BF_u_obs_LEP: Outlier detection for observation for the log-exponential...

In nathansam/SMLN: Bayesian Survival Analysis Using Shape Mixtures of Log-Normal Distributions

Outlier detection for observation for the log-exponential power model

Description

This returns a unique number corresponding to the Bayes Factor associated to the test M_0: Λ_{obs} = λ_{ref} versus M_1: Λ_{obs}\neq λ_{ref} (with all other Λ_j,\neq obs free). The value of λ_{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 Λ_{obs} = λ_{ref} needs to be generated

Usage

BF_u_obs_LEP(
  N,
  thin,
  burn,
  ref,
  obs,
  Time,
  Cens,
  X,
  chain,
  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 u_{ref}. Vallejos & Steel recommends this value be set to 1.6 +1_α for the LEP model.
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
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 (ε_l) for set observations (default value: 0.5).
eps_r	Upper imprecision (ε_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 (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])
alpha <- mean(LEP[, 11])
uref <- 1.6 + 1 / alpha
LEP.Outlier <- BF_u_obs_LEP(N = 100, thin = 20, burn =1 , ref = uref,
                            obs = 1, Time = cancer[, 1], Cens = cancer[, 2],
                            cancer[, 3:11], chain = LEP)

nathansam/SMLN documentation built on May 14, 2022, 9:07 p.m.