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

## Description

Estimate LR exceedance probabilities (with importance sampling)

## Usage

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

## Arguments

 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.

## Details

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.

## Value

numeric (vector) with estimated probabilities

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 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) 

DNAprofiles documentation built on Jan. 15, 2017, 9:27 p.m.