get the highest posterior density (HPD) interval
hpd(object, parm, level = 0.95, HPD = TRUE)dataframe containing HPD intervals for the parameters
the output model from fitting a (network) meta analysis/regression model
a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.
the probability which the HPD interval will cover
a logical value indicating whether HPD or equal-tailed credible interval should be computed; by default, TRUE
A \(100(1-\alpha)\)% HPD interval for \(\theta\) is given by $$R(\pi_\alpha) = {\theta: \pi(\theta| D) \ge \pi_\alpha},$$ where \(\pi_\alpha\) is the largest constant that satisfies \(P(\theta \in R(\pi_\alpha)) \ge 1-\alpha\). hpd computes the HPD interval from an MCMC sample by letting \(\theta_{(j)}\) be the \(j\)th smallest of the MCMC sample, \({\theta_i}\) and denoting $$R_j(n) = (\theta_{(j)}, \theta_{(j+[(1-\alpha)n])}),$$ for \(j=1,2,\ldots,n-[(1-\alpha)n]\). Once \(\theta_i\)'s are sorted, the appropriate \(j\) is chosen so that $$\theta_{(j+[(1-\alpha)n])} - \theta_{(j)} = \min_{1\le j \leq n-[(1-\alpha)n]} (\theta_{(j+[(1-\alpha)n])} - \theta_{(j)}).$$
Chen, M. H., & Shao, Q. M. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8(1), 69-92.