Vienna University of Technology

About: Vienna University of Technology is a education organization based out in Vienna, Austria. It is known for research contribution in the topics: Laser & Context (language use). The organization has 16723 authors who have published 49341 publications receiving 1302168 citations.

Statistical Methods for Non-Precise Data

Abstract: Non-Precise Data and Their Formal Description Non-Precise Data Non-Precise Numbers and Characterizing Functions Construction of Characterizing Functions Non-Precise Vectors Functions of Non-Precise Quantities and Non-Precise Functions Descriptive Statistics with Non-Precise Data Non-Precise Samples Histograms for Non-Precise Data Cumulative Sums for Non-Precise Data Empirical Distribution Function for Non-Precise Data Empirical Fractiles for Non-Precise Data Foundations for Statistical Inference with Non-Precise Data Combination of Non-Precise Observations Sample Moment for Non-Precise Observations Sequences of Non-Precise Observations Classical Statistical Inference for Non-Precise Data Point Estimators for Parameters Confidence Regions for Parameters Nonparametric Estimation Statistical Tests and Non-Precise Data Bayesian Inference for Non-Precise Data Bayes' Theorem for Non-Precise Data Bayesian Confidence Regions Based on Non-Precise Data Non-Precise Predictive Distributions Non-Precise a priori Distributions Bayes Theorem for Non-Precise a priori Distribution and Non-Precise Data Bayesian Decisions Based on Non-Precise Information Outlook References List of Symbols Index

On a problem of optimal transport under marginal martingale constraints

Abstract: The basic problem of optimal transportation consists in minimizing the expected costs $\mathbb{E} [c(X_{1},X_{2})]$ by varying the joint distribution $(X_{1},X_{2})$ where the marginal distributions of the random variables $X_{1}$ and $X_{2}$ are fixed. Inspired by recent applications in mathematical finance and connections with the peacock problem, we study this problem under the additional condition that $(X_{i})_{i=1,2}$ is a martingale, that is, $\mathbb{E} [X_{2}|X_{1}]=X_{1}$. We establish a variational principle for this problem which enables us to determine optimal martingale transport plans for specific cost functions. In particular, we identify a martingale coupling that resembles the classic monotone quantile coupling in several respects. In analogy with the celebrated theorem of Brenier, the following behavior can be observed: If the initial distribution is continuous, then this “monotone martingale” is supported by the graphs of two functions $T_{1},T_{2}:\mathbb{R} \to\mathbb{R}$.

Unambiguous identification of fungi: where do we stand and how accurate and precise is fungal DNA barcoding?

Abstract: True fungi (Fungi) and fungus-like organisms (e.g. Mycetozoa, Oomycota) constitute the second largest group of organisms based on global richness estimates, with around 3 million predicted species. Compared to plants and animals, fungi have simple body plans with often morphologically and ecologically obscure structures. This poses challenges for accurate and precise identifications. Here we provide a conceptual framework for the identification of fungi, encouraging the approach of integrative (polyphasic) taxonomy for species delimitation, i.e. the combination of genealogy (phylogeny), phenotype (including autecology), and reproductive biology (when feasible). This allows objective evaluation of diagnostic characters, either phenotypic or molecular or both. Verification of identifications is crucial but often neglected. Because of clade-specific evolutionary histories, there is currently no single tool for the identification of fungi, although DNA barcoding using the internal transcribed spacer (ITS) remains a first diagnosis, particularly in metabarcoding studies. Secondary DNA barcodes are increasingly implemented for groups where ITS does not provide sufficient precision. Issues of pairwise sequence similarity-based identifications and OTU clustering are discussed, and multiple sequence alignment-based phylogenetic approaches with subsequent verification are recommended as more accurate alternatives. In metabarcoding approaches, the trade-off between speed and accuracy and precision of molecular identifications must be carefully considered. Intragenomic variation of the ITS and other barcoding markers should be properly documented, as phylotype diversity is not necessarily a proxy of species richness. Important strategies to improve molecular identification of fungi are: (1) broadly document intraspecific and intragenomic variation of barcoding markers; (2) substantially expand sequence repositories, focusing on undersampled clades and missing taxa; (3) improve curation of sequence labels in primary repositories and substantially increase the number of sequences based on verified material; (4) link sequence data to digital information of voucher specimens including imagery. In parallel, technological improvements to genome sequencing offer promising alternatives to DNA barcoding in the future. Despite the prevalence of DNA-based fungal taxonomy, phenotype-based approaches remain an important strategy to catalog the global diversity of fungi and establish initial species hypotheses.