A multivariate structure with pairwise correlations instead of mutual independence allows for a better capture of multipollutant properties.
In the UK or the USA, the relationship between the state and civil society is changing from mutual independence to a cross-sectoral partnership, and boundaries between these different sectors may gradually disappear.
We chose a χ2 test to evaluate the mutual independence of positions in order to extract from this set the couples of potential synthetic lethality.
Especially in the context of QTL detection, the collinearity of the putative predictors (SNP) in genome-wide dense marker data may cause problems in multi-locus models that assume mutual independence of predictors a priori, such as scattering of QTL signals over several markers.
The assumption of mutual independence of the events within a subject is equivalent to the assumption of independent increments in the counting process inside each individual.
It should be clear that pairwise independence is not equivalent to mutual independence but in an ICA context, it is relevant to recall the following proposition, which is a direct consequence of Darmois' theorem ([25], p. 294): Let s be a random vector with mutually independent components, and x=G s.
If this assumption of mutual independence is true, an over-representation of statistically significant SNPs in this region constitutes evidence that this region is associated with the phenotype, with the extent of over-representation indicating the strength of the evidence.
However, literature review finds that most of the BSS based fault detectors did not address the dependence/correlation between different moving components in the gear systems; particularly, the popular used independent component analysis (ICA) assumes mutual independence of different vibration sources.
Once the connection probabilities between metabolites and reactions are estimated from the model, and assuming their mutual independence, the probability that a certain combination ν of metabolites co-occur in a reaction r is (1) where the subindex m corresponds to metabolites in the predefined set ν and m' to those not included.
Although the theorem has since been generalized, [18] mutual independence would clearly not be an optimal arrangement for scientists either within a cross-functional project team or in the larger working group charged with such decisions.
