# cal_h_dist: Calibration of the Hellinger distance In ra4bayesmeta: Reference Analysis for Bayesian Meta-Analysis

## Description

By default (if `output="shift"`), this function returns the mean of a unit-variance normal distribution, such that the Hellinger distance between this distribution and the standard normal distribution equals the given value. Offers the option to return the area of overlap (if `output="ao"`) between these two unit-variance normal distributions instead. Gives an intuitive interpretation of Hellinger distance values.

## Usage

 `1` ```cal_h_dist(h, output="shift") ```

## Arguments

 `h` vector of Hellinger distances, consisting of real numbers in [0,1] `output` either `"shift"` or `"ao"`. Specifies if the output should be given as the shift between two unit-varaince normal distributions or as the area of overlap (AO) between these unit-varaince normal distributions

## Details

For a given Hellinger distance h, there is a mean μ(h), such that

H(N(μ(h), 1), N(0, 1))=h,

where H denotes the Hellinger distance. See Roos et al. (2015), Sect. 2.2 for details.

If `output="shift"`, the function returns the shift μ(h) between the two unit-variance normal distributions. If `output="ao"`, the function returns the area of overlap between the N(μ(h), 1) and N(0, 1) distributions. This area of overlap is given by

AO(μ(h)) = Φ(μ(h)/2 ;μ(h), 1) + 1 - Φ(μ(h)/2 ;0, 1),

where Φ(. ;μ, σ^2) denotes the cumulative distribution function of the normal distribution with mean μ and variance σ^2. See Ott et al. (2021, Section 3.5) for more information on this area of overlap calibration.

## Value

A vector of means (if `output="shift"`) or areas of overlap (if `output="ao"`), respectively.

## 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

Ott, M., Plummer, M., Roos, M. How vague is vague? How informative is informative? Reference analysis for Bayesian meta-analysis. Manuscript revised for Statistics in Medicine. 2021.

## Examples

 ```1 2 3 4``` ```# calibration in terms of shifts cal_h_dist(h=c(0.1, 0.5, 0.9)) # calibration in terms of areas of overlap cal_h_dist(h=c(0.1, 0.5, 0.9), output="ao") ```

ra4bayesmeta documentation built on April 23, 2021, 9:06 a.m.