Cox posterior via the partial likelihood — Ghosalcoxpost • rmorie

pi(beta | data) is proportional to pi(beta) times the partial likelihood. Using the partial likelihood as if it were a likelihood is not an approximation to be apologised for: section 13.6.1 shows the resulting posterior has the right asymptotics, because the partial likelihood already carries all the information about beta that the unknown baseline leaves available.

Usage

Ghosalcoxpost(beta0 = 0.6, n = 400, prior_sd = 2, seed = 42)

Arguments

beta0: True log hazard ratio.
n: Sample size.
prior_sd: Normal prior standard deviation, positive.
seed: Seed for the deterministic draws.

Value

List with estimate (posterior mean), error, method.

Details

Formula: log pi(b | data) = -b^2/(2 prior_sd^2)

sum_i [b z_i - log sum_{j in R_i} exp(b z_j)], on a grid.

References

Ghosal & van der Vaart (2017), Fundamentals of Nonparametric Bayesian Inference, CUP, section 13.6.1.

Examples

Ghosalcoxpost()
#> $estimate
#> [1] 0.6237003
#> 
#> $error
#> [1] 0.02370027
#> 
#> $method
#> [1] "Cox posterior (GvdV 2017 sec. 13.6.1)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"