Banana-shaped 2-D target

A 2-D "banana" density obtained by warping an isotropic Gaussian through the map \((z_1, z_2) \mapsto (z_1, z_2 + \tfrac{1}{2}(z_1^2 - 1))\). The map has unit Jacobian, so the resulting density is exactly normalised.

Usage

banana_target(with_samples = FALSE, n = 2000L, seed = 1L)

Arguments

with_samples

If TRUE, attach n exact samples drawn by the change-of-variables trick. Default FALSE — the target then exposes only its log_density, which is the regime-(iii) use case.

n

Number of samples to attach when with_samples = TRUE.

seed

Optional integer seed used when drawing the samples.

Value

A gmm_target in dimension 2.

See also

Other targets: donut_target(), epanechnikov_target(), gmm_target_from_samples(), maxent_target(), mixture_target()

Examples

b <- banana_target()
b
#> <gmm_target>: "banana" in p = 2 dimensions
#>   log_density : supplied
#>   samples     : <absent>
#>   normalised  : TRUE
#>   log Z(f)    : 0
b@log_density(matrix(c(0, 0, 1, 0), ncol = 2, byrow = TRUE))
#> [1] -1.962877 -2.337877