Outlier detection for observation for the log-Laplace 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_LLAP(obs, ref, X, chain)

Arguments

obs: Indicates the number of the observation under analysis
ref: Reference value \(\lambda_{ref}\) or \(u_{ref}\)
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 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.

LLAP <- MCMC_LLAP(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 : -0.82 
#>  Initial beta 2 : -0.08 
#>  Initial beta 3 : -0.14 
#>  Initial beta 4 : 1.12 
#>  Initial beta 5 : 0.28 
#>  Initial beta 6 : 0.3 
#>  Initial beta 7 : -0.5 
#>  Initial beta 8 : 1.38 
#>  Initial beta 9 : -1.56 
#> 
#> Sampling initial sigma^2 from a Gamma(2, 2) distribution
#> Initial sigma^2 : 0.34 
#> 
LLAP.outlier <- BF_lambda_obs_LLAP(1,1, X = cancer[, 3:11], chain = LLAP)