Table 1

Formulas for computing partial variances and partial correlations

Definition

True value

Estimate


Covariance matrix:

cov(Xk, Xl) = σkl

Σ = (σkl)

S = (skl)

Concentration matrix:

Ω = Σ-1

Ω = (ωkl)

Variances:

var(Xk) = σkk = <a onClick="popup('http://www.biomedcentral.com/1752-0509/1/37/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/1/37/mathml/M5">View MathML</a>

σkk

skk

Partial variances

var(Xk|Xk) = <a onClick="popup('http://www.biomedcentral.com/1752-0509/1/37/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/1/37/mathml/M6">View MathML</a> = <a onClick="popup('http://www.biomedcentral.com/1752-0509/1/37/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/1/37/mathml/M4">View MathML</a> = <a onClick="popup('http://www.biomedcentral.com/1752-0509/1/37/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/1/37/mathml/M7">View MathML</a>

<a onClick="popup('http://www.biomedcentral.com/1752-0509/1/37/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/1/37/mathml/M6">View MathML</a>

<a onClick="popup('http://www.biomedcentral.com/1752-0509/1/37/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/1/37/mathml/M8">View MathML</a>

Correlations:

corr(Xk, Xl) = ρkl = σkl (σkk σll)-1/2

P = (ρkl)

R = (rkl)

Partial correlations:

corr(Xk, Xl|Xk, l) = <a onClick="popup('http://www.biomedcentral.com/1752-0509/1/37/mathml/M9','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/1/37/mathml/M9">View MathML</a>

<a onClick="popup('http://www.biomedcentral.com/1752-0509/1/37/mathml/M10','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/1/37/mathml/M10">View MathML</a>

<a onClick="popup('http://www.biomedcentral.com/1752-0509/1/37/mathml/M11','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/1/37/mathml/M11">View MathML</a>


Index i runs from 1 to n (sample size), and indices k and l run from 1 to p (dimension). A tilde denotes a "partial" quantity.

Opgen-Rhein and Strimmer BMC Systems Biology 2007 1:37   doi:10.1186/1752-0509-1-37

Open Data