Log-marginal Likelihood estimator for the log-student's t model

Usage

LML_LST(
  thin,
  Time,
  Cens,
  X,
  chain,
  Q = 1,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)

Arguments

thin: Thinning period.
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)

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 : 0.9 
#>  Initial beta 2 : -1.12 
#>  Initial beta 3 : -2.53 
#>  Initial beta 4 : -0.92 
#>  Initial beta 5 : 1.87 
#>  Initial beta 6 : 0.97 
#>  Initial beta 7 : -0.33 
#>  Initial beta 8 : 0.04 
#>  Initial beta 9 : -0.47 
#> 
#> Sampling initial sigma^2 from a Gamma(2, 2) distribution
#> Initial sigma^2 : 1.48 
#> 
#> Sampling initial nu from a Gamma(2, 2) distribution
#> Initial nu : 0.53 
#> 
#> AR nu : 0.35 

LST.LML <- LML_LST(thin = 20, Time = cancer[, 1], Cens = cancer[, 2],
                   X = cancer[, 3:11], chain = LST)
#> AR nu : 0.42 
#> Likelihood ordinate ready!
#> Prior ordinate ready!
#> AR nu : 0 
#> Reduced chain.sigma2 ready!
#> Posterior ordinate nu ready!
#> Posterior ordinate sigma2 ready!
#> AR nu : 0 
#> Reduced chain.beta ready!
#> Posterior ordinate beta ready!