dhsplus: The Horseshoe+ Prior Distribution

In jrnold/bayz: Miscellaneous Bayesian functions

Description

The Horseshoe+ Prior Distribution

Usage

dhsplus(x, tau = 1, location = 0)

rhsplus(n, tau = 1, location = 0)

Arguments

x	A numeric vector of quantiles
tau	numeric vector. The scale parameter
location	numeric vector. The location parameter.
n	Number of samples to draw

Details

There is no exact closed form for the density of the horseshoe distribution.

The Horseshoe+ Prior Distribution is defined hierarchically as,

x_i | λ_i \sim N(0, λ_i^2) λ_i | η_i \sim C^{+}(0, η_i) η_i | η_i \sim C^{+}(0, 1)

Integrating over η_i, the density of λ_i is,

p(λ_i) = \frac{4}{π^2} \frac{\log(λ_i)}{λ_i^2 - 1} .

There is no closed form representation of the density, but it is bounded by,

1 / (pi^2 * sqrt(2 pi)) * log(1 + 4 / theta^2) < p_HS+ (theta) <= 1 / (pi^2 * abs(theta))

Value

A numeric vector

References

Bhadra, A., Datta, J., Polson, N. G., Willard, B. (2016) “The Horseshoe+ Estimator of Ultra-Sparse Signals”. Bayesian Analysis, doi:10.1214/16-BA1028

jrnold/bayz documentation built on May 5, 2019, 5:52 p.m.