Mixture-of-kernels density prior — Ghosalmixturebasisprior • rmorie

f = sum_k w_k K(x; theta_k) with Dirichlet weights. Unlike the histogram the mixture is smooth, and unlike a fixed basis its components move: the locations are themselves random, which is what lets a small number of components track structure anywhere on the domain.

Usage

Ghosalmixturebasisprior(x, K = 5, seed = 42, bandwidth = 0.15)

Arguments

x: Evaluation points.
K: Number of mixture components, at least 1.
seed: Seed for the deterministic draws.
bandwidth: Kernel bandwidth, positive.

Value

List with estimate (mean density), density, weights, locations, method.

Details

Formula: w ~ Dirichlet(1, ..., 1) by gamma normalisation, theta_k ~ U(0, 1), f(x) = sum_k w_k phi((x - theta_k)/h) / h.

References

Ghosal & van der Vaart (2017), Fundamentals of Nonparametric Bayesian Inference, CUP, section 2.3.3.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Ghosalmixturebasisprior(V)
#> $estimate
#> [1] 0.0008958677
#> 
#> $density
#> [1]  7.166941e-03  1.163146e-18  1.284368e-53 7.076151e-108 1.945036e-181
#> [6] 2.667359e-274  0.000000e+00  0.000000e+00
#> 
#> $weights
#> [1] 0.17980837 0.44302412 0.20560515 0.15459947 0.01696289
#> 
#> $locations
#> [1] 0.20343511 0.10357424 0.49549866 0.09342766 0.68894637
#> 
#> $method
#> [1] "Dirichlet kernel mixture (GvdV 2017 sec. 2.3.3)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"