pri_par_epsilon_grid: Grid computation for epsilon-local sensitivity
In sl4bayesmeta: Sensitivity and learning for Bayesian meta-analysis

Description Usage Arguments Details Value References See Also Examples

Starting with a base prior from a one-parameter family, this function determines the parameters of two priors from the same parametric family which have the given Hellinger distance to the base prior. The available one-parameter distributions are half-normal, exponential, half-Cauchy and Lomax with shape parameter fixed at 1.

1 2	pri_par_epsilon_grid(AA0_HN, AA0_EXP, AA0_HC, AA0_LMX, grid_epsilon=0.00354)

`AA0_HN`	scale parameter of the base half-normal prior
`AA0_EXP`	scale parameter of the base exponential prior
`AA0_HC`	scale parameter of the base half-Cauchy prior
`AA0_LMX`	scale parameter of the base Lomax prior with shape parameter=1
`grid_epsilon`	value for epsilon, the Hellinger distance between the base prior and the "lower"/"upper" prior on the grid

This 1-dimensional epsilon grid is needed for computation of the epsilon-local sensitivity in the function sensitivity_learning_table. See Ott et al. (2020) for a brief description of this methodology and Roos et al. (2015) for more details. The default value for grid_epsilon corresponds to the Hellinger distance between two normal distribution with unit variance and a difference in means of 0.01, see Roos et al. (2015, Sect. 2.2) for calibration and interpretation of Hellinger distance values.

A list of the following eight scale parameter values:

`p_HN_l`	parameter of the "lower" half-normal prior on the grid
`p_HN_u`	parameter of the "upper" half-normal prior on the grid
`p_EXP_l`	parameter of the "lower" exponential prior on the grid
`p_EXP_u`	parameter of the "upper" exponential prior on the grid
`p_HC_l`	parameter of the "lower" half-Cauchy prior on the grid
`p_HC_u`	parameter of the "upper" half-Cauchy prior on the grid
`p_LMX_l`	scale parameter of the "lower" Lomax prior (with shape parameter=1) on the grid
`p_LMX_u`	scale parameter of the "upper" Lomax prior (with shape parameter=1) on the grid

Ott, M., Hunanyan, S., Held, L., Roos, M. Sensitivity quantification in Bayesian meta-analysis. Manuscript revised for Research Synthesis Methods. 2020.

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

sensitivity_learning_table, cal_h_dist

# epsilon grid for 5 % tail-adjusted priors with 
# reference threshold UU=1 and epsilon = 0.00354 (default)
pri_par_epsilon_grid(AA0_HN=pri_par_adjust_static(UU=1)$p_HN, 
                     AA0_EXP=pri_par_adjust_static(UU=1)$p_EXP,
                     AA0_HC=pri_par_adjust_static(UU=1)$p_HC,
                     AA0_LMX=pri_par_adjust_static(UU=1)$p_LMX)