Evaluation of the Kullback-Leibler Discrepancy for Model Selection in Open Population Capture-Recapture Models

The objective of this paper is to introduce the logical basis of AIC-based model selection to persons analyzing capture-recapture data and to explore the key theorettical aspect of AIC based model selection, for open-model capture-recapture, needed for AIC to perform well in this context. Almost all previous work on AIC assumes a Gaussian model; that assumption does not hold for capture-recapture models. Assuming the Cormack-Jolly-Seber model as the true model, we used numerical methods to evaluate the expectation of the log-likelihood relative to Akaike's target predictive log-likelihood. The use of this particular target criterion was motivated by the idea of using the Kullback-Leibler discrepancy for model selection, for which Akaike found the bias of the sample log-likelihood was asymptotically K, where K = the number of estimated (by MLE) parameters. In some sense, then, AIC is a bias-adjusted log-likelihood. For a set of 81 plausible cases, we evaluated this bias almost exactly. The ratio of this bias to the first order theory (bias of K) and to second order theory (K + a sample size adjustment) is essentially 1 for these 81 cases. Thus, AIC should be a suitable basis for model selection in open model capture-recapture.     

Parameter Identifiability and Estimation of HIV/AIDS Dynamic Models

We use a technique from engineering (Xia and Moog, in IEEE Trans. Autom. Contr. 48(2):330–336, 2003; Jeffrey and Xia, in Tan, W.Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, 2005) to investigate the algebraic identifiability of a popular three-dimensional HIV/AIDS dynamic model containing six unknown parameters. We find that not all six parameters in the model can be identified if only the viral load is measured, instead only four parameters and the product of two parameters (N and λ) are identifiable. We introduce the concepts of an identification function and an identification equation and propose the multiple time point (MTP) method to form the identification function which is an alternative to the previously developed higher-order derivative (HOD) method (Xia and Moog, in IEEE Trans. Autom. Contr. 48(2):330–336, 2003; Jeffrey and Xia, in Tan, W.Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, 2005). We show that the newly proposed MTP method has advantages over the HOD method in the practical implementation. We also discuss the effect of the initial values of state variables on the identifiability of unknown parameters. We conclude that the initial values of output (observable) variables are part of the data that can be used to estimate the unknown parameters, but the identifiability of unknown parameters is not affected by these initial values if the exact initial values are measured with error. These noisy initial values only increase the estimation error of the unknown parameters. However, having the initial values of the latent (unobservable) state variables exactly known may help to identify more parameters. In order to validate the identifiability results, simulation studies are performed to estimate the unknown parameters and initial values from simulated noisy data. We also apply the proposed methods to a clinical data set to estimate HIV dynamic parameters. Although we have developed the identifiability methods based on an HIV dynamic model, the proposed methodologies are generally applicable to any ordinary differential equation systems.     

Information-Theoretic Model Selection and Model Averaging for Closed-Population Capture-Recapture Studies

Specification of an appropriate model is critical to valid statistical inference. Given the “true model” for the data is unknown, the goal of model selection is to select a plausible approximating model that balances model bias and sampling variance. Model selection based on information criteria such as AIC or its variant AIC_c, or criteria like CAIC, has proven useful in a variety of contexts including the analysis of open-population capture-recapture data. These criteria have not been intensively evaluated for closed-population capture-recapture models, which are integer parameter models used to estimate population size (N), and there is concern that they will not perform well. To address this concern, we evaluated AIC, AIC_c, and CAIC model selection for closed-population capture-recapture models by empirically assessing the quality of inference for the population size parameter N. We found that AIC-, AIC_c-, and CAIC-selected models had smaller relative mean squared errors than randomly selected models, but that confidence interval coverage on N was poor unless unconditional variance estimates (which incorporate model uncertainty) were used to compute confidence intervals. Overall, AIC and AIC_c outperformed CAIC, and are preferred to CAIC for selection among the closed-population capture-recapture models we investigated. A model averaging approach to estimation, using AIC, AIC_c, or CAIC to estimate weights, was also investigated and proved superior to estimation using AIC-, AIC_c-, or CAIC-selected models. Our results suggested that, for model averaging, AIC or AIC_c should be favored over CAIC for estimating weights.     

Model-free Analysis of Protein Dynamics: Assessment of Accuracy and Model Selection Protocols Based on Molecular Dynamics Simulation

The popular model-free approach to analyze NMR relaxation measurements has been examined using artificial amide (15)N relaxation data sets generated from a 10 nanosecond molecular dynamics trajectory of a dihydrofolate reductase ternary complex in explicit water. With access to a detailed picture of the underlying internal motions, the efficacy of model-free analysis and impact of model selection protocols on the interpretation of NMR data can be studied. In the limit of uncorrelated global tumbling and internal motions, fitting the relaxation data to the model-free models can recover a significant amount of quantitative information on the internal dynamics. Despite a slight overestimation, the generalized order parameter is quite accurately determined. However, the model-free analysis appears to be insensitive to the presence of nanosecond time scale motions with relatively small magnitude. For such cases, the effective correlation time can be significantly underestimated. As a result, proteins appear to be more rigid than they really are. The model selection protocols have a major impact on the information one can reliably obtain. The commonly employed protocol based on step-up hypothesis testing has severe drawbacks of oversimplification and underfitting. The consequences are that the order parameter is more severely overestimated and the correlation time more severely underestimated. Instead, model selection based on Bayesian Information Criteria (BIC), recently introduced to the model-free analysis by d'Auvergne and Gooley (2003), provides a better balance between bias and variance. More appropriate models can be selected, leading to improved estimate of both the order parameter and correlation time. In addition, the computational cost is significantly reduced and subjective parameters such as the significance level are unnecessary.     

陆地生态系统物质交换模型

陆地生态系统物质交换模型是生态系统水、碳、养分循环研究的重要方向和极具发展前景的不可替代的手段.本文对近年来发展的众多陆地生态系统物质交换模型进行了归类:1)根据建模思路不同分为经验模型、过程模型和混合模型;2)根据物质传输机制的不同分为生物物理模型和生物地球化学模型;3)根据对植被结构处理方式的不同分为单层模型、双层模型和多层模型;4)根据模型应用性不同分为诊断性模型和预测性模型;5)根据构建模型的逻辑结构不同分为自下而上模型和由上而下模型;6)根据研究尺度的不同分为生态系统尺度模型、景观尺度模型和区域尺度模型;7)根据植物生理过程的不同分为光合作用模型和蒸腾作用模型.最后对不同类型模型的优缺点进行综合分析,探讨了新的发展方向.     

拟似然非线性模型中的置信域：几何法

对拟似然非线性模型在欧氏内积实间建立了修改的Ｂａｔｅｓ＆Ｗａｔｔｓ几何结构，基于此几何结构，导出了参数和子集系数的与统计曲率有关的三种近似置信域，进一步推广和发展了Ｈａｍｉｌｔｏｎ ｅｔ ａｌ．（１９８２）。Ｈａｍｉｌｔｏｎ（１９８６）和Ｗｅｉ（１９９４，１９９８）等人的相应结果。     

Plant Demography and Habitat: A Comparative Approach

Abstract Progress in plant demography will depend upon being able to synthesize a large body of data and this requires a means of comparing populations between sites and species. We have employed a comparative technique using elasticity analysis of stage-projection matrices to partition the contributions of fecundity (F), survival (L) and growth (G) to the finite rate of increase λ. Ordination of populations of 77 perennial herbs and trees in G-L-F space has shown that species segregate in this triangular space according to their life history and habitat. In the present paper we use the correspondence between demographic parameters and habitat revealed by this method to predict how succession and a variety of environmental factors such as grazing and fire are likely to alter the demography of populations and ultimately to change the composition of communities.     

Optimal Experimental Design and Accuracy of Parameter Estimation for Nonlinear Regression Models Used in Long-term Selection

An experimental design problem is considered for the analysis of long-term selection experiments with nonlinear regression models. For a 3-parametric exponential regression function whose parameters have also a reasonable biological interpretation approximate formulas for the determination of the necessary number of observations at each generation are constructed in such a way that the half expected length of an (1 — α)-confidence interval for a chosen parameter is not greater than a given value. In this sense the accuracy of the parameter estimators can be described.     

Learning Rates and States from Biophysical Time Series: A Bayesian Approach to Model Selection and Single-Molecule FRET Data

Time series data provided by single-molecule Förster resonance energy transfer (smFRET) experiments offer the opportunity to infer not only model parameters describing molecular complexes, e.g., rate constants, but also information about the model itself, e.g., the number of conformational states. Resolving whether such states exist or how many of them exist requires a careful approach to the problem of model selection, here meaning discrimination among models with differing numbers of states. The most straightforward approach to model selection generalizes the common idea of maximum likelihood—selecting the most likely parameter values—to maximum evidence: selecting the most likely model. In either case, such an inference presents a tremendous computational challenge, which we here address by exploiting an approximation technique termed variational Bayesian expectation maximization. We demonstrate how this technique can be applied to temporal data such as smFRET time series; show superior statistical consistency relative to the maximum likelihood approach; compare its performance on smFRET data generated from experiments on the ribosome; and illustrate how model selection in such probabilistic or generative modeling can facilitate analysis of closely related temporal data currently prevalent in biophysics. Source code used in this analysis, including a graphical user interface, is available open source via http://vbFRET.sourceforge.net.     

The Onset and Extinction of Neural Spiking: A Numerical Bifurcation Approach

We study the onset of neural spiking when the equilibrium rest state loses stability by the change of a critical parameter, the applied current. In the case of the well-known Morris-Lecar model, we start from a complete numerical study of the bifurcation diagram in the most relevant two-parameter range. This diagram includes all equilibrium and limit cycle bifurcations, thus correcting and completing earlier studies.We discuss and classify the behavior of the spiking orbits, when increasing or decreasing the applied current. A complete classification can be extracted from the complete bifurcation diagram. It is based on three components: bifurcation type of the equilibrium at the loss of stability, subcritical behavior in the limit of decreasing the applied current and supercritical behavior in the limit of increasing the applied current.     

A Deep Feature Learning Model for Pneumonia Detection Applying a Combination of mRMR Feature Selection and Machine Learning Models

Pneumonia is one of the diseases that people may encounter in any period of their lives. Approximately 18% of infectious diseases are caused by pneumonia. This disease may result in death in the following stages. In order to diagnose pneumonia as a medical condition, lung X-ray images are routinely examined by the field experts in the clinical practice. In this study, lung X-ray images that are available for the diagnosis of pneumonia were used. The convolutional neural network was employed as feature extractor, and some of existing convolutional neural network models that are AlexNet, VGG-16 and VGG-19 were utilized so as to realize this specific task. Then, the number of deep features was reduced from 1000 to 100 by using the minimum redundancy maximum relevance algorithm for each deep model. Accordingly, we achieved 100 deep features from each deep model, and we combined these features so as to provide an efficient feature set consisting of totally 300 deep features. In this step of the experiment, this feature set was given as an input to the decision tree, k-nearest neighbors, linear discriminant analysis, linear regression, and support vector machine learning models. Finally, all models ensured promising results, especially linear discriminant analysis yielded the most efficient results with an accuracy of 99.41%. Consequently, the results point out that the deep features provided robust and consistent features for pneumonia detection, and minimum redundancy maximum relevance method was found a beneficial tool to reduce the dimension of the feature set.     

The Evolution of Codon Preferences in Drosophila: A Maximum-Likelihood Approach to Parameter Estimation and Hypothesis Testing

Synonymous codon usage in related species may differ as a result of variation in mutation biases, differences in the overall strength and efficiency of selection, and shifts in codon preference—the selective hierarchy of codons within and between amino acids. We have developed a maximum-likelihood method to employ explicit population genetic models to analyze the evolution of parameters determining codon usage. The method is applied to twofold degenerate amino acids in 50 orthologous genes from D. melanogaster and D. virilis. We find that D. virilis has significantly reduced selection on codon usage for all amino acids, but the data are incompatible with a simple model in which there is a single difference in the long-term N _e, or overall strength of selection, between the two species, indicating shifts in codon preference. The strength of selection acting on codon usage in D. melanogaster is estimated to be |N _e s|≈ 0.4 for most CT-ending twofold degenerate amino acids, but 1.7 times greater for cysteine and 1.4 times greater for AG-ending codons. In D. virilis, the strength of selection acting on codon usage for most amino acids is only half that acting in D. melanogaster but is considerably greater than half for cysteine, perhaps indicating the dual selection pressures of translational efficiency and accuracy. Selection coefficients in orthologues are highly correlated (ρ= 0.46), but a number of genes deviate significantly from this relationship. Received: 20 December 1998 / Accepted: 17 February 1999     

Multilevel Selection in Models of Prebiotic Evolution: Compartments and Spatial Self-organization

In this paper we explore the impact of new levels ofselection in models of early evolution.We contrast two types of higher levels of selection. On the one hand we look at spatially explicitmodels of replicators in which, by a process of self-organization, new levels of selection ariseas large scale spatial patterns with a dynamics of their own. Alternatively externally imposedlevels of selection above the basic replicators are created by enclosing the replicators in vesicles.In this paper we first review some results on the impact of emerging higher levels of selection onthe evolutionary persistence of interacting co-evolvingreplicator systems. Moreover, we presenta vesicle model, which can potentially integrate emerging and imposed levels of selection. We use the models to examinethe classical problem information integration in early evolution.Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1025754907141     

Idealized, Inaccurate but Successful: A Pragmatic Approach to Evaluating Models in Theoretical Ecology

Ecologists attempt to understand the diversity of life with mathematical models. Often, mathematical models contain simplifying idealizations designed to cope with the blooming, buzzing confusion of the natural world. This strategy frequently issues in models whose predictions are inaccurate. Critics of theoretical ecology argue that only predictively accurate models are successful and contribute to the applied work of conservation biologists. Hence, they think that much of the mathematical work of ecologists is poor science. Against this view, I argue that model building is successful even when models are predictively inaccurate for at least three reasons: models allow scientists to explore the possible behaviors of ecological systems; models give scientists simplified means by which they can investigate more complex systems by determining how the more complex system deviates from the simpler model; and models give scientists conceptual frameworks through which they can conduct experiments and fieldwork. Critics often mistake the purposes of model building, and once we recognize this, we can see their complaints are unjustified. Even though models in ecology are not always accurate in their assumptions and predictions, they still contribute to successful science.     

Multilevel Selection in Models of Prebiotic Evolution II: A Direct Comparison of Compartmentalization and Spatial Self-Organization

Multilevel selection has been indicated as an essential factor for the evolution of complexity in interacting RNA-like replicator systems. There are two types of multilevel selection mechanisms: implicit and explicit. For implicit multilevel selection, spatial self-organization of replicator populations has been suggested, which leads to higher level selection among emergent mesoscopic spatial patterns (traveling waves). For explicit multilevel selection, compartmentalization of replicators by vesicles has been suggested, which leads to higher level evolutionary dynamics among explicitly imposed mesoscopic entities (protocells). Historically, these mechanisms have been given separate consideration for the interests on its own. Here, we make a direct comparison between spatial self-organization and compartmentalization in simulated RNA-like replicator systems. Firstly, we show that both mechanisms achieve the macroscopic stability of a replicator system through the evolutionary dynamics on mesoscopic entities that counteract that of microscopic entities. Secondly, we show that a striking difference exists between the two mechanisms regarding their possible influence on the long-term evolutionary dynamics, which happens under an emergent trade-off situation arising from the multilevel selection. The difference is explained in terms of the difference in the stability between self-organized mesoscopic entities and externally imposed mesoscopic entities. Thirdly, we show that a sharp transition happens in the long-term evolutionary dynamics of the compartmentalized system as a function of replicator mutation rate. Fourthly, the results imply that spatial self-organization can allow the evolution of stable folding in parasitic replicators without any specific functionality in the folding itself. Finally, the results are discussed in relation to the experimental synthesis of chemical Darwinian systems and to the multilevel selection theory of evolutionary biology in general. To conclude, novel evolutionary directions can emerge through interactions between the evolutionary dynamics on multiple levels of organization. Different multilevel selection mechanisms can produce a difference in the long-term evolutionary trend of identical microscopic entities.     

On Finding and Using Identifiable Parameter Combinations in Nonlinear Dynamic Systems Biology Models and COMBOS: A Novel Web Implementation

Parameter identifiability problems can plague biomodelers when they reach the quantification stage of development, even for relatively simple models. Structural identifiability (SI) is the primary question, usually understood as knowing which of P unknown biomodel parameters p ₁,…, p_i,…, p_P are-and which are not-quantifiable in principle from particular input-output (I-O) biodata. It is not widely appreciated that the same database also can provide quantitative information about the structurally unidentifiable (not quantifiable) subset, in the form of explicit algebraic relationships among unidentifiable p_i. Importantly, this is a first step toward finding what else is needed to quantify particular unidentifiable parameters of interest from new I–O experiments. We further develop, implement and exemplify novel algorithms that address and solve the SI problem for a practical class of ordinary differential equation (ODE) systems biology models, as a user-friendly and universally-accessible web application (app)–COMBOS. Users provide the structural ODE and output measurement models in one of two standard forms to a remote server via their web browser. COMBOS provides a list of uniquely and non-uniquely SI model parameters, and–importantly-the combinations of parameters not individually SI. If non-uniquely SI, it also provides the maximum number of different solutions, with important practical implications. The behind-the-scenes symbolic differential algebra algorithms are based on computing Gröbner bases of model attributes established after some algebraic transformations, using the computer-algebra system Maxima. COMBOS was developed for facile instructional and research use as well as modeling. We use it in the classroom to illustrate SI analysis; and have simplified complex models of tumor suppressor p53 and hormone regulation, based on explicit computation of parameter combinations. It’s illustrated and validated here for models of moderate complexity, with and without initial conditions. Built-in examples include unidentifiable 2 to 4-compartment and HIV dynamics models.     

A Continuous Labour Supply Model in Microsimulation: A Life-Cycle Modelling Approach with Heterogeneity and Uncertainty Extension

This paper advances a structural inter-temporal model of labour supply that is able to simulate the dynamics of labour supply in a continuous setting and addresses two main drawbacks of most existing models. The first limitation is the inability to incorporate individual heterogeneity as every agent is sharing the same parameters of the utility function. The second one is the strong assumption that individuals make decisions in a world of perfect certainty. Essentially, this paper offers an extension of marginal-utility-of-wealth-constant labour supply functions known as “Frisch functions” under certainty and uncertainty with homogenous and heterogeneous preferences. The lifetime models based on the fixed effect vector decomposition yield the most stable simulation results, under both certain and uncertain future wage assumptions. Due to its improved accuracy and stability, this lifetime labour supply model is particularly suitable for enhancing the performance of the life cycle simulation models, thus providing a better reference for policymaking.     

ATM and ATR Check in on Origins: A Dynamic Model for Origin Selection and Activation

Initiation of DNA replication occurs at origins of replication, traditionally defined by specific sequence elements. Sequence-dependent initiation of replication is the rule in prokaryotes and in the yeast Saccharomyces cereviseae. However, sequence-dependent initiation does not appear to be absolutely required in metazoan eukaryotes. Origin firing is instead likely dependent on stochastic initiation from chromatin-defined loci, despite the demonstration of some specific origins. Based on some recent observations in Xenopus laevis egg extracts and in mammalian cell culture, we propose that timing of origin firing is dependent on feedback from active replicons. This dynamic regulation of replication is mediated by sensing of ongoing replication by the DNA-damage checkpoint kinases ATM and ATR, which in turn downregulate neighboring and distal origins and replicons by inhibition of the S-phase kinases Cdk2 and Cdc7 and by inhibition of the replicative Mcm helicase. Origin selection, activation, and replicon progression are therefore constrained in both space and time via feedback from the cell cycle and ongoing replication.