exact.q: Compute exact LR exceedance probabilities
In DNAprofiles: DNA Profiling Evidence Analysis

Description Usage Arguments Details Value Examples

Compute exact LR exceedance probabilities

1	exact.q(t, dists)

`t`	numeric (vector), threshold
`dists`	list of per-locus probability distributions of a likelihood ratio

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 computes q_{t|H} by brute force.

numeric (vector) with estimated probabilities

data(freqsNLsgmplus)

x <- sample.profiles(N = 1, freqsNLsgmplus)

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

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

set.seed(100)

# estimate P(PI>1e4) for true PO
sim.q(t=1e4,dists=hp)

# estimate P(PI>1e4) for unrelated pairs
sim.q(t=1e4,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=1e4,dists=hd,dists.sample=hp)

# compare to exact values
exact.q(t = 1e4, dists=hp)
exact.q(t = 1e4, dists=hd)