p ̂ y, PD is an estimate of the joint probability density function (pdf) of dimension PD over all P (here, P = 2) output channels, and p ̂ y q, D is the estimated multivariate pdf for channel q of dimension D. Matrix W captures all the impulse response coefficients of the demixing filters, with a detailed description of its structure given in [31, 32].
The multivariate pdfs for a correlation vector (exploiting the CP property) under both hypotheses (i.e., presence and absence of primary) are calculated.
While the example presented (Table 4 and Figure 3) used only a single CNP as an illustration, the LRTS can be calculated for multiple SNPs analyzed simultaneously through specification of a multivariate pdf.
Based on Sklar's theorem [29], any arbitrary multivariate pdf f X (x) can be expressed as the product of two terms: the marginal pdf of dimensions ( {f}_{{mathtt{X}}_j}left({x}_jright),kern0.24em j=1:d ) and the copula density function c X as shown in Eq. (2).
The corresponding multivariate pdf is given in the following form: Figure 3 Illustration of the proposed dependency model.
The likelihood of y i is computed by the following multivariate pdf [19, 20]: p ( y i ) ∝ exp - ∑ b = 1 B | y i b | 2. (10).
It is shown in (3) that a multivariate PDF is constructed by multiplying a copula density function and a set of marginal PDFs in which the copula density function can be selected independent of the margins.
where f(x) is the multivariate pdf.
For n markers, the multivariate pdf is given by the following equation (Eq. 3).
