13 research outputs found
Equations defining probability tree models
Coloured probability tree models are statistical models coding conditional
independence between events depicted in a tree graph. They are more general
than the very important class of context-specific Bayesian networks. In this
paper, we study the algebraic properties of their ideal of model invariants.
The generators of this ideal can be easily read from the tree graph and have a
straightforward interpretation in terms of the underlying model: they are
differences of odds ratios coming from conditional probabilities. One of the
key findings in this analysis is that the tree is a convenient tool for
understanding the exact algebraic way in which the sum-to-1 conditions on the
parameter space translate into the sum-to-one conditions on the joint
probabilities of the statistical model. This enables us to identify necessary
and sufficient graphical conditions for a staged tree model to be a toric
variety intersected with a probability simplex.Comment: 22 pages, 4 figure
Equivalence Classes of Staged Trees
In this paper we give a complete characterization of the statistical
equivalence classes of CEGs and of staged trees. We are able to show that all
graphical representations of the same model share a common polynomial
description. Then, simple transformations on that polynomial enable us to
traverse the corresponding class of graphs. We illustrate our results with a
real analysis of the implicit dependence relationships within a previously
studied dataset.Comment: 18 pages, 4 figure
Sensitivity analysis in multilinear probabilistic models
Sensitivity methods for the analysis of the outputs of discrete Bayesian networks have been extensively studied and implemented in different software packages. These methods usually focus on the study of sensitivity functions and on the impact of a parameter change to the ChanâDarwiche distance. Although not fully recognized, the majority of these results rely heavily on the multilinear structure of atomic probabilities in terms of the conditional probability parameters associated with this type of network. By defining a statistical model through the polynomial expression of its associated defining conditional probabilities, we develop here a unifying approach to sensitivity methods applicable to a large suite of models including extensions of Bayesian networks, for instance context-specific ones. Our algebraic approach enables us to prove that for models whose defining polynomial is multilinear both the ChanâDarwiche distance and any divergence in the family of Ï-divergences are minimized for a certain class of multi-parameter contemporaneous variations when parameters are proportionally covaried
Discovery of statistical equivalence classes using computer algebra
Discrete statistical models supported on labelled event trees can be
specified using so-called interpolating polynomials which are generalizations
of generating functions. These admit a nested representation. A new algorithm
exploits the primary decomposition of monomial ideals associated with an
interpolating polynomial to quickly compute all nested representations of that
polynomial. It hereby determines an important subclass of all trees
representing the same statistical model. To illustrate this method we analyze
the full polynomial equivalence class of a staged tree representing the best
fitting model inferred from a real-world dataset.Comment: 26 pages, 9 figure
Staged tree models with toric structure
A staged tree model is a discrete statistical model encoding relationships
between events. These models are realised by directed trees with coloured
vertices. In algebro-geometric terms, the model consists of points inside a
toric variety. For certain trees, called balanced, the model is in fact the
intersection of the toric variety and the probability simplex. This gives the
model a straightforward description, and has computational advantages. In this
paper we show that the class of staged tree models with a toric structure
extends far outside of the balanced case, if we allow a change of coordinates.
It is an open problem whether all staged tree models have toric structure
Global projections of the soil microbiome in the Anthropocene
Aim: Soil microbes are essential for maintenance of lifeâsupporting ecosystem services, but projections of how these microbes will be affected by global change scenarios are lacking. Therefore, our aim was to provide projections of future soil microbial distribution using several scenarios of global change. Location: Global. Time period: 1950â2090. Major taxa studied: Bacteria and fungi. Methods: We used a global database of soil microbial communities across six continents to estimate past and future trends of the soil microbiome. To do so, we used structural equation models to include the direct and indirect effects of changes in climate and land use in our predictions, using current climate (temperature and precipitation) and landâuse projections between 1950 and 2090. Results: Local bacterial richness will increase in all scenarios of change in climate and land use considered, although this increase will be followed by a generalized community homogenization process affecting > 85% of terrestrial ecosystems. Changes in the relative abundance of functional genes associated with the increases in bacterial richness are also expected. Based on an ecological cluster analysis, our results suggest that phylotypes such as Geodermatophilus spp. (typical desert bacteria), Mycobacterium sp. (which are known to include important human pathogens), Streptomyces mirabilis (major producers of antibiotic resistance genes) or potential fungal soilâborne plant pathogens belonging to Ascomycota fungi (Venturia spp., Devriesia spp.) will become more abundant in their communities. Main conclusions: Our results provide evidence that climate change has a stronger influence on soil microbial communities than change in land use (often including deforestation and agricultural expansion), although most of the effects of climate are indirect, through other environmental variables (e.g., changes in soil pH). The same was found for microbial functions such as the prevalence of phosphate transport genes. We provide reliable predictions about the changes in the global distribution of microbial communities, showing an increase in alpha diversity and a homogenization of soil microbial communities in the Anthropocene.This manuscript was developed from discussions within the German Centre of Integrative Biodiversity Research funded by the Deutsche Forschungsgemeinschaft (DFG FZT118). C.A.G. and N.E. acknowledge funding by iDiv (DFG FZT118) Flexpool proposals 34600850 and 34600844. N.E. acknowledges funding by the DFG (FOR 1451) and the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 677232). E.D. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG GRK 2297 â314838170), MathCoRe. M.D.-B. acknowledges support from the Marie Sklodowska-Curie Actions of the Horizon 2020 Framework Program H2020-MSCA-IF-2016 under REA grant agreement number 702057. F.T.M. acknowledges support from the European Research Council grant agreement number 647038 (BIODESERT)
Research-Data Management Planning in the German Mathematical Community
In this paper we discuss the notion of research data for the field of
mathematics and report on the status quo of research-data management and
planning. A number of decentralized approaches are presented and compared to
needs and challenges faced in three use cases from different mathematical
subdisciplines. We highlight the importance of tailoring research-data
management plans to mathematicians' research processes and discuss their usage
all along the data life cycle
Entwicklungsförderung und GewaltprĂ€vention fĂŒr junge Menschen. Impulse des DFK-SachverstĂ€ndigenrates fĂŒr die Auswahl & DurchfĂŒhrung wirksamer Programme. Ein Leitfaden fĂŒr die Praxis
Die Stiftung Deutsches Forum fĂŒr KriminalprĂ€vention (DFK) befasst sich kontinuierlich und
schwerpunktmĂ€Ăig mit der Frage, wie GewaltprĂ€vention systematisch und nachhaltig gestaltet
und verbreitet werden kann. Ergebnis ist der vorliegende Leitfaden âEntwicklungsförderung und GewaltprĂ€vention
fĂŒr junge Menschenâ, der im Rahmen des 18. Deutschen PrĂ€ventionstages (DPT) in Bielefeld
vorgestellt und diskutiert wird. Er knĂŒpft an die Expertise âGelingensbedingungen fĂŒr die PrĂ€vention
von interpersonaler Gewalt im Kindes- und Jugendalterâ an und erweitert die fördernde
und prÀventive Perspektive insbesondere um Aspekte der EffektivitÀt, der Messung von Wirksamkeit
und UmsetzungsqualitĂ€t sowie der Implementierung in Kitas und Schulen. SchlieĂlich
werden Fragen des Transfers und einer weitergehenden Verbreitung (Dissemination) von wirksamen
und praxistauglichen PrÀventionsangeboten erörtert.
Der Leitfaden richtet sich an professionelle Praktiker, aber auch an Entscheidungsverantwortliche
in Institutionen, in Verwaltung und nicht zuletzt in Politik