bci {bayestestR}  R Documentation 
Bias Corrected and Accelerated Interval (BCa)
Description
Compute the Bias Corrected and Accelerated Interval (BCa) of posterior distributions.
Usage
bci(x, ...)
bcai(x, ...)
## S3 method for class 'numeric'
bci(x, ci = 0.95, verbose = TRUE, ...)
## S3 method for class 'data.frame'
bci(x, ci = 0.95, verbose = TRUE, ...)
## S3 method for class 'MCMCglmm'
bci(x, ci = 0.95, verbose = TRUE, ...)
## S3 method for class 'sim.merMod'
bci(
x,
ci = 0.95,
effects = c("fixed", "random", "all"),
parameters = NULL,
verbose = TRUE,
...
)
## S3 method for class 'sim'
bci(x, ci = 0.95, parameters = NULL, verbose = TRUE, ...)
## S3 method for class 'emmGrid'
bci(x, ci = 0.95, verbose = TRUE, ...)
## S3 method for class 'stanreg'
bci(
x,
ci = 0.95,
effects = c("fixed", "random", "all"),
component = c("location", "all", "conditional", "smooth_terms", "sigma",
"distributional", "auxiliary"),
parameters = NULL,
verbose = TRUE,
...
)
## S3 method for class 'brmsfit'
bci(
x,
ci = 0.95,
effects = c("fixed", "random", "all"),
component = c("conditional", "zi", "zero_inflated", "all"),
parameters = NULL,
verbose = TRUE,
...
)
## S3 method for class 'BFBayesFactor'
bci(x, ci = 0.95, verbose = TRUE, ...)
## S3 method for class 'get_predicted'
bci(x, ci = 0.95, use_iterations = FALSE, verbose = TRUE, ...)
Arguments
x 
Vector representing a posterior distribution, or a data frame of such
vectors. Can also be a Bayesian model. bayestestR supports a wide range
of models (see, for example, 
... 
Currently not used. 
ci 
Value or vector of probability of the (credible) interval  CI
(between 0 and 1) to be estimated. Default to 
verbose 
Toggle off warnings. 
effects 
Should results for fixed effects, random effects or both be returned? Only applies to mixed models. May be abbreviated. 
parameters 
Regular expression pattern that describes the parameters
that should be returned. Metaparameters (like 
component 
Should results for all parameters, parameters for the conditional model or the zeroinflated part of the model be returned? May be abbreviated. Only applies to brmsmodels. 
use_iterations 
Logical, if 
Details
Unlike equaltailed intervals (see eti()
) that typically exclude 2.5%
from each tail of the distribution and always include the median, the HDI is
not equaltailed and therefore always includes the mode(s) of posterior
distributions. While this can be useful to better represent the credibility
mass of a distribution, the HDI also has some limitations. See spi()
for
details.
The 95%
or 89%
Credible Intervals (CI)
are two reasonable ranges to characterize the uncertainty related to the
estimation (see here
for a discussion about the differences between these two values).
The 89%
intervals (ci = 0.89
) are deemed to be more stable than, for
instance, 95%
intervals (Kruschke, 2014). An effective sample size
of at least 10.000 is recommended if one wants to estimate 95%
intervals
with high precision (Kruschke, 2014, p. 183ff). Unfortunately, the
default number of posterior samples for most Bayes packages (e.g., rstanarm
or brms
) is only 4.000 (thus, you might want to increase it when fitting
your model). Moreover, 89 indicates the arbitrariness of interval limits 
its only remarkable property is being the highest prime number that does not
exceed the already unstable 95%
threshold (McElreath, 2015).
However, 95%
has some advantages too. For instance, it
shares (in the case of a normal posterior distribution) an intuitive
relationship with the standard deviation and it conveys a more accurate image
of the (artificial) bounds of the distribution. Also, because it is wider, it
makes analyses more conservative (i.e., the probability of covering 0 is
larger for the 95%
CI than for lower ranges such as 89%
), which is a good
thing in the context of the reproducibility crisis.
A 95%
equaltailed interval (ETI) has 2.5%
of the distribution on either
side of its limits. It indicates the 2.5th percentile and the 97.5h
percentile. In symmetric distributions, the two methods of computing credible
intervals, the ETI and the HDI, return similar results.
This is not the case for skewed distributions. Indeed, it is possible that parameter values in the ETI have lower credibility (are less probable) than parameter values outside the ETI. This property seems undesirable as a summary of the credible values in a distribution.
On the other hand, the ETI range does change when transformations are applied to the distribution (for instance, for a log odds scale to probabilities): the lower and higher bounds of the transformed distribution will correspond to the transformed lower and higher bounds of the original distribution. On the contrary, applying transformations to the distribution will change the resulting HDI.
Value
A data frame with following columns:

Parameter
The model parameter(s), ifx
is a modelobject. Ifx
is a vector, this column is missing. 
CI
The probability of the credible interval. 
CI_low
,CI_high
The lower and upper credible interval limits for the parameters.
References
DiCiccio, T. J. and B. Efron. (1996). Bootstrap Confidence Intervals. Statistical Science. 11(3): 189–212. 10.1214/ss/1032280214
See Also
Other ci:
ci()
,
cwi()
,
eti()
,
hdi()
,
si()
,
spi()
Examples
posterior < rnorm(1000)
bci(posterior)
bci(posterior, ci = c(0.80, 0.89, 0.95))