H_normal {ra4bayesmeta}

Approximate moment-based Hellinger distance computation between two probability densities

Description

Computes the Hellinger distance between the two probability densities with the given means and standard deviations using a normal approximation and moment-matching. Applies a moment-based analytical formula, which is exact for normal densities.

Usage

H_normal(mean1, sd1, mean2, sd2)

Arguments

mean1

mean of the first density.

sd1

standard deviation of the first density.

mean2

mean of the second density.

sd2

standard deviation of the second density.

Details

The Hellinger distance between two normal densities can be computed analytically and it only depends on the means and the standard deviations of these two densities. Any density can be approximated to the first order by a normal distribution. Thus, this moment-based formula can also be applied to non-normal densities to obtain an approximate estimate of the Hellinger distance. This approximation relies on moment-matching, i.e. the non-normal densities are approximated by normal densities with the same means and standard deviations. See Roos et al. (2021), Section 3.3, for the formula and for additional information.

Note that the Hellinger distance is invariant with respect to one-to-one transformations of both densities. For the between-study standard deviation \tau, the density of log(\tau) can be approximated by a normal density.

Value

A real number in [0,1].

References

Roos, M., Hunanyan, S., Bakka, H., & Rue, H. (2021). Sensitivity and identification quantification by a relative latent model complexity perturbation in Bayesian meta-analysis. Biometrical Journal 63, 1555–1574. doi:10.1002/bimj.202000193

See Also

H

Examples

H_normal(mean1 = 0, sd1 = 1, mean2 = 1, sd2 = 2)