Penalized Maximum Likelihood Estimator for Finite Skew-Laplace-Normal Mixtures

Skew-Laplace-Normal Mixture models is a more flexible framework than the normal mixture models for heterogeneous data with asymmetric behaviors. But it’s likelihood function have some bad math properties, such as the unboundedness of likelihood function and the divergency of skewness parameter, it often mislead statistic inference. In this paper, we given a penalizing the likelihood function method to deal with these problem simultaneously, and we given the detail of proof on parameter have strongly consistency. We also give a modified penalized EM-type algorithms to compute penalized estimators.

Nonparametric Bayesian Learning of Infinite Multivariate Generalized Normal Mixture Models and Its Applications

This paper addresses the problem of data vectors modeling, classification and recognition using infinite mixture models, which have been shown to be an effective alternative to finite mixtures in terms of selecting the optimal number of clusters. In this work, we propose a novel approach for localized features modelling using an infinite mixture model based on multivariate generalized Normal distributions (inMGNM). The statistical mixture is learned via a nonparametric MCMC-based Bayesian approach in order to avoid the crucial problem of model over-fitting and to allow uncertainty in the number of mixture components. Robust descriptors are derived from encoding features with the Fisher vector method, which considers higher order statistics. These descriptors are combined with a linear support vector machine classifier in order to achieve higher accuracy. The efficiency and merits of the proposed nonparametric Bayesian learning approach, while comparing it to other different methods, are demonstrated via two challenging applications, namely texture classification and human activity categorization.

The Nature of Espeletia Species

Species are often regarded as basic units of study in biology, following the presumption that they are real and discrete natural entities. But several biologists wonder if species are arbitrary divisions that do not correspond to discrete natural groups of organisms. Two issues must be addressed to solve this controversy, but few studies seem to do so. The first is whether organisms form sympatric and synchronic groups that are distinct in terms of phenotypes and genome-wide allele frequencies, often called “good species.” Alternatives to “good species” include “cryptic species,” syngameons and, more generally, cases in which phenotypes and genome-wide allele frequencies reflect contrasting evolutionary histories. The second issue is the degree to which species taxa (i.e., taxonomic classification at the species level) reflect natural groups of organisms or constitute arbitrary divisions of biological diversity. Here, we empirically addressed both issues by studying plants of the Andean genus Espeletia (Asteraceae). We collected a geographically dense sample of 538 specimens from the paramo de Sumapaz, in the Cordillera Oriental of Colombia. Additionally, we examined 165 herbarium specimens previously collected by other researchers in this region, or from taxa known to occur there. We tested for the existence of phenotypic groups using normal mixture models and data on 13 quantitative characters. Among 307 specimens with all 13 measurements, we found six distinct phenotypic groups in sympatry. We also tested for the existence of groups defined by genome-wide allele frequencies, using ancestry models and data on 2,098 single nucleotide polymorphisms. Among 77 specimens with complete genomic data, we found three groups in sympatry, with high levels of admixture. Concordance between groups defined by phenotype and genome-wide allele frequencies was low, suggesting that phenotypes and genome-wide allele frequencies reflect contrasting evolutionary histories. Moreover, the high levels of admixture suggest that Espeletia plants form a syngameon in the paramo de Sumapaz. To determine the extent to which species taxa corresponded to phenotypic and genomic groups, we used data on 12 phenotypic characters to assign 307 specimens to species taxa, according to descriptions of species taxa in the most recent monograph of Espeletia. This sample included 27 specimens cited in the monograph. Remarkably, only one out of 307 specimens in our sample fell inside any of the phenotypic ranges reported in the monograph for the species taxa known to occur in the paramo de Sumapaz. These results show that species taxa in Espeletia are delineations of largely empty phenotypic space that miss biological diversity.