Increasing-process prior via an exponentiated Gaussian process

F(t) = int_0^t exp(W(s)) ds is strictly increasing BY CONSTRUCTION for any Gaussian path W: the monotonicity constraint is absorbed into the parameterisation rather than imposed on the prior, which is what makes the posterior tractable. Trapezoid integration of the exponentiated draw here.

Usage

Ghosalgpincreasingprior(x, length = 0.5, seed = 42)

Arguments

x: Evaluation points; sorted internally.
length: Squared-exponential length scale, positive.
seed: Seed for the deterministic draws.

Value

List with estimate (terminal value), F, increasing, method.

Details

Formula: F(x_i) = F(x_{i-1})

(exp(W_i) + exp(W_{i-1})) (x_i - x_{i-1}) / 2.

References

Ghosal & van der Vaart (2017), Fundamentals of Nonparametric Bayesian Inference, CUP, section 2.2.2.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Ghosalgpincreasingprior(V)
#> $estimate
#> [1] 9.603033
#> 
#> $F
#> [1] 0.0000000 0.9755317 3.6502558 7.1932530 8.4649111 8.7238115 8.9239030
#> [8] 9.6030327
#> 
#> $increasing
#> [1] TRUE
#> 
#> $method
#> [1] "exponentiated-GP increasing process (GvdV 2017 sec. 2.2.2)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"