# dbVariance: Covariance matrix of cell counts in DNA database comparison In DNAtools: Tools for Analysing Forensic Genetic DNA Data

 dbVariance R Documentation

## 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.