Efficient and accurate experimental design for enzyme kinetics: Bayesian studies reveal a systematic approach

In areas such as drug development, clinical diagnosis and biotechnology research, acquiring details about the kinetic parameters of enzymes is crucial. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. We demonstrate that a Bayesian approach (the use of prior knowledge) can produce major gains quantifiable in terms of information, productivity and accuracy of each experiment. Developing the use of Bayesian Utility functions, we have used a systematic method to identify the optimum experimental designs for a number of kinetic model data sets. This has enabled the identification of trends between kinetic model types, sets of design rules and the key conclusion that such designs should be based on some prior knowledge of K-M and/or the kinetic model. We suggest an optimal and iterative method for selecting features of the design such as the substrate range, number of measurements and choice of intermediate points. The final design collects data suitable for accurate modelling and analysis and minimises the error in the parameters estimated. (C) 2003 Elsevier Science B.V. All rights reserved.

Qualitative modelling of sustainable energy scenarios: An application and extension of the Bon Qualitative Input-Output model

Climate change is one of the major challenges facing economic systems at the start of the 21st century. Reducing greenhouse gas emissions will require both restructuring the energy supply system (production) and addressing the efficiency and sufficiency of the social uses of energy (consumption). The energy production system is a complicated supply network of interlinked sectors with 'knock-on' effects throughout the economy. End use energy consumption is governed by complex sets of interdependent cultural, social, psychological and economic variables driven by shifts in consumer preference and technological development trajectories. To date, few models have been developed for exploring alternative joint energy production-consumption systems. The aim of this work is to propose one such model. This is achieved in a methodologically coherent manner through integration of qualitative input-output models of production, with Bayesian belief network models of consumption, at point of final demand. The resulting integrated framework can be applied either (relatively) quickly and qualitatively to explore alternative energy scenarios, or as a fully developed quantitative model to derive or assess specific energy policy options. The qualitative applications are explored here.

Skilloscopy: Bayesian modeling of decision makers' skill

This paper proposes and demonstrates an approach, Skilloscopy, to the assessment of decision makers. In an increasingly sophisticated, connected and information-rich world, decision making is becoming both more important and more difficult. At the same time, modelling decision-making on computers is becoming more feasible and of interest, partly because the information-input to those decisions is increasingly on record. The aims of Skilloscopy are to rate and rank decision makers in a domain relative to each other: the aims do not include an analysis of why a decision is wrong or suboptimal, nor the modelling of the underlying cognitive process of making the decisions. In the proposed method a decision-maker is characterised by a probability distribution of their competence in choosing among quantifiable alternatives. This probability distribution is derived by classic Bayesian inference from a combination of prior belief and the evidence of the decisions. Thus, decision-makers’ skills may be better compared, rated and ranked. The proposed method is applied and evaluated in the gamedomain of Chess. A large set of games by players across a broad range of the World Chess Federation (FIDE) Elo ratings has been used to infer the distribution of players’ rating directly from the moves they play rather than from game outcomes. Demonstration applications address questions frequently asked by the Chess community regarding the stability of the Elo rating scale, the comparison of players of different eras and/or leagues, and controversial incidents possibly involving fraud. The method of Skilloscopy may be applied in any decision domain where the value of the decision-options can be quantified.

Hierarchical analysis of production efficiency in a coastal trawl fishery

We present, pedagogically, the Bayesian approach to composed error models under alternative, hierarchical characterizations; demonstrate, briefly, the Bayesian approach to model comparison using recent advances in Markov Chain Monte Carlo (MCMC) methods; and illustrate, empirically, the value of these techniques to natural resource economics and coastal fisheries management, in particular. The Bayesian approach to fisheries efficiency analysis is interesting for at least three reasons. First, it is a robust and highly flexible alternative to commonly applied, frequentist procedures, which dominate the literature. Second,the Bayesian approach is extremely simple to implement, requiring only a modest addition to most natural-resource economist tool-kits. Third, despite its attractions, applications of Bayesian methodology in coastal fisheries management are few.

Forecasting with Bayesian multivariate vintage-based VARs

We consider the forecasting of macroeconomic variables that are subject to revisions, using Bayesian vintage-based vector autoregressions. The prior incorporates the belief that, after the first few data releases, subsequent ones are likely to consist of revisions that are largely unpredictable. The Bayesian approach allows the joint modelling of the data revisions of more than one variable, while keeping the concomitant increase in parameter estimation uncertainty manageable. Our model provides markedly more accurate forecasts of post-revision values of inflation than do other models in the literature.

Calibration and evaluation of individual-based models using Approximate Bayesian Computation

This paper investigates the feasibility of using approximate Bayesian computation (ABC) to calibrate and evaluate complex individual-based models (IBMs). As ABC evolves, various versions are emerging, but here we only explore the most accessible version, rejection-ABC. Rejection-ABC involves running models a large number of times, with parameters drawn randomly from their prior distributions, and then retaining the simulations closest to the observations. Although well-established in some fields, whether ABC will work with ecological IBMs is still uncertain. Rejection-ABC was applied to an existing 14-parameter earthworm energy budget IBM for which the available data consist of body mass growth and cocoon production in four experiments. ABC was able to narrow the posterior distributions of seven parameters, estimating credible intervals for each. ABC’s accepted values produced slightly better fits than literature values do. The accuracy of the analysis was assessed using cross-validation and coverage, currently the best available tests. Of the seven unnarrowed parameters, ABC revealed that three were correlated with other parameters, while the remaining four were found to be not estimable given the data available. It is often desirable to compare models to see whether all component modules are necessary. Here we used ABC model selection to compare the full model with a simplified version which removed the earthworm’s movement and much of the energy budget. We are able to show that inclusion of the energy budget is necessary for a good fit to the data. We show how our methodology can inform future modelling cycles, and briefly discuss how more advanced versions of ABC may be applicable to IBMs. We conclude that ABC has the potential to represent uncertainty in model structure, parameters and predictions, and to embed the often complex process of optimizing an IBM’s structure and parameters within an established statistical framework, thereby making the process more transparent and objective.

Bayesian analysis of uncertainty in the GlobCover 2009 land cover product at climate model grid scale

Land cover data derived from satellites are commonly used to prescribe inputs to models of the land surface. Since such data inevitably contains errors, quantifying how uncertainties in the data affect a model’s output is important. To do so, a spatial distribution of possible land cover values is required to propagate through the model’s simulation. However, at large scales, such as those required for climate models, such spatial modelling can be difficult. Also, computer models often require land cover proportions at sites larger than the original map scale as inputs, and it is the uncertainty in these proportions that this article discusses. This paper describes a Monte Carlo sampling scheme that generates realisations of land cover proportions from the posterior distribution as implied by a Bayesian analysis that combines spatial information in the land cover map and its associated confusion matrix. The technique is computationally simple and has been applied previously to the Land Cover Map 2000 for the region of England and Wales. This article demonstrates the ability of the technique to scale up to large (global) satellite derived land cover maps and reports its application to the GlobCover 2009 data product. The results show that, in general, the GlobCover data possesses only small biases, with the largest belonging to non–vegetated surfaces. In vegetated surfaces, the most prominent area of uncertainty is Southern Africa, which represents a complex heterogeneous landscape. It is also clear from this study that greater resources need to be devoted to the construction of comprehensive confusion matrices.

Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics

The purpose of this paper is to develop a Bayesian analysis for nonlinear regression models under scale mixtures of skew-normal distributions. This novel class of models provides a useful generalization of the symmetrical nonlinear regression models since the error distributions cover both skewness and heavy-tailed distributions such as the skew-t, skew-slash and the skew-contaminated normal distributions. The main advantage of these class of distributions is that they have a nice hierarchical representation that allows the implementation of Markov chain Monte Carlo (MCMC) methods to simulate samples from the joint posterior distribution. In order to examine the robust aspects of this flexible class, against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. Further, some discussions on the model selection criteria are given. The newly developed procedures are illustrated considering two simulations study, and a real data previously analyzed under normal and skew-normal nonlinear regression models. (C) 2010 Elsevier B.V. All rights reserved.

Semiparametric Bayesian measurement error modeling

This work presents a Bayesian semiparametric approach for dealing with regression models where the covariate is measured with error. Given that (1) the error normality assumption is very restrictive, and (2) assuming a specific elliptical distribution for errors (Student-t for example), may be somewhat presumptuous; there is need for more flexible methods, in terms of assuming only symmetry of errors (admitting unknown kurtosis). In this sense, the main advantage of this extended Bayesian approach is the possibility of considering generalizations of the elliptical family of models by using Dirichlet process priors in dependent and independent situations. Conditional posterior distributions are implemented, allowing the use of Markov Chain Monte Carlo (MCMC), to generate the posterior distributions. An interesting result shown is that the Dirichlet process prior is not updated in the case of the dependent elliptical model. Furthermore, an analysis of a real data set is reported to illustrate the usefulness of our approach, in dealing with outliers. Finally, semiparametric proposed models and parametric normal model are compared, graphically with the posterior distribution density of the coefficients. (C) 2009 Elsevier Inc. All rights reserved.

A Bayesian Semiparametric Approach for Solving the Discrete Calibration Problem

In this article, we introduce a semi-parametric Bayesian approach based on Dirichlet process priors for the discrete calibration problem in binomial regression models. An interesting topic is the dosimetry problem related to the dose-response model. A hierarchical formulation is provided so that a Markov chain Monte Carlo approach is developed. The methodology is applied to simulated and real data.

Skew-normal linear calibration: a Bayesian perspective

In this paper, we present a Bayesian approach for estimation in the skew-normal calibration model, as well as the conditional posterior distributions which are useful for implementing the Gibbs sampler. Data transformation is thus avoided by using the methodology proposed. Model fitting is implemented by proposing the asymmetric deviance information criterion, ADIC, a modification of the ordinary DIC. We also report an application of the model studied by using a real data set, related to the relationship between the resistance and the elasticity of a sample of concrete beams. Copyright (C) 2008 John Wiley & Sons, Ltd.

Genetic heterogeneity of residual variance : estimation of variance components using double hierarchical generalized linear models

Background: The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms. Results: We propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model. Conclusions: We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.

Structural modelling of Eu3+-based siloxane-poly( oxyethylene) nanohybrids

The modelling of the local structure of sol-gel derived Eu3+-based organic/inorganic hybrids is reported, based on Small-Angle X-ray Scattering (SAXS), photoluminescence and mid-infrared spectroscopy. The hybrid matrix of these organically modified silicates, classed as di-ureasils and termed U(2000) and U(600), is formed by poly( oxyethylene) (POE) chains of variable length grafted to siloxane domains by means of urea cross-linkages. Europium triflate, Eu(CF3SO3)(3), was incorporated in the two di-ureasil matrices with compositions 400 greater than or equal ton greater than or equal to 10, n is the molar ratio of ether oxygens per Eu3+. The SAXS data for undoped hybrids (n=infinity) show the presence of a well-defined peak attributed to the existence of a liquid-like spatial correlation of siloxane rich domains embedded in the polymer matrix and located at the ends of the organic segments. The obtained siloxane particle gyration radius Rg(1) is around 5 Angstrom (error within 10%), whereas the interparticle distance d is 25 +/-2 Angstrom and 40 +/-2 Angstrom, for U(600) and U(2000), respectively. For the Eu3+-based nanocomposites the formation of a two-level hierarchical local structure is discerned. The primary level is constituted by strongly spatially correlated siloxane particles of gyration radius Rg(1) (4-6 and 3-8 Angstrom, errors within 5%, for U(600())n Eu(CF3SO3)(3), 200 greater than or equal ton greater than or equal to 40, and U(2000)(n)Eu(CF3SO3)(3), 400 greater than or equal ton greater than or equal to 40, respectively) forming large clusters of gyration radius Rg(2) (approximate to 75 +/- 10 Angstrom). The local coordination of Eu3+ in both di-ureasil series is described combining the SAXS, photoluminescence and mid-infrared results. In the di-ureasils containing long polymer chains, U(2000)(n)Eu(CF3SO3)(3), the cations interact exclusively with the carbonyl oxygens atoms of the urea bridges at the siloxane-POE interface. In the hybrids containing shorter chains, U(600)(n)Eu(CF3SO3)(3) with n ranging from 200 to 60, the Eu3+ ions interact solely with the ether-type oxygens of the polymer chains. Nevertheless, in this latter family of hybrids a distinct Eu3+ local site environment involving the urea cross-linkages is detected when the europium content is increased up to n=40.

Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC

Linear mixed effects models are frequently used to analyse longitudinal data, due to their flexibility in modelling the covariance structure between and within observations. Further, it is easy to deal with unbalanced data, either with respect to the number of observations per subject or per time period, and with varying time intervals between observations. In most applications of mixed models to biological sciences, a normal distribution is assumed both for the random effects and for the residuals. This, however, makes inferences vulnerable to the presence of outliers. Here, linear mixed models employing thick-tailed distributions for robust inferences in longitudinal data analysis are described. Specific distributions discussed include the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted, and the Gibbs sampler and the Metropolis-Hastings algorithms are used to carry out the posterior analyses. An example with data on orthodontic distance growth in children is discussed to illustrate the methodology. Analyses based on either the Student-t distribution or on the usual Gaussian assumption are contrasted. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process for modelling distributions of the random effects and of residuals in linear mixed models, and the MCMC implementation allows the computations to be performed in a flexible manner.

Reinforcing and expanding the predictions of the disturbance vicariance hypothesis in Amazonian harlequin frogs: A molecular phylogenetic and climate envelope modelling approach

The disturbance vicariance hypothesis (DV) has been proposed to explain speciation in Amazonia, especially its edge regions, e. g. in eastern Guiana Shield harlequin frogs (Atelopus) which are suggested to have derived from a cool-adapted Andean ancestor. In concordance with DV predictions we studied that (i) these amphibians display a natural distribution gap in central Amazonia; (ii) east of this gap they constitute a monophyletic lineage which is nested within a pre-Andean/western clade; (iii) climate envelopes of Atelopus west and east of the distribution gap show some macroclimatic divergence due to a regional climate envelope shift; (iv) geographic distributions of climate envelopes of western and eastern Atelopus range into central Amazonia but with limited spatial overlap. We tested if presence and apparent absence data points of Atelopus were homogenously distributed with Ripley's K function. A molecular phylogeny (mitochondrial 16S rRNA gene) was reconstructed using Maximum Likelihood and Bayesian Inference to study if Guianan Atelopus constitute a clade nested within a larger genus phylogeny. We focused on climate envelope divergence and geographic distribution by computing climatic envelope models with MaxEnt based on macroscale bioclimatic parameters and testing them by using Schoener's index and modified Hellinger distance. We corroborated existing DV predictions and, for the first time, formulated new DV predictions aiming on species' climate envelope change. Our results suggest that cool-adapted Andean Atelopus ancestors had dispersed into the Amazon basin and further onto the eastern Guiana Shield where, under warm conditions, they were forced to change climate envelopes. © 2010 The Author(s).