Regression analysis of spatial data.

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

To select or to weigh: a comparative study of linear combination schemes for superparent-one-dependence estimators

We conduct a large-scale comparative study on linearly combining superparent-one-dependence estimators (SPODEs), a popular family of seminaive Bayesian classifiers. Altogether, 16 model selection and weighing schemes, 58 benchmark data sets, and various statistical tests are employed. This paper's main contributions are threefold. First, it formally presents each scheme's definition, rationale, and time complexity and hence can serve as a comprehensive reference for researchers interested in ensemble learning. Second, it offers bias-variance analysis for each scheme's classification error performance. Third, it identifies effective schemes that meet various needs in practice. This leads to accurate and fast classification algorithms which have an immediate and significant impact on real-world applications. Another important feature of our study is using a variety of statistical tests to evaluate multiple learning methods across multiple data sets.

Toxic substances in blood: an analysis of current recommendations under a Bayesian (decision) approach

This article extends existing discussion in literature on probabilistic inference and decision making with respect to continuous hypotheses that are prevalent in forensic toxicology. As a main aim, this research investigates the properties of a widely followed approach for quantifying the level of toxic substances in blood samples, and to compare this procedure with a Bayesian probabilistic approach. As an example, attention is confined to the presence of toxic substances, such as THC, in blood from car drivers. In this context, the interpretation of results from laboratory analyses needs to take into account legal requirements for establishing the 'presence' of target substances in blood. In a first part, the performance of the proposed Bayesian model for the estimation of an unknown parameter (here, the amount of a toxic substance) is illustrated and compared with the currently used method. The model is then used in a second part to approach-in a rational way-the decision component of the problem, that is judicial questions of the kind 'Is the quantity of THC measured in the blood over the legal threshold of 1.5 μg/l?'. This is pointed out through a practical example.

Adaptive MCMC methods with applications in environmental and geophysical models

This work presents new, efficient Markov chain Monte Carlo (MCMC) simulation methods for statistical analysis in various modelling applications. When using MCMC methods, the model is simulated repeatedly to explore the probability distribution describing the uncertainties in model parameters and predictions. In adaptive MCMC methods based on the Metropolis-Hastings algorithm, the proposal distribution needed by the algorithm learns from the target distribution as the simulation proceeds. Adaptive MCMC methods have been subject of intensive research lately, as they open a way for essentially easier use of the methodology. The lack of user-friendly computer programs has been a main obstacle for wider acceptance of the methods. This work provides two new adaptive MCMC methods: DRAM and AARJ. The DRAM method has been built especially to work in high dimensional and non-linear problems. The AARJ method is an extension to DRAM for model selection problems, where the mathematical formulation of the model is uncertain and we want simultaneously to fit several different models to the same observations. The methods were developed while keeping in mind the needs of modelling applications typical in environmental sciences. The development work has been pursued while working with several application projects. The applications presented in this work are: a winter time oxygen concentration model for Lake Tuusulanjärvi and adaptive control of the aerator; a nutrition model for Lake Pyhäjärvi and lake management planning; validation of the algorithms of the GOMOS ozone remote sensing instrument on board the Envisat satellite of European Space Agency and the study of the effects of aerosol model selection on the GOMOS algorithm.

Communicative and Anticipatory Decision-Making Supported by Bayesian Networks

The purpose of this research is to draw up a clear construction of an anticipatory communicative decision-making process and a successful implementation of a Bayesian application that can be used as an anticipatory communicative decision-making support system. This study is a decision-oriented and constructive research project, and it includes examples of simulated situations. As a basis for further methodological discussion about different approaches to management research, in this research, a decision-oriented approach is used, which is based on mathematics and logic, and it is intended to develop problem solving methods. The approach is theoretical and characteristic of normative management science research. Also, the approach of this study is constructive. An essential part of the constructive approach is to tie the problem to its solution with theoretical knowledge. Firstly, the basic definitions and behaviours of an anticipatory management and managerial communication are provided. These descriptions include discussions of the research environment and formed management processes. These issues define and explain the background to further research. Secondly, it is processed to managerial communication and anticipatory decision-making based on preparation, problem solution, and solution search, which are also related to risk management analysis. After that, a solution to the decision-making support application is formed, using four different Bayesian methods, as follows: the Bayesian network, the influence diagram, the qualitative probabilistic network, and the time critical dynamic network. The purpose of the discussion is not to discuss different theories but to explain the theories which are being implemented. Finally, an application of Bayesian networks to the research problem is presented. The usefulness of the prepared model in examining a problem and the represented results of research is shown. The theoretical contribution includes definitions and a model of anticipatory decision-making. The main theoretical contribution of this study has been to develop a process for anticipatory decision-making that includes management with communication, problem-solving, and the improvement of knowledge. The practical contribution includes a Bayesian Decision Support Model, which is based on Bayesian influenced diagrams. The main contributions of this research are two developed processes, one for anticipatory decision-making, and the other to produce a model of a Bayesian network for anticipatory decision-making. In summary, this research contributes to decision-making support by being one of the few publicly available academic descriptions of the anticipatory decision support system, by representing a Bayesian model that is grounded on firm theoretical discussion, by publishing algorithms suitable for decision-making support, and by defining the idea of anticipatory decision-making for a parallel version. Finally, according to the results of research, an analysis of anticipatory management for planned decision-making is presented, which is based on observation of environment, analysis of weak signals, and alternatives to creative problem solving and communication.

Sélection de modèle d'imputation à partir de modèles bayésiens hiérarchiques linéaires multivariés

Les logiciels utilisés sont Splus et R.

Big Decisions and Sparse Data: Adapting Scientific Publishing to the Needs of Practical Conservation

The biggest challenge in conservation biology is breaking down the gap between research and practical management. A major obstacle is the fact that many researchers are unwilling to tackle projects likely to produce sparse or messy data because the results would be difficult to publish in refereed journals. The obvious solution to sparse data is to build up results from multiple studies. Consequently, we suggest that there needs to be greater emphasis in conservation biology on publishing papers that can be built on by subsequent research rather than on papers that produce clear results individually. This building approach requires: (1) a stronger theoretical framework, in which researchers attempt to anticipate models that will be relevant in future studies and incorporate expected differences among studies into those models; (2) use of modern methods for model selection and multi-model inference, and publication of parameter estimates under a range of plausible models; (3) explicit incorporation of prior information into each case study; and (4) planning management treatments in an adaptive framework that considers treatments applied in other studies. We encourage journals to publish papers that promote this building approach rather than expecting papers to conform to traditional standards of rigor as stand-alone papers, and believe that this shift in publishing philosophy would better encourage researchers to tackle the most urgent conservation problems.

Benchmarking consensus model quality assessment for protein fold recognition

Background: Selecting the highest quality 3D model of a protein structure from a number of alternatives remains an important challenge in the field of structural bioinformatics. Many Model Quality Assessment Programs (MQAPs) have been developed which adopt various strategies in order to tackle this problem, ranging from the so called "true" MQAPs capable of producing a single energy score based on a single model, to methods which rely on structural comparisons of multiple models or additional information from meta-servers. However, it is clear that no current method can separate the highest accuracy models from the lowest consistently. In this paper, a number of the top performing MQAP methods are benchmarked in the context of the potential value that they add to protein fold recognition. Two novel methods are also described: ModSSEA, which based on the alignment of predicted secondary structure elements and ModFOLD which combines several true MQAP methods using an artificial neural network. Results: The ModSSEA method is found to be an effective model quality assessment program for ranking multiple models from many servers, however further accuracy can be gained by using the consensus approach of ModFOLD. The ModFOLD method is shown to significantly outperform the true MQAPs tested and is competitive with methods which make use of clustering or additional information from multiple servers. Several of the true MQAPs are also shown to add value to most individual fold recognition servers by improving model selection, when applied as a post filter in order to re-rank models. Conclusion: MQAPs should be benchmarked appropriately for the practical context in which they are intended to be used. Clustering based methods are the top performing MQAPs where many models are available from many servers; however, they often do not add value to individual fold recognition servers when limited models are available. Conversely, the true MQAP methods tested can often be used as effective post filters for re-ranking few models from individual fold recognition servers and further improvements can be achieved using a consensus of these methods.

Sparse model identification using orthogonal forward regression with basis pursuit and D-optimality

An efficient model identification algorithm for a large class of linear-in-the-parameters models is introduced that simultaneously optimises the model approximation ability, sparsity and robustness. The derived model parameters in each forward regression step are initially estimated via the orthogonal least squares (OLS), followed by being tuned with a new gradient-descent learning algorithm based on the basis pursuit that minimises the l(1) norm of the parameter estimate vector. The model subset selection cost function includes a D-optimality design criterion that maximises the determinant of the design matrix of the subset to ensure model robustness and to enable the model selection procedure to automatically terminate at a sparse model. The proposed approach is based on the forward OLS algorithm using the modified Gram-Schmidt procedure. Both the parameter tuning procedure, based on basis pursuit, and the model selection criterion, based on the D-optimality that is effective in ensuring model robustness, are integrated with the forward regression. As a consequence the inherent computational efficiency associated with the conventional forward OLS approach is maintained in the proposed algorithm. Examples demonstrate the effectiveness of the new approach.

Experimental design and model construction algorithms for radial basis function networks

New construction algorithms for radial basis function (RBF) network modelling are introduced based on the A-optimality and D-optimality experimental design criteria respectively. We utilize new cost functions, based on experimental design criteria, for model selection that simultaneously optimizes model approximation, parameter variance (A-optimality) or model robustness (D-optimality). The proposed approaches are based on the forward orthogonal least-squares (OLS) algorithm, such that the new A-optimality- and D-optimality-based cost functions are constructed on the basis of an orthogonalization process that gains computational advantages and hence maintains the inherent computational efficiency associated with the conventional forward OLS approach. The proposed approach enhances the very popular forward OLS-algorithm-based RBF model construction method since the resultant RBF models are constructed in a manner that the system dynamics approximation capability, model adequacy and robustness are optimized simultaneously. The numerical examples provided show significant improvement based on the D-optimality design criterion, demonstrating that there is significant room for improvement in modelling via the popular RBF neural network.

Robust nonlinear model identification methods using forward regression

In this correspondence new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness via combined parameter regularization and new robust structural selective criteria. In parallel to parameter regularization, we use two classes of robust model selection criteria based on either experimental design criteria that optimizes model adequacy, or the predicted residual sums of squares (PRESS) statistic that optimizes model generalization capability, respectively. Three robust identification algorithms are introduced, i.e., combined A- and D-optimality with regularized orthogonal least squares algorithm, respectively; and combined PRESS statistic with regularized orthogonal least squares algorithm. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalization scheme in orthogonal least squares or regularized orthogonal least squares has been extended such that the new algorithms are computationally efficient. Numerical examples are included to demonstrate effectiveness of the algorithms.

Improving sequence-based fold recognition by using 3D model quality assessment

Motivation: The ability of a simple method (MODCHECK) to determine the sequence–structure compatibility of a set of structural models generated by fold recognition is tested in a thorough benchmark analysis. Four Model Quality Assessment Programs (MQAPs) were tested on 188 targets from the latest LiveBench-9 automated structure evaluation experiment. We systematically test and evaluate whether the MQAP methods can successfully detect native-likemodels. Results: We show that compared with the other three methods tested MODCHECK is the most reliable method for consistently performing the best top model selection and for ranking the models. In addition, we show that the choice of model similarity score used to assess a model's similarity to the experimental structure can influence the overall performance of these tools. Although these MQAP methods fail to improve the model selection performance for methods that already incorporate protein three dimension (3D) structural information, an improvement is observed for methods that are purely sequence-based, including the best profile–profile methods. This suggests that even the best sequence-based fold recognition methods can still be improved by taking into account the 3D structural information.

How large is congressional dependence in agriculture. Bayesian inference about ‘scale’ and ‘scope’ in measuring a spatial externality

The political economy literature on agriculture emphasizes influence over political outcomes via lobbying conduits in general, political action committee contributions in particular and the pervasive view that political preferences with respect to agricultural issues are inherently geographic. In this context, ‘interdependence’ in Congressional vote behaviour manifests itself in two dimensions. One dimension is the intensity by which neighboring vote propensities influence one another and the second is the geographic extent of voter influence. We estimate these facets of dependence using data on a Congressional vote on the 2001 Farm Bill using routine Markov chain Monte Carlo procedures and Bayesian model averaging, in particular. In so doing, we develop a novel procedure to examine both the reliability and the consequences of different model representations for measuring both the ‘scale’ and the ‘scope’ of spatial (geographic) co-relations in voting behaviour.

Parametric preference functionals under risk in the gain domain: a Bayesian analysis

The performance of rank dependent preference functionals under risk is comprehensively evaluated using Bayesian model averaging. Model comparisons are made at three levels of heterogeneity plus three ways of linking deterministic and stochastic models: the differences in utilities, the differences in certainty equivalents and contextualutility. Overall, the"bestmodel", which is conditional on the form of heterogeneity is a form of Rank Dependent Utility or Prospect Theory that cap tures the majority of behaviour at both the representative agent and individual level. However, the curvature of the probability weighting function for many individuals is S-shaped, or ostensibly concave or convex rather than the inverse S-shape commonly employed. Also contextual utility is broadly supported across all levels of heterogeneity. Finally, the Priority Heuristic model, previously examined within a deterministic setting, is estimated within a stochastic framework, and allowing for endogenous thresholds does improve model performance although it does not compete well with the other specications considered.

Joint data assimilation of satellite reflectance and net ecosystem exchange data constrains ecosystem carbon fluxes at a high-elevation subalpine forest

We utilized an ecosystem process model (SIPNET, simplified photosynthesis and evapotranspiration model) to estimate carbon fluxes of gross primary productivity and total ecosystem respiration of a high-elevation coniferous forest. The data assimilation routine incorporated aggregated twice-daily measurements of the net ecosystem exchange of CO2 (NEE) and satellite-based reflectance measurements of the fraction of absorbed photosynthetically active radiation (fAPAR) on an eight-day timescale. From these data we conducted a data assimilation experiment with fifteen different combinations of available data using twice-daily NEE, aggregated annual NEE, eight-day f AP AR, and average annual fAPAR. Model parameters were conditioned on three years of NEE and fAPAR data and results were evaluated to determine the information content from the different combinations of data streams. Across the data assimilation experiments conducted, model selection metrics such as the Bayesian Information Criterion and Deviance Information Criterion obtained minimum values when assimilating average annual fAPAR and twice-daily NEE data. Application of wavelet coherence analyses showed higher correlations between measured and modeled fAPAR on longer timescales ranging from 9 to 12 months. There were strong correlations between measured and modeled NEE (R2, coefficient of determination, 0.86), but correlations between measured and modeled eight-day fAPAR were quite poor (R2 = −0.94). We conclude that this inability to determine fAPAR on eight-day timescale would improve with the considerations of the radiative transfer through the plant canopy. Modeled fluxes when assimilating average annual fAPAR and annual NEE were comparable to corresponding results when assimilating twice-daily NEE, albeit at a greater uncertainty. Our results support the conclusion that for this coniferous forest twice-daily NEE data are a critical measurement stream for the data assimilation. The results from this modeling exercise indicate that for this coniferous forest, average annuals for satellite-based fAPAR measurements paired with annual NEE estimates may provide spatial detail to components of ecosystem carbon fluxes in proximity of eddy covariance towers. Inclusion of other independent data streams in the assimilation will also reduce uncertainty on modeled values.