pmvt_MLMC: Applying the multi-level Monte Carlo (MLMC) technique to the pmvt function The function uses `NLevel1 = 1` for `m = m2` and the same exponential tilting parameter as `m = m1` to compute one MC estimate. This MC estimate is used to correct the bias from the Vecchia approximation

Description

Applying the multi-level Monte Carlo (MLMC) technique to the pmvt function The function uses NLevel1 = 1 for m = m2 and the same exponential tilting parameter as m = m1 to compute one MC estimate. This MC estimate is used to correct the bias from the Vecchia approximation

Usage

pmvt_MLMC(
  lower,
  upper,
  delta,
  df,
  locs = NULL,
  covName = "matern15_isotropic",
  covParms = c(1, 0.1, 0),
  m1 = 30,
  m2 = 100,
  sigma = NULL,
  reorder = 0,
  NLevel1 = 12,
  NLevel2 = 10000,
  verbose = FALSE,
  retlog = FALSE,
  ...
)

Value

estimated MVT probability and estimation error

Arguments

lower: lower bound vector for TMVT
upper: upper bound vector for TMVT
delta: MVT shifting parameter
df: degrees of freedom
locs: location (feature) matrix n X d
covName: covariance function name from the `GpGp` package
covParms: parameters for `covName`
m1: the smaller Vecchia conditioning set size for Level 1 MC
m2: the bigger Vecchia conditioning set size for Level 2 MC
sigma: dense covariance matrix, not needed when `locs` is not null
reorder: whether to reorder integration variables. `0` for no, `1` for FIC-based univariate ordering, `2` for Vecchia-based univariate ordering, and `3` for univariate reordering, which appeared faster than `2`
NLevel1: first level Monte Carlo sample size
NLevel2: second level Monte Carlo sample size
verbose: verbose or not
retlog: TRUE or FALSE for whether to return loglk or not
...: could be m_ord for conditioning set size for reordering