D_H2: Squared Hellinger distance between two normal densities

In hunansona/ed4bhm: Empirical Determinacy for Bayesian Hierarchical Models

Squared Hellinger distance between two normal densities

Description

Computes the squared Hellinger distance between two normal densities parametrized by means mb, mw and standard deviations sdb, sdw.

Usage

D_H2(mb, sdb, mw, sdw)

Arguments

mb	mean of the first (base) normal density
sdb	standard deviation of the first (base) normal density
mw	mean of the second (weighted) normal density
sdw	standard deviation of the second (weighted) normal density

Details

H^2(π_1, π_w) = 1 - BC(π_1, π_w), where Bhattacharyya coefficient (BC) is a symmetric measure of affinity (Roos et al., 2015, Roos et al., 2021).

BC(π_1(ψ | y), π_w(ψ | y)) = \int_{-∞}^{∞} √{π_1(ψ | y) π_w(ψ | y)} d ψ.

BC between two normal densities reads

BC(π^N_1, π^N_w) = √{\frac{σ_1 σ_w}{\frac{σ^2_1+σ^2_w}{2} }} \exp ( -\frac{ (μ_w-μ_1)^2 }{4(σ^2_w + σ^2_1)} ),

For more details refer to Hunanyan et al., 2021.

Value

A numeric value between (0, 1).

References

Roos, M., Martins, T., Held, L., Rue, H. (2015). Sensitivity analysis for Bayesian hierarchical models. Bayesian Analysis 10(2), 321-349. https://projecteuclid.org/euclid.ba/1422884977

Roos, M., Hunanyan, S., Bakka, H., Rue, H. (2021). Sensitivity and identification quantification by a relative latent model complexity perturbation in the Bayesian meta-analysis. Biometrical Journal. URL https://doi.org/10.1002/bimj.202000193

Hunanyan, S., Roos, M., Plummer, M., Rue, H. (2021). Quantification of empirical determinacy: the impact of likelihood weighting on posterior location and spread in Bayesian meta-analysis estimated with JAGS and INLA. Bayesian Analaysis (under review). https://arxiv.org/abs/2109.11870.

See Also

D_BCS, D_BCL

Examples

D_H2(mb=0.4, sdb=0.3, mw=0.42, sdw=0.32)

hunansona/ed4bhm documentation built on June 15, 2022, 6:42 p.m.