hpd function

get the highest posterior density (HPD) interval

hpd(object, parm, level = 0.95, HPD = TRUE)

Arguments

• object: the output model from fitting a (network) meta analysis/regression model
• parm: 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.
• level: the probability which the HPD interval will cover
• HPD: a logical value indicating whether HPD or equal-tailed credible interval should be computed; by default, TRUE

Returns

dataframe containing HPD intervals for the parameters

Details

A $100(1-\alpha)$% HPD interval for $\theta$ is given by

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

for $j=1,2,\ldots,n-[(1-\alpha)n]$. Once $\theta_i$'s are sorted, the appropriate $j$ is chosen so that

References

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.