| hpd {metapack} | R Documentation |
get the highest posterior density (HPD) interval
Description
get the highest posterior density (HPD) interval
Usage
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 |
Details
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 jth 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)}).
Value
dataframe containing HPD intervals for the parameters
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.