dbVariance: Covariance matrix of cell counts in DNA database comparison

In DNAtools: Tools for Analysing Forensic Genetic DNA Data

Covariance matrix of cell counts in DNA database comparison

Description

Computes the covariance matrix for the cell counts when comparing DNA profiles in a DNA database. For every pair of DNA profiles in a database the number of matching and partial matching loci is recorded. A match is declared if the two DNA profiles coincide for both alleles in a locus and a partial-match is recorded if only one allele is shared between the profiles. With a total of L loci the number of matching loci is 0,...,L and partial number of matches is 0,...,L-m, where m is the number of matching loci. The expression is given by:

{n\choose2}Var[M(G_{i_1},G_{i_2})] + 6*{n\choose3}Cov[M(G_{i_1},G_{i_2}),M(G_{i_1},G_{i_3})] + 6*{n\choose4}Cov[M(G_{i_1},G_{i_2}),M(G_{i_3},G_{i_4})]

Usage

dbVariance(probs, theta = 0, n = 1, collapse = FALSE)

Arguments

probs	List of vectors with allele probabilities for each locus
theta	The coancestery coefficient. If a vector of different theta values are supplied a list of covariance matrices is returned. Note it is faster to give a vector of theta values as argument than calculating each matrix at the time.
n	Number of DNA profiles in the database. If n=1 is supplied a list of the components for computing the variance is returned. That is, the variance and two covariances on the right hand side of the equation above.
collapse	Logical, default FALSE. If TRUE the covariance matrix is collapsed such that it relates to (2*m+p)-vectors of total number of matching alleles rather than (m,p)-matrix.

Details

Computes the covariance matrix of the cell counts using a recursion formula. See Tvedebrink et al (2011) for details.

Value

Returns a covariance matrix for the cell counts.

Author(s)

James Curran and Torben Tvedebrink

References

T Tvedebrink, PS Eriksen, J Curran, HS Mogensen, N Morling. 'Analysis of matches and partial-matches in Danish DNA reference profile database'. Forensic Science International: Genetics, 2011.

Examples

  ## Not run: 
  ## Simulate some allele frequencies:
  freqs <-  replicate(10, { g = rgamma(n=10,scale=4,shape=3); g/sum(g)}, simplify=FALSE)
  ## List of elements needed to compute the covariance matrix.
  ## Useful option when the covariance needs to be computed for varying
  ## database sizes but for identical theta-value.
  comps <- dbVariance(freqs,theta=0,n=1)
  ## Covariance for a DB with 1000 DNA profiles
  cov1000 <- dbVariance(freqs,theta=0,n=1000)
  ## The result is the same as:
  comps1000 <- choose(1000,2)*comps$V1 + 6*choose(1000,3)*comps$V2 + 6*choose(1000,4)*comps$V3
  
## End(Not run)

DNAtools documentation built on March 18, 2022, 7:01 p.m.