# PV: Predictive value of the maximum likelihood estimator of the... In forensim: Statistical tools for the interpretation of forensic DNA mixtures

## Description

The `PV` function implements the predictive value of the maximum likelihood estimator of the number of contributors to a DNA mixture

## Usage

 `1` ```PV(mat, prior) ```

## Arguments

 `mat` matrix giving the estimates of the conditional probabilities that the maximum likelihood estimator classifies a given stain as a mixture of i contributors given that there are k contributor(s) to the stain. Estimates i must be given in columns for each possible value of the number of contributors given in rows. `prior` numeric vector giving the prior probabilities of encountering a mixture of i contributors. `prior` must be of length the number of rows in `mat`.

## Value

Vector of the predictive values

## Author(s)

Hinda Haned <[email protected]>

## References

Haned H., Pene L., Sauvage F., Pontier D., The predictive value of the maximum likelihood estimator of the number of contributors to a DNA mixture, submitted, 2010.

maximum likelihood estimator `likestim`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```# the following examples reproduce some of the calculations appearing # in the article cited above, for illustrative purpose, the maximum #number of contributors is set here to 5 #matcondi: Table 2 in Haned et al. (2010) matcondi<-matrix(c(1,rep(0,4),0,0.998,0.005,0,0,0,0.002,0.937,0.067,0,0,0,0.058, 0.805,0.131,rep(0,3),0.127,0.662,rep(0,3),0.001,0.207),ncol=6) #prior defined by a forensic expert (Table 3 in Haned et al., 2010) prior1<-c(0.45,0.04,0.30,0.15,0.06) #uniform prior, for each mixture type, the probability of occurrence is 1/5, #5 being the threshold for the number of contributors prior2<-c(rep(1/5,5)) #predictive values for prior1 PV(matcondi,prior1) #for prior2 PV(matcondi, prior2) ```