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.
cal_h_dist(h, output="shift")A vector of means (if output="shift") or areas of overlap (if output="ao"), respectively.
vector of Hellinger distances, consisting of real numbers in [0,1]
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
For a given Hellinger distance h, there is a mean \(\mu(h)\), such that $$H(N(\mu(h), 1), N(0, 1))=h,$$ where H denotes the Hellinger distance. See Roos et al. (2015), Sect. 2.2 for details.
If output="shift", the function returns the shift \(\mu(h)\) between
the two unit-variance normal distributions.
If output="ao", the function returns
the area of overlap between the \(N(\mu(h), 1)\) and \(N(0, 1)\) distributions.
This area of overlap is given by
$$AO(\mu(h)) = \Phi(\mu(h)/2 ;\mu(h), 1) + 1 - \Phi(\mu(h)/2 ;0, 1),$$
where \(\Phi(. ;\mu, \sigma^2)\) denotes the cumulative distribution function of
the normal distribution with mean \(\mu\) and variance \(\sigma^2\).
See Ott et al. (2021, Section 3.5) for more information on this area of overlap calibration.
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. (2021). How vague is vague? How informative is informative? Reference analysis for Bayesian meta-analysis. Statistics in Medicine 40, 4505--4521. tools:::Rd_expr_doi("10.1002/sim.9076")
# 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")
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