H(t) = sum over tau_k <= t of J_k with (J_k, tau_k) drawn from a
Poisson process carrying the beta-process Levy intensity. Building
the path from its jumps rather than from grid increments is what makes
the pure-jump, nondecreasing structure explicit – a beta process has
no continuous part at all.
Usage
Ghosalbppathgen(c = 1.5, t_max = 1, n_jumps = 300, seed = 42)
Arguments
- c
Concentration, positive.
- t_max
Time horizon.
- n_jumps
Number of jumps simulated.
- seed
Seed for the deterministic draws.
Value
List with estimate (terminal value),
n_jumps, pure_jump_nondecreasing, method.
Details
Formula: tau_k ~ U(0, t_max), J_k ~ Be(1, c) c 5 / n_jumps, and the
path is the running total of the jumps in time order.
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 13.3.3.
Examples
Ghosalbppathgen()
#> $estimate
#> [1] 3.159651
#>
#> $n_jumps
#> [1] 300
#>
#> $pure_jump_nondecreasing
#> [1] TRUE
#>
#> $method
#> [1] "BP Poisson-jump path (GvdV 2017 sec. 13.3.3)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
