scholarly journals Estimation of graphical models whose conditional independence graphs are interval graphs and its application to modelling linkage disequilibrium

2009 ◽  
Vol 53 (5) ◽  
pp. 1818-1828 ◽  
Author(s):  
Alun Thomas
Keyword(s):  
Linkage Disequilibrium ◽  
Graphical Models ◽  
Conditional Independence ◽  
Interval Graphs ◽  
Independence Graphs

Seasonal Variability of Relationship between Main Ionospheric Characteristics and Solar/Geomagnetic Indices via Graphical Models of Conditional Independences

2021 ◽  
Author(s):  
Kateřina Podolská ◽  
Petra Koucká Knížová ◽  
Jaroslav Chum
Keyword(s):  
Time Series ◽  
Graphical Models ◽  
Seasonal Variations ◽  
Conditional Independence ◽  
Solar Cycles ◽  
Seasonal Differences ◽  
Ionospheric Response ◽  
Geomagnetic Indices ◽  
Before And After ◽  
Independence Graphs

<p>We investigated seasonal variations of relationships between main ionospheric characteristics and solar and geomagnetic indices in longitudinal perspective. We consider statistically significant differences in connections of ionospheric response to the F10.7cm, R, and Kp indices on seasonal time-scales during years 1975 – 2010 covering 21<sup>st</sup> – 23<sup>rd</sup> Solar Cycles. The periods of 21 days before and after Winter/Summer Solstices and Vernal/Autumnal Equinoces are considered as season. The foF2 time series in our analysis represent measurements of daily observational data which were obtained using mid-latitude (41.4°N – 54°N) ionosondes (Chilton, Slough RL052/SL051, Juliusruh/Rugen JR055, Boulder BC840). We used local time noon 5-hour foF2 averages. For the investigation, we used seasonal differences method of conditional independence graphs (CIG) models. Significant seasonal variations are visible during ascending and descending phases of Solar cycles.</p>

scholarly journals Conditional independence test by generalized Kendall’s tau with generalized odds ratio

2017 ◽  
Vol 27 (11) ◽  
pp. 3224-3235 ◽  
Author(s):  
Shuang Ji ◽  
Jing Ning ◽  
Jing Qin ◽  
Dean Follmann
Keyword(s):  
Graphical Models ◽  
Odds Ratio ◽  
Conditional Independence ◽  
Model Building ◽  
Association Studies ◽  
Test Procedure ◽  
Finite Sample ◽  
Test Statistic ◽  
Kendall’S Tau ◽  
Kendall's Tau

Determining conditional dependence is a challenging but important task in both model building and in applications such as genetic association studies and graphical models. Research on this topic has focused on kernel-based methods or has used categorical conditioning variables because of the challenge of the curse of dimensionality. To overcome this challenge, we propose a class of tests for conditional independence without any restriction on the distribution of the conditioning variables. The proposed test statistic can be treated as a generalized weighted Kendall’s tau, in which the generalized odds ratio is utilized as a weight function to account for the distance between different values of the conditioning variables. The test procedure has desirable asymptotic properties and is easy to implement. We evaluate the finite sample performance of the proposed test through simulation studies and illustrate it using two real data examples.

scholarly journals One-component regular variation and graphical modeling of extremes

2016 ◽  
Vol 53 (3) ◽  
pp. 733-746 ◽  
Author(s):  
Adrien Hitz ◽  
Robin Evans
Keyword(s):  
Graphical Models ◽  
Regular Variation ◽  
Conditional Independence ◽  
Probability Distributions ◽  
Value Theory ◽  
High Dimensional ◽  
Regularly Varying Functions ◽  
Graphical Modeling ◽  
Multivariate Extreme Value Theory ◽  
Regularly Varying

AbstractThe problem of inferring the distribution of a random vector given that its norm is large requires modeling a homogeneous limiting density. We suggest an approach based on graphical models which is suitable for high-dimensional vectors. We introduce the notion of one-component regular variation to describe a function that is regularly varying in its first component. We extend the representation and Karamata's theorem to one-component regularly varying functions, probability distributions and densities, and explain why these results are fundamental in multivariate extreme-value theory. We then generalize the Hammersley–Clifford theorem to relate asymptotic conditional independence to a factorization of the limiting density, and use it to model multivariate tails.

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