The posterior_interval function computes Bayesian posterior uncertainty
intervals. These intervals are often referred to as credible
intervals. This documentation is largely inspired and adapted from the same function documentation from rstanarm.
# S3 method for stapDP posterior_interval(object, prob = 0.95, pars = NULL, ...)
| object | stapDP object |
|---|---|
| prob | A number \(p \in (0,1)\) indicating the desired
probability mass to include in the intervals. The default is to report
\(95\)% intervals ( |
| pars | vector of parameter names |
| ... | ignored |
A matrix with two columns and as many rows as model parameters (or
the subset of parameters specified by pars.
For a given value of prob, \(p\), the columns
correspond to the lower and upper \(100p\)% interval limits and have the
names \(100\alpha/2\)% and \(100(1 - \alpha/2)\)%, where \(\alpha
= 1-p\). For example, if prob=0.95 is specified (a \(95\)%
interval), then the column names will be "2.5%" and "97.5%",
respectively.
Unlike for a frenquentist confidence interval, it is valid to say that, conditional on the data and model, we believe that with probability \(p\) the value of a parameter is in its \(100p\)% posterior interval. This intuitive interpretation of Bayesian intervals is often erroneously applied to frequentist confidence intervals. See Morey et al. (2015) for more details on this issue and the advantages of using Bayesian posterior uncertainty intervals (also known as credible intervals).
Gelman, A. and Carlin, J. (2014). Beyond power calculations: assessing Type S (sign) and Type M (magnitude) errors. Perspectives on Psychological Science. 9(6), 641--51.
Morey, R. D., Hoekstra, R., Rouder, J., Lee, M. D., and Wagenmakers, E. (2016). The fallacy of placing confidence in confidence intervals. Psychonomic Bulletin & Review. 23(1), 103--123.