Statistics for Spatial Data.

Model selection is a topic of special relevance in molecular phylogenetics that affects many, if not all, stages of phylogenetic inference. Here we discuss some fundamental concepts and techniques of model selection in the context of phylogenetics. We start by reviewing different aspects of the selection of substitution models in phylogenetics from a theoretical, philosophical and practical point of view, and summarize this comparison in table format. We argue that the most commonly implemented model selection approach, the hierarchical likelihood ratio test, is not the optimal strategy for model selection in phylogenetics, and that approaches like the Akaike Information Criterion (AIC) and Bayesian methods offer important advantages. In particular, the latter two methods are able to simultaneously compare multiple nested or nonnested models, assess model selection uncertainty, and allow for the estimation of phylogenies and model parameters using all available models (model-averaged inference or multimodel inference). We also describe how the relative importance of the different parameters included in substitution models can be depicted. To illustrate some of these points, we have applied AIC-based model averaging to 37 mitochondrial DNA sequences from the subgenus Ohomopterus (genus Carabus) ground beetles described by Sota and Vogler (2001). (AIC; Bayes factors; BIC; likelihood ratio tests; model averaging; model uncertainty; model selection; multimodel inference.) It is clear that models of nucleotide substitution (henceforth models of evolution) play a significant role in molecular phylogenetics, particularly in the context of distance, maximum likelihood (ML), and Bayesian es- timation. We know that the use of one or other model affects many, if not all, stages of phylogenetic inference. For example, estimates of phylogeny, substitution rates, bootstrap values, posterior probabilities, or tests of the molecular clock are clearly influenced by the model of evolution used in the analysis (Buckley, 2002; Buckley

Model Selection and Model Averaging in Phylogenetics: Advantages of Akaike Information Criterion and Bayesian Approaches Over Likelihood Ratio Tests

SIMULATED ANNEALING. Combinatorial Optimization. Simulated Annealing. Asymptotic Convergence. Finite-Time Approximation. Simulated Annealing in Practice. Parallel Simulated Annealing Algorithms. BOLTZMANN MACHINES. Neural Computing. Boltzmann Machines. Combinatorial Optimization and Boltzmann Machines. Classification and Boltzmann Machines. Learning and Boltzmann Machines. Appendix. Bibliography. Indices.

Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing.

Coupled nonnegative matrix factorization (CNMF) unmixing is proposed for the fusion of low-spatial-resolution hyperspectral and high-spatial-resolution multispectral data to produce fused data with high spatial and spectral resolutions. Both hyperspectral and multispectral data are alternately unmixed into end member and abundance matrices by the CNMF algorithm based on a linear spectral mixture model. Sensor observation models that relate the two data are built into the initialization matrix of each NMF unmixing procedure. This algorithm is physically straightforward and easy to implement owing to its simple update rules. Simulations with various image data sets demonstrate that the CNMF algorithm can produce high-quality fused data both in terms of spatial and spectral domains, which contributes to the accurate identification and classification of materials observed at a high spatial resolution.

/pdf/coupled-nonnegative-matrix-factorization-unmixing-for-2xxno0scnu.pdf

Coupled Nonnegative Matrix Factorization Unmixing for Hyperspectral and Multispectral Data Fusion

http://directory.umm.ac.id/Data%20Elmu/jurnal/J-a/Journal%20of%20Econometrics/Vol101.Issue1.2001/2183.pdf

Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models

Maximum likelihood principle and model selection when the true model is unspecified

Employing computer vision to extract useful information from images and videos is becoming a key technique for identifying phenotypic changes in plants. Here, we review the emerging aspects of computer vision for automated plant phenotyping. Recent advances in image analysis empowered by machine learning-based techniques, including convolutional neural network-based modeling, have expanded their application to assist high-throughput plant phenotyping. Combinatorial use of multiple sensors to acquire various spectra has allowed us to noninvasively obtain a series of datasets, including those related to the development and physiological responses of plants throughout their life. Automated phenotyping platforms accelerate the elucidation of gene functions associated with traits in model plants under controlled conditions. Remote sensing techniques with image collection platforms, such as unmanned vehicles and tractors, are also emerging for large-scale field phenotyping for crop breeding and precision agriculture. Computer vision-based phenotyping will play significant roles in both the nowcasting and forecasting of plant traits through modeling of genotype/phenotype relationships.

Computer vision-based phenotyping for improvement of plant productivity: a machine learning perspective

Thermal infrared measurements of Band 6 acquired by Landsat TM sensor have lower spatial resolution than those of the other six bands. The authors propose a statistical approach to enhance the resolution of low spatial resolution image by using remaining bands. They employ a multivariate normal distribution for the seven band values. The values of Band 6 are predicted by the conditional expectations. Validity of their procedure is examined by mean squared errors based on actual images.

Enhancement of low spatial resolution image based on high resolution-bands

Several measures assessing accuracy of land-cover classification are available, e.g., overall and class-averaged accuracies. Also the kappa statistic is widely used for this purpose. The authors discuss properties of these criteria and point out that the kappa statistic has an unfavorable feature. They propose an alternative coefficient based on Kullback-Leibler information. A test statistic for significance difference between coefficients is also established. Further, the Bayes risk, which takes types of misclassifications into account, is discussed. Their assessment measures are examined through actual error matrices by Z. Ma and R. L. Redmond (1995).

Accuracy and inaccuracy assessments in land-cover classification

We consider a supervised classification of hyperspectral data using AdaBoost with stump functions as base classifiers. We used the bootstrap method without replacement to improve stability and accuracy and to reduce overtraining. We randomly split a data set into two subsets: one for training and the other one for validation. Subsampling and training/validation steps were repeated to derive the final classifier by the majority vote of the classifiers. This method enabled us to estimate variable relevance to the classification. The relevance measure was used to estimate prior probabilities of the variables for random combinations. In numerical experiments with multispectral and hyperspectral data, the proposed method performed extremely well and showed itself to be superior to support vector machines, artificial neural networks, and other well-known classification methods.

Ryuei Nishii

Papers

Maximum likelihood principle and model selection when the true model is unspecified

Computer vision-based phenotyping for improvement of plant productivity: a machine learning perspective

Enhancement of low spatial resolution image based on high resolution-bands

Accuracy and inaccuracy assessments in land-cover classification

Hyperspectral Image Classification by Bootstrap AdaBoost With Random Decision Stumps