Outlier detection for observation for the log-student's t model

This returns a unique number corresponding to the Bayes Factor associated to the test \(M_0: \Lambda_{obs} = \lambda_{ref}\) versus \(M_1: \Lambda_{obs}\neq \lambda_{ref}\) (with all other \(\Lambda_j,\neq obs\) free). The value of \(\lambda_{ref}\) is required as input. The user should expect long running times for the log-Student’s t model, in which case a reduced chain given \(\Lambda_{obs} = \lambda_{ref}\) needs to be generated

Usage

BF_lambda_obs_LST(
  N,
  thin,
  burn,
  ref,
  obs,
  Time,
  Cens,
  X,
  chain,
  Q = 1,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  ar = 0.44
)

Arguments

N: Total number of iterations. Must be a multiple of thin.
thin: Thinning period.
burn: Burn-in period
ref: Reference value \(\lambda_{ref}\) or \(u_{ref}\)
obs: Indicates the number of the observation under analysis
Time: Vector containing the survival times.
Cens: Censoring indication (1: observed, 0: right-censored).
X: Design matrix with dimensions \(n\) x \(k\) where \(n\) is the number of observations and \(k\) is the number of covariates (including the intercept).
chain: MCMC chains generated by a BASSLINE MCMC function
Q: Update period for the \(\lambda_{i}\)’s
prior: Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
set: Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
eps_l: Lower imprecision \((\epsilon_l)\) for set observations (default value: 0.5).
eps_r: Upper imprecision \((\epsilon_r)\) for set observations (default value: 0.5)
ar: Optimal acceptance rate for the adaptive Metropolis-Hastings updates

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LST <- MCMC_LST(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
#> Sampling initial betas from a Normal(0, 1) distribution
#> Initial beta 1 : -0.42 
#>  Initial beta 2 : 0.07 
#>  Initial beta 3 : -0.82 
#>  Initial beta 4 : -0.45 
#>  Initial beta 5 : -0.19 
#>  Initial beta 6 : -0.39 
#>  Initial beta 7 : -0.52 
#>  Initial beta 8 : -0.72 
#>  Initial beta 9 : 0.99 
#> 
#> Sampling initial sigma^2 from a Gamma(2, 2) distribution
#> Initial sigma^2 : 0.46 
#> 
#> Sampling initial nu from a Gamma(2, 2) distribution
#> Initial nu : 0.41 
#> 
#> AR nu : 0.38 

LST.Outlier <- BF_lambda_obs_LST(N = 100, thin = 20 , burn = 1, ref = 1,
                                 obs = 1, Time = cancer[, 1],
                                 Cens = cancer[, 2], X = cancer[, 3:11],
                                 chain = LST)
#> AR nu : 0.32