PAML, currently in version 4, is a package of programs for phylogenetic analyses of DNA and protein sequences using maximum likelihood (ML). The programs may be used to compare and test phylogenetic trees, but their main strengths lie in the rich repertoire of evolutionary models implemented, which can be used to estimate parameters in models of sequence evolution and to test interesting biological hypotheses. Uses of the programs include estimation of synonymous and nonsynonymous rates (d(N) and d(S)) between two protein-coding DNA sequences, inference of positive Darwinian selection through phylogenetic comparison of protein-coding genes, reconstruction of ancestral genes and proteins for molecular restoration studies of extinct life forms, combined analysis of heterogeneous data sets from multiple gene loci, and estimation of species divergence times incorporating uncertainties in fossil calibrations. This note discusses some of the major applications of the package, which includes example data sets to demonstrate their use. The package is written in ANSI C, and runs under Windows, Mac OSX, and UNIX systems. It is available at -- (http://abacus.gene.ucl.ac.uk/software/paml.html).

/pdf/paml-4-phylogenetic-analysis-by-maximum-likelihood-2gg19rsgos.pdf

PAML 4: Phylogenetic Analysis by Maximum Likelihood

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Statistics for Spatial Data.

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

The talk with present the key results of the IPCC Working Group III 5th assessment report. Concluding four years of intense scientific collaboration by hundreds of authors from around the world, the report responds to the request of the world's governments for a comprehensive, objective and policy neutral assessment of the current scientific knowledge on mitigating climate change. The report has been extensively reviewed by experts and governments to ensure quality and comprehensiveness.

Climate change 2014 - Mitigation of climate change

Interpolation of a spatially correlated random process is used in many scientific areas. The best unbiased linear predictor, often called a kriging predictor in geostatistical science, requires the solution of a (possibly large) linear system based on the covariance matrix of the observations. In this article, we show that tapering the correct covariance matrix with an appropriate compactly supported positive definite function reduces the computational burden significantly and still leads to an asymptotically optimal mean squared error. The effect of tapering is to create a sparse approximate linear system that can then be solved using sparse matrix algorithms. Monte Carlo simulations support the theoretical results. An application to a large climatological precipitation dataset is presented as a concrete and practical illustration.

https://www.zora.uzh.ch/id/eprint/21612/2/ZORA-21612V.pdf

Covariance Tapering for Interpolation of Large Spatial Datasets

In this paper, we present classes of kernels for machine learning from a statistics perspective. Indeed, kernels are positive definite functions and thus also covariances. After discussing key properties of kernels, as well as a new formula to construct kernels, we present several important classes of kernels: anisotropic stationary kernels, isotropic stationary kernels, compactly supported kernels, locally stationary kernels, nonstationary kernels, and separable nonstationary kernels. Compactly supported kernels and separable nonstationary kernels are of prime interest because they provide a computational reduction for kernel-based methods. We describe the spectral representation of the various classes of kernels and conclude with a discussion on the characterization of nonlinear maps that reduce nonstationary kernels to either stationarity or local stationarity.

/pdf/classes-of-kernels-for-machine-learning-a-statistics-1uadpki8kb.pdf

Classes of kernels for machine learning: a statistics perspective

This book reviews the state-of-the-art advances in skew-elliptical distributions and provides many new developments in a single volume, collecting theoretical results and applications previously scattered throughout the literature. The main goal of this research area is to develop flexible parametric classes of distributions beyond the classical normal distribution. The book is divided into two parts. The first part discusses theory and inference for skew-elliptical distribution. The second part presents applications and case studies in areas such as economics, finance, oceanography, climatology, environmetrics, engineering, image processing, astronomy, and biomedical science.

Skew-Elliptical Distributions and Their Applications : A Journey Beyond Normality

On fundamental skew distributions

Geostatistical approaches to modeling spatio-temporal data rely on parametric covariance models and rather stringent assumptions, such as stationarity, separability and full symmetry. This paper reviews recent advances in the literature on space-time covariance functions in light of the aforementioned notions, which are illustrated using wind data from Ireland. Experiments with time-forward kriging predictors suggest that the use of more complex and more realistic covariance models results in improved predictive performance.

Marc G. Genton

Papers

Covariance Tapering for Interpolation of Large Spatial Datasets

Classes of kernels for machine learning: a statistics perspective

Skew-Elliptical Distributions and Their Applications : A Journey Beyond Normality

On fundamental skew distributions

Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry