sim.q: Estimate LR exceedance probabilities (with importance...
In DNAprofiles: DNA Profiling Evidence Analysis

Description Usage Arguments Details Value Examples

Estimate LR exceedance probabilities (with importance sampling)

1	sim.q(t, dists, N = 1e+05, dists.sample = dists)

`t`	numeric (vector), threshold
`dists`	list of per-locus probability distributions of a likelihood ratio
`N`	integer, number of samples
`dists.sample`	if dists.sample is not equal to dists, then importance sampling is applied. Sampling is done according to dists.sample, while exceedance probabilities are estimated for dists.

For a combined likelihood ratio

LR=LR_1 LR_2 \times LR_m,

define q_{t|H} as the probability that the LR exceeds t under hypothesis H, i.e.:

q_{t|H} := P(LR>t|H).

The hypothesis H can be H_p, H_d or even another hypothesis. The current function estimates q_{t|H} by taking N samples from the distributions specified by the dists parameter and computing the empirical fraction of the product of the samples that exceeds t.

Importance sampling can be used by supplying different distributions to sample from and to estimate the exceedance probabilities for. For instance, the exceedance probability for H_d can be estimated by sampling from H_p and an appropriate weighting of the samples. See the paper and examples for details.

numeric (vector) with estimated probabilities

data(freqsNLngm)

# dist of PI for true parent/offspring pairs
hp <- ki.dist(hyp.1="PO",hyp.2="UN",hyp.true="PO",freqs.ki=freqsNLngm)

# dist of PI for unrelated pairs
hd <- ki.dist(hyp.1="PO",hyp.2="UN",hyp.true="UN",freqs.ki=freqsNLngm)

set.seed(100)

# estimate P(PI>1e6) for true PO
sim.q(t=1e6,dists=hp)

# estimate P(PI>1e6) for unrelated pairs
sim.q(t=1e6,dists=hd) # small probability, so no samples exceed t=1e6

# importance sampling can estimate the small probability reliably
# by sampling from H_p and weighting the samples appropriately
sim.q(t=1e6,dists=hd,dists.sample=hp)