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

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

Usage

calc_WoE_wTwR_integrate_wT_mc_markerwise(
  xT,
  xR,
  shape1T_H1,
  shape2T_H1,
  shape1T_H2,
  shape2T_H2,
  wR,
  p,
  n_samples = 1000
)

Arguments

xT: profile from case (of 0, 1, 2)
xR: profile from suspect (of 0, 1, 2)
shape1T_H1: Under $H_1$ (in $LR$'s numerator), wT has beta prior on (0, 0.5) with parameters shape1T_H1 and shape2T_H1
shape2T_H1: see shape1T_Hp
shape1T_H2: Under $H_2$ (in $LR$'s denominator), wT has beta prior (on 0-0.5) with parameters shape1T_H2 and shape2T_H2
shape2T_H2: see shape1T_H2
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

Details

Results from this can be compared to those from calc_WoE_wTwR_integrate_wT_exact_markerwise().

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()
#> [1]  0.5976032 -1.3971946

shpT <- get_beta_parameters(mu = 1e-2, sigmasq = 1e-5, a = 0, b = 0.5)
# curve(dbeta05(x, shpT[1], shpT[2]), from = 0, to = 0.1, n = 1001)
calc_WoE_wTwR_integrate_wT_mc_markerwise(
  xT = c(0, 0), 
  xR = c(0, 1), 
  shape1T_H1 = shpT[1], shape2T_H1 = shpT[2],
  shape1T_H2 = shpT[1], shape2T_H2 = shpT[2],
  wR = 1e-5, 
  p = c(0.25, 0.25, 0.5),
  n_samples = 1000)
#> [1]  0.5975074 -1.4141442
  
calc_WoE_wTwR_integrate_wT_exact_markerwise(
  xT = c(0, 0), 
  xR = c(0, 1), 
  shape1T_H1 = shpT[1], shape2T_H1 = shpT[2],
  shape1T_H2 = shpT[1], shape2T_H2 = shpT[2],
  wR = 1e-5, 
  p = c(0.25, 0.25, 0.5))
#> [1]  0.5975988 -1.3976413