Log-marginal likelihood estimator for the log-exponential power model

Usage

LML_LEP(
  thin,
  Time,
  Cens,
  X,
  chain,
  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
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=100 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations (especially for the log-exponential power model).

LEP <- MCMC_LEP(N = 100, thin = 2, burn = 20, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
#> Sampling initial betas from a Normal(0, 1) distribution
#> Initial beta 1 : -1.19 
#>  Initial beta 2 : -0.24 
#>  Initial beta 3 : 0.15 
#>  Initial beta 4 : 0.95 
#>  Initial beta 5 : -1.37 
#>  Initial beta 6 : 0 
#>  Initial beta 7 : 0.62 
#>  Initial beta 8 : -1.02 
#>  Initial beta 9 : 1.39 
#> 
#> Sampling initial sigma^2 from a Gamma(2, 2) distribution
#> Initial sigma^2 : 0.33 
#> 
#> Sampling initial alpha from a Uniform(1, 2) distribution
#> Initial alpha : 1.75 
#> 
#> AR beta 1 : 0.61 
#>  AR beta 2 : 0.55 
#>  AR beta 3 : 0.58 
#>  AR beta 4 : 0.65 
#>  AR beta 5 : 0.72 
#>  AR beta 6 : 0.02 
#>  AR beta 7 : 0.06 
#>  AR beta 8 : 0.02 
#>  AR beta 9 : 0.62 
#> AR sigma2 : 0.68 
#> AR alpha : 0.04 
LEP.LML <- LML_LEP(thin = 2, Time = cancer[, 1], Cens = cancer[, 2],
                   X = cancer[, 3:11], chain = LEP)
#> AR beta 1 : 0.55 
#>  AR beta 2 : 0.65 
#>  AR beta 3 : 0.68 
#>  AR beta 4 : 0.71 
#>  AR beta 5 : 0.79 
#>  AR beta 6 : 0.06 
#>  AR beta 7 : 0.06 
#>  AR beta 8 : 0.05 
#>  AR beta 9 : 0.7 
#> AR sigma2 : 0.93 
#> AR alpha : 0.13 
#> Likelihood ordinate ready!
#> Prior ordinate ready!
#> AR beta 1 : 0.5 
#>  AR beta 2 : 0.61 
#>  AR beta 3 : 0.7 
#>  AR beta 4 : 0.62 
#>  AR beta 5 : 0.8 
#>  AR beta 6 : 0 
#>  AR beta 7 : 0.02 
#>  AR beta 8 : 0 
#>  AR beta 9 : 0.71 
#> AR sigma2 : 0.96 
#> AR alpha : 0 
#> Reduced chain.sigma2 ready!
#> Posterior ordinate alpha ready!
#> AR beta 1 : 0.57 
#>  AR beta 2 : 0.61 
#>  AR beta 3 : 0.73 
#>  AR beta 4 : 0.74 
#>  AR beta 5 : 0.77 
#>  AR beta 6 : 0.01 
#>  AR beta 7 : 0.04 
#>  AR beta 8 : 0.01 
#>  AR beta 9 : 0.67 
#> AR sigma2 : 0 
#> AR alpha : 0 
#> Reduced chain.beta ready
#> !Posterior ordinate sigma2 ready!
#> [1] 0
#> AR beta 1 : 0 
#>  AR beta 2 : 0.63 
#>  AR beta 3 : 0.7 
#>  AR beta 4 : 0.62 
#>  AR beta 5 : 0.71 
#>  AR beta 6 : 0.01 
#>  AR beta 7 : 0.11 
#>  AR beta 8 : 0.01 
#>  AR beta 9 : 0.55 
#> AR sigma2 : 0 
#> AR alpha : 0 
#> [1] 1
#> AR beta 1 : 0 
#>  AR beta 2 : 0 
#>  AR beta 3 : 0.68 
#>  AR beta 4 : 0.54 
#>  AR beta 5 : 0.68 
#>  AR beta 6 : 0 
#>  AR beta 7 : 0.05 
#>  AR beta 8 : 0.02 
#>  AR beta 9 : 0.55 
#> AR sigma2 : 0 
#> AR alpha : 0 
#> [1] 2
#> AR beta 1 : 0 
#>  AR beta 2 : 0 
#>  AR beta 3 : 0 
#>  AR beta 4 : 0.6 
#>  AR beta 5 : 0.67 
#>  AR beta 6 : 0.01 
#>  AR beta 7 : 0.04 
#>  AR beta 8 : 0.01 
#>  AR beta 9 : 0.62 
#> AR sigma2 : 0 
#> AR alpha : 0 
#> [1] 3
#> AR beta 1 : 0 
#>  AR beta 2 : 0 
#>  AR beta 3 : 0 
#>  AR beta 4 : 0 
#>  AR beta 5 : 0.73 
#>  AR beta 6 : 0.01 
#>  AR beta 7 : 0 
#>  AR beta 8 : 0 
#>  AR beta 9 : 0.7 
#> AR sigma2 : 0 
#> AR alpha : 0 
#> [1] 4
#> AR beta 1 : 0 
#>  AR beta 2 : 0 
#>  AR beta 3 : 0 
#>  AR beta 4 : 0 
#>  AR beta 5 : 0 
#>  AR beta 6 : 0 
#>  AR beta 7 : 0.05 
#>  AR beta 8 : 0 
#>  AR beta 9 : 0.65 
#> AR sigma2 : 0 
#> AR alpha : 0 
#> [1] 5
#> AR beta 1 : 0 
#>  AR beta 2 : 0 
#>  AR beta 3 : 0 
#>  AR beta 4 : 0 
#>  AR beta 5 : 0 
#>  AR beta 6 : 0 
#>  AR beta 7 : 0.13 
#>  AR beta 8 : 0.01 
#>  AR beta 9 : 0.65 
#> AR sigma2 : 0 
#> AR alpha : 0 
#> [1] 6
#> AR beta 1 : 0 
#>  AR beta 2 : 0 
#>  AR beta 3 : 0 
#>  AR beta 4 : 0 
#>  AR beta 5 : 0 
#>  AR beta 6 : 0 
#>  AR beta 7 : 0 
#>  AR beta 8 : 0.06 
#>  AR beta 9 : 0.7 
#> AR sigma2 : 0 
#> AR alpha : 0 
#> [1] 7
#> AR beta 1 : 0 
#>  AR beta 2 : 0 
#>  AR beta 3 : 0 
#>  AR beta 4 : 0 
#>  AR beta 5 : 0 
#>  AR beta 6 : 0 
#>  AR beta 7 : 0 
#>  AR beta 8 : 0 
#>  AR beta 9 : 0.71 
#> AR sigma2 : 0 
#> AR alpha : 0 
#> [1] 8
#> AR beta 1 : 0 
#>  AR beta 2 : 0 
#>  AR beta 3 : 0 
#>  AR beta 4 : 0 
#>  AR beta 5 : 0 
#>  AR beta 6 : 0 
#>  AR beta 7 : 0 
#>  AR beta 8 : 0 
#>  AR beta 9 : 0 
#> AR sigma2 : 0 
#> AR alpha : 0 
#> Posterior ordinate beta ready!