Compute the posterior probabilities for P(m|n0) for a given prior P(m) and observed vector n0 of locus counts

where m ranges from 1 to \(m_{\max}\) and \(n_0\) is the observed locus counts.

pContrib(n0, probs = NULL, m.prior = rep(1/m.max, m.max), m.max = 8, theta = 0)

Arguments

n0	Vector of observed allele counts - same length as the number of loci.
probs	List of vectors with allele probabilities for each locus
m.prior	A vector with prior probabilities (summing to 1), where the length of m.prior determines the plausible range of m
m.max	Derived from the length of m.prior, and if m.prior=NULL a uniform prior is speficied by m.max: m.prior = rep(1/m.max,m.max).
theta	The coancestery coefficient

Value

Returns a vector P(m|n0) for m=1,...,m.max

Details

Computes a vector P(m|n0) evaluated over the plausible range 1,...,m.max.

References

T. Tvedebrink (2014). 'On the exact distribution of the number of alleles in DNA mixtures', International Journal of Legal Medicine; 128(3):427--37. <https://doi.org/10.1007/s00414-013-0951-3>

Examples

  ## Simulate some allele frequencies:
  freqs <-  simAlleleFreqs()
  m <- 2
  n0 <- sapply(freqs, function(px){
                            peaks = unique(sample(length(px),
                                             size = 2 * m,
                                             replace = TRUE,
                                             prob = px))
                            return(length(peaks))
                       })
  ## Compute P(m|n0) for m=1,...,4 and the sampled n0
  pContrib(n0=n0,probs=freqs,m.max=4)
#>    P(m=1|n0)    P(m=2|n0)    P(m=3|n0)    P(m=4|n0) 
#> 0.000000e+00 9.999777e-01 2.229176e-05 1.361702e-11