Calculate WoE for a profile for sample-specific error probabilities integrated over the donor prior distribution using Monte Carlo integration

Note that this is the expected value of log10 of $LR$ under a prior of $w_t$. An alternative is implemented in calc_WoE_wTwR_integrate_wT_mc_markerwise() where a WoE for each marker is calculated by integrating over the prior of $w_t$ separately under $H_1$ and $H_2$.

Usage

calc_WoE_wTwR_integrate_wT_mc(
  xT,
  xR,
  shape1T,
  shape2T,
  wR,
  p,
  n_samples = 1000
)

Arguments

xT

profile from case (of 0, 1, 2)

xR

profile from suspect (of 0, 1, 2)

shape1T

wT has beta prior on (0, 0.5) with parameters shape1T and shape2T

shape2T

see shape1T_Hp

wR

error probability for PoI sample

p

list of genotype probabilities (same length as xT/xR, or vector of length 3 for reuse)

n_samples

number of random samples from each prior distribution

Examples

calc_LRs_wTwR(xT = c(0, 0), xR = c(0, 1), wT = 1e-2, wR = 1e-5, p = c(0.25, 0.25, 0.5)) |> log10() |> sum()
#> [1] -0.7995914

shpT <- get_beta_parameters(mu = 1e-2, sigmasq = 1e-7, a = 0, b = 0.5)
# curve(dbeta05(x, shpT[1], shpT[2]), from = 0, to = 0.1, n = 1001)
z1 <- calc_WoE_wTwR_integrate_wT_mc(
  xT = c(0, 0), 
  xR = c(0, 1), 
  shape1T = shpT[1], shape2T = shpT[2],
  wR = 1e-5, 
  p = c(0.25, 0.25, 0.5),
  n_samples = 1000)
z1$WoE
#> [1] -0.7995317
z1$WoEs; sum(z1$WoEs)
#> [1]  0.5976002 -1.3971319
#> [1] -0.7995317

z2 <- calc_WoE_wTwR_integrate_wT_num(
  xT = c(0, 0), 
  xR = c(0, 1), 
  shape1T = shpT[1], shape2T = shpT[2], 
  wR = 1e-5, 
  p = c(0.25, 0.25, 0.5))
z2$WoE
#> [1] -0.7998079
z2$WoEs; sum(z2$WoEs)
#> [1]  0.597603 -1.397411
#> [1] -0.7998079