TwoLevelLR: Two Level Multivariate Likelihood ratio
In ForensicDocument: Quantification and evaluation tools for forensic document examiners

Description Usage Arguments Details Value Author(s) References See Also Examples

Computes a two level multivariate likelihood ratio.

1	TwoLevelLR(data1, data2, background, n.iter = 1100, n.burnin = 100, nw)

`data1`	measurements from the 'reference' material.
`data2`	measurements from the 'questioned' material.
`background`	background parameters for the overall and group means, within- and between group variances and covariances matrice.
`n.iter`	number of MCMC iterations. Default is `10000`.
`n.burnin`	number of burn-in iterations. Default is `1000`.
`nw`	degrees of freedom for the inverse Wishart distribution. Considering p variables in the data, nw must be > 2*p+4.

This methodology has been developed by Bozza et al. (2008) for the assesment of evidence through the derivation of a likelihood ratio for multivariate data. It allows to take into account the correlation between variables, and the non-constant variability within sources.

In the context of handwritten expertise suppose that: (i) an anonymous letter (i.e. the questioned document) is available for comparative analysis, and (ii) written material from a suspect is selected for comparative purposes (i.e. the reference document. For the compuation of the likelihood ratio, we consider the following propositions of interest:

H_pthe suspect is the author of the questioned document;
H_dthe suspect is not the author of the questioned document - a random person wrote the document.

The value of the log likelihood ratio (log(LR)).

Silvia Bozza
Alexandre Thiery

Bozza S, Taroni F, Marquis R and Schmittbuhl M (2008). "Probabilistic evaluation of handwriting evidence: likelihood ratio for authorship." Journal of the Royal Statistical Society: Series C (Applied Statistics), 57 (3), pp. 329-341.

TwoLevelLR_Background

## Not run: 
## Example where Hp is true.
## That is, when the suspect is the author of the questioned document

## DATASET: We use the `characterO` dataset. It contains the extracted Fourier (`n.fourier = 4`) parameters from 554 handwritten character loops, written by 11 writers. For more information, see `?characterO`.
data(characterO)

## PARAMETERS:
# data1: (reference document), the first 23 characters of writer 1
# data1: (questioned document), the last 23 characters of writer 1
# background: data from the remaining 10 writers
# n.iter: 11000
# n.burnin: 1000
# nw: 50


# data1, data2
data_reference = subset(characterO$measurements[,-1], subset = (characterO$info$writer == 1))[1:23,]
data_questioned = subset(characterO$measurements[,-1], subset = (characterO$info$writer == 1))[-(1:23),]

# background
subset = characterO$info$writer != 1
data_back = subset(characterO$measurements[,-1], subset = subset)
background = TwoLevelLR_Background(data_back, fac = as.factor(characterO$info$writer[subset]))

# others
n.iter = 11000
n.burnin = 1000
nw  = 50

# compute LLR
LLR = TwoLevelLR(data1 = data_reference,
                 data2 = data_questioned,
                 background = background,
                 n.iter = n.iter, n.burnin = n.burnin,
                 nw = nw)
LLR

## End(Not run)