Deviance information criterion for the log-exponential power model

Deviance information criterion is based on the deviance function \(D(\theta, y) = -2 log(f(y|\theta))\) but also incorporates a penalization factor of the complexity of the model

Usage

DIC_LEP(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)

Arguments

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

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 (especially for the log-exponential power model).

LEP <- MCMC_LEP(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 : -0.45 
#>  Initial beta 2 : 0.64 
#>  Initial beta 3 : 0.26 
#>  Initial beta 4 : -0.58 
#>  Initial beta 5 : 1.12 
#>  Initial beta 6 : 1.43 
#>  Initial beta 7 : 0.38 
#>  Initial beta 8 : -0.93 
#>  Initial beta 9 : -0.47 
#> 
#> Sampling initial sigma^2 from a Gamma(2, 2) distribution
#> Initial sigma^2 : 0.41 
#> 
#> Sampling initial alpha from a Uniform(1, 2) distribution
#> Initial alpha : 1.54 
#> 
#> AR beta 1 : 0.68 
#>  AR beta 2 : 0.75 
#>  AR beta 3 : 0.83 
#>  AR beta 4 : 0.77 
#>  AR beta 5 : 0.86 
#>  AR beta 6 : 0.03 
#>  AR beta 7 : 0.1 
#>  AR beta 8 : 0.03 
#>  AR beta 9 : 0.8 
#> AR sigma2 : 0.87 
#> AR alpha : 0.09 
LEP.DIC <- DIC_LEP(Time = cancer[, 1], Cens = cancer[, 2],
                   X = cancer[, 3:11], chain = LEP)
#> Effective number of parameters : 70.75 
#> Actual number of parameters : 11