KL Divergence Between Target and Induced K_J PMFs

Computes the KL divergence \(D_{KL}(p^* \| p_{a,b})\) between a target PMF and the induced marginal PMF of \(K_J\) under \(\alpha \sim Gamma(a, b)\).

Usage

kl_divergence_K(target_pmf, a, b, J, M = .QUAD_NODES_DEFAULT)

Arguments

target_pmf

Numeric vector; target PMF for K_J. Can have length J (support k=1,...,J) or J+1 (support k=0,...,J, where k=0 is ignored).

a

Numeric; shape parameter of Gamma hyperprior (a > 0).

b

Numeric; rate parameter of Gamma hyperprior (b > 0).

J

Integer; sample size.

M

Integer; number of quadrature nodes. Default: 80.

Value

Numeric scalar; \(D_{KL}(p^* \| p_{a,b})\) (non-negative).

See also

kl_divergence_pmf, DPprior_a2_kl

Examples

J <- 50
target <- rep(1/J, J)  # uniform target over k=1,...,J
kl_divergence_K(target, a = 2, b = 1, J = J)
#> [1] 10.49288