Neutral-to-the-right Levy (Laplace) functional

E exp(-int f dM) = exp(-int (1 - exp(-f u)) dnu) is the Levy-Khinchine formula for an independent-increment process. It is the only handle on an NTR prior that stays closed form, and every posterior update in the section is carried out through it rather than through a density. Computed exactly here for a discrete Levy measure.

Usage

Ghosalntrlevy(f_vals, nu_masses)

Arguments

f_vals: Values of the test function at the atoms of nu.
nu_masses: Masses of the discrete Levy measure, non-negative.

Value

List with estimate (the Laplace functional), exponent, method.

Details

Formula: exponent = sum_j m_j (1 - exp(-f_j)); value = exp(-exponent).

References

Ghosal & van der Vaart (2017), Fundamentals of Nonparametric Bayesian Inference, CUP, section 13.4.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Ghosalntrlevy(V, V)
#> $estimate
#> [1] 5.813393e-16
#> 
#> $exponent
#> [1] 35.0812
#> 
#> $method
#> [1] "NTR Laplace functional (GvdV 2017 sec. 13.4)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"