Beta-process definition

BP(c, H0) gives the cumulative hazard INDEPENDENT Beta increments, dH(t) ~ Be(c dH0(t), c(1 - dH0(t))). Putting the prior on the hazard rather than on the survival function is what makes right censoring conjugate, which is the whole reason the beta process is the standard survival prior. The path is simulated on a grid with H0 the unit-exponential cumulative hazard.

Usage

Ghosalbetaprocdef(grid_t, c = 2, Lambda0_rate = 1, seed = 42)

Arguments

grid_t

Increasing grid of time points.

c

Concentration of the beta increments, positive.

Lambda0_rate

Rate of the base cumulative hazard.

seed

Seed for the deterministic draws.

Value

List with estimate (terminal cumulative hazard), cum_hazard, nondecreasing, method.

Details

Formula: H(t_k) = sum_{j <= k} dH_j, dH_j ~ Be(c dH0_j, c(1 - dH0_j)).

References

Ghosal & van der Vaart (2017), Fundamentals of Nonparametric Bayesian Inference, CUP, section 13.3.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Ghosalbetaprocdef(V)
#> $estimate
#> [1] 8
#> 
#> $cum_hazard
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $nondecreasing
#> [1] TRUE
#> 
#> $method
#> [1] "beta process (GvdV 2017 sec. 13.3)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"