomycin serum levels into a clinical computer program (MB; USC*PACK PC collection; University of Southern California, USA) by utilising a 2-compartment Bayesian population model. The correlation between observed and predicted serum peak and trough concentrations were evaluated for both the non-fitted and fitted models by linear regression analysis. There was a significant correlation between observed and predicted concentrations using the fitted model (r = 0.97, P < 0.05). There was no significant correlation of these concentrations in the non-fitted model (r = 0.8). This study shows that the Bayesian programme is able to accurately predict future vancomycin concentrations in our local Asian population. It is possible to optimise patients dosage regimens with the knowledge of two concentrations of vancomycin in order to achieve targeted therapeutic goals.

Aged↗
PubMedDate not supplied

Bayesian communication: a clinically significant paradigm for electronic publication.

OBJECTIVE: To develop a model for Bayesian communication to enable readers to make reported data more relevant by including their prior knowledge and values. BACKGROUND: To change their practice, clinicians need good evidence, yet they also need to make new technology applicable to their local knowledge and circumstances. Availability of the Web has the potential for greatly affecting the scientific communication process between research and clinician. Going beyond format changes and hyperlinking, Bayesian communication enables readers to make reported data more relevant by including their prior knowledge and values. This paper addresses the needs and implications for Bayesian communication. FORMULATION: Literature review and development of specifications from readers', authors', publishers', and computers' perspectives consistent with formal requirements for Bayesian reasoning. RESULTS: Seventeen specifications were developed, which included eight for readers (express prior knowledge, view effect size and variability, express threshold, make inferences, view explanation, evaluate study and statistical quality, synthesize multiple studies, and view prior beliefs of the community), three for authors (protect the author's investment, publish enough information, make authoring easy), three for publishers (limit liability, scale up, and establish a business model), and two for computers (incorporate into reading process, use familiar interface metaphors). A sample client-only prototype is available at http://omie.med.jhmi.edu/bayes. CONCLUSION: Bayesian communication has formal justification consistent with the needs of readers and can best be implemented in an online environment. Much research must be done to establish whether the formalism and the reality of readers' needs can meet.

Bayes Theorem↗
PubMed2004

Modelling blood-brain barrier partitioning using Bayesian neural nets.

We have employed three families of molecular molecular descriptors, together with Bayesian regularized neural nets, to model the partitioning of a diverse range of drugs and other small molecules across the blood-brain barrier (BBB). The relative efficacy of each descriptors class is compared, and the advantages of flexible, parsimonious, model free mapping methods, like Bayesian neural nets, illustrated. The relative importance of the molecular descriptors for the most predictive BBB model were determined by use of automatic relevance determination (ARD), and compared with the important descriptors from other literature models of BBB partitioning.

Bayes Theorem↗
PubMed1985

A Bayesian approach to nonlinear random effects models.

Nonlinear random effects models are considered from the Bayesian point of view. The method of analysis follows closely that of Lindley and Smith (1972, Journal of the Royal Statistical Society, Series B 34, 1-42). The numerical method is related to the EM algorithm.

Analysis of Variance↗
PubMed2004

Empirical Bayes estimates generated in a hierarchical summary ROC analysis agreed closely with those of a full Bayesian analysis.

BACKGROUND AND OBJECTIVE: A range of fixed-effect and random-effects meta-analytic methods are available to obtain summary estimates of measures of diagnostic test accuracy. The hierarchical summary receiver operating characteristic (HSROC) model proposed by Rutter and Gatsonis in 2001 represents a general framework for the meta-analysis of diagnostic test studies that allows different parameters to be defined as a fixed effect or random effects within the same model. The Bayesian method used for fitting the model is complex, however, and the model is not widely used. The objective of this report is to show how the model may be fitted using the SAS procedure NLMIXED and to compare the results to the fully Bayesian analysis using an example. METHODS: The HSROC model, its assumptions, and its interpretation are described. The advantages of this model over the usual summary ROC (SROC) regression model are outlined. A complex example is used to compare the estimated SROC curves, expected operating points, and confidence intervals using the alternative approaches to fitting the model. RESULTS: The empirical Bayes estimates obtained using NLMIXED agree closely with those obtained using the fully Bayesian analysis. CONCLUSION: This alternative and more straightforward method for fitting the HSROC model makes the model more accessible to meta-analysts.

Bayes Theorem↗
PubMed2005

The establishment of Bayesian Coronary Artery Disease Prediction model.

This poster will demonstrate how we build up the module of Bayesian Coronary Artery Disease Predicting Evidence-Based Medicine. The system-module may help the young professional understand the effect of factors for referring patients to take the invasive examination of Angiographic.Moreover, the non-invasive information-tech also can perform as the screening tool on a clinical or a community-based epidemiology.

Bayes Theorem↗
PubMed2003

A Bayesian neural network approach for modelling censored data with an application to prognosis after surgery for breast cancer.

A Bayesian framework is introduced to carry out Automatic Relevance Determination (ARD) in feedforward neural networks to model censored data. A procedure to identify and interpret the prognostic group allocation is also described. These methodologies are applied to 1616 records routinely collected at Christie Hospital, in a monthly cohort study with 5-year follow-up. Two cohort studies are presented, for low- and high-risk patients allocated by standard clinical staging. The results of contrasting the Partial Logistic Artificial Neural Network (PLANN)-ARD model with the proportional hazards model are that the two are consistent, but the neural network may be more specific in the allocation of patients into prognostic groups. With automatic model selection, the regularised neural network is more conservative than the default stepwise forward selection procedure implemented by SPSS with the Akaike Information Criterion.

Bayes Theorem↗
PubMed2002

Bayesian methods for missing covariates in cure rate models.

We propose methods for Bayesian inference for missing covariate data with a novel class of semiparametric survival models with a cure fraction. We allow the missing covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one dimensional conditional distributions. We assume that the missing covariates are missing at random (MAR) throughout. We propose an informative class of joint prior distributions for the regression coefficients and the parameters arising from the covariate distributions. The proposed class of priors are shown to be useful in recovering information on the missing covariates especially in situations where the missing data fraction is large. Properties of the proposed prior and resulting posterior distributions are examined. Also, model checking techniques are proposed for sensitivity analyses and for checking the goodness of fit of a particular model. Specifically, we extend the Conditional Predictive Ordinate (CPO) statistic to assess goodness of fit in the presence of missing covariate data. Computational techniques using the Gibbs sampler are implemented. A real data set involving a melanoma cancer clinical trial is examined to demonstrate the methodology.

Bayes Theorem↗
PubMed2005

[Bayesian regularized BP neural network model for quantitative relationship between the electrochemical reduction potential and molecular structures of chlorinated aromatic compounds].

Bayesian regularized BP neural network (BRBPNN) technique was applied in QSPR model in environmental field. The BRBPNN model for quantitative relationship between the electrochemical reduction potential (ERP) and chemical structures of 87 chlorinated aromatic compounds was established. The structure descriptor pool is consisted of Cl number (Cl), molecular weight (MW) and 6 quantum chemistry parameters which are calculated by MOPAC2000 built in ChemOffice2004, including energy of the highest occupied molecular orbital (E(HOMO)), energy of the lowest occupied molecular orbital (E(LUMO)), heat of formation(HF), dipole(DIP), electronic energy(EE), core-core repulsion(CCR). The achieved optimal network structure was 6-20-1, which possessed stronger fitting and prediction capacity than that of the stepwise linear regression and with the correlation coefficients square and the mean square error for the training set and the test set as 0.999 and 0.000105, 0.965 and 0.00159 respectively. The sum of square weights between each input neuron and the hidden layer of BRBPNN(6-20-1) indicate the effect of descriptor on the electric potential declining in the order of ELUMO > EHOMO > HF> CCR > EE > DIP. The scatter diagrams show that the EE descriptors had positive effect on ERP, and ELUMO, HF, DIP had negative effects, and EHOMO and CCR showed ambiguous effects. Results show that Bayesian regularized BP neural network is of automated regularization parameter selection capability and thus may ensure the excellent generation ability and robustness. This study threw more light on the applicability of electrochemical treatment for the chlorinated aromatic compounds and the analysis on electrochemical reduction mechanism.

Bayes Theorem↗
PubMed2004

Risk factors for the prevalence of porcine cysticercosis in Mbulu District, Tanzania.

To estimate prevalence of and risk factors for the prevalence of porcine cysticercosis in Mbulu District, Tanzania, 770 live pigs were examined by lingual examination in 21 villages. Structured observations and questionnaire interviews were used to assess pig rearing practices and household use of latrines. Associations between factors were analyzed using a Bayesian hierarchical model to obtain prevalence odds ratio (OR) and 95% Bayesian Credible Intervals (95% BCI). Prevalence was 17.4% (village-specific range 3.2-46.7%). Prevalence of porcine cysticercosis was considerably higher in pigs reared in households lacking latrines than in those reared in households that were using latrines (OR = 2.04; 95% BCI = 1.25, 3.45). About 96% of the pigs were kept under free-range conditions. This study suggests the need for further studies in order to design and implement effective prevention and control measures for porcine cysticercosis in Mbulu District, Tanzania.

Animal Husbandry↗