Returns a summary of a posterior distribution for a single
parameter / value. It is based on personal preference. Notably, it does not
only use `bayestestR::describe_posterior`

, an excellent function,
because of the desire to also describe the percentage of the full posterior
distribution that is at or exceeding the value of a
Minimally Important Difference (MID). MIDs are used in clinical studies with outcome
measures where there are pre-defined differences that are considered clinically
important, which is distinct from the ROPE or general credible intervals capturing
uncertainty.

## Arguments

- x
The posterior distribution of a parameter

- CI
A numeric value indicating the desired width of the credible interval. Defaults to

`0.99`

currently, but this is subject to change. a 99% interval was chosen as the default as there have been recent arguments made in the realm of meta science that there are, essentially, too many false positives and that many of the “findings” in science are not able to be replicated. In any case, users should ideally specify a desired CI width, and not rely on defaults.- CIType
A character string indicating the type of credible interval, passed on to the

`ci`

function as the method for CIs.- ROPE
Either left as

`NULL`

, the default, or a numeric vector of length 2, specifying the lower and upper thresholds for the Region of Practical Equivalence (ROPE).- MID
Either left as

`NULL`

, the default, or a numeric vector of length 2, specifying the lower and upper thresholds for a Minimally Important Difference (MID). Unlike the ROPE, percentages for the MID are calculated as at or exceeding the bounds specified by this argument, whereas the ROPE is the percentage of the posterior at or inside the bounds specified.

## Value

A `data.table`

with the mean, `M`

- M
the mean of the posterior samples

- Mdn
the median of the posterior samples

- LL
the lower limit of the credible interval

- UL
the upper limit of the credible interval

- PercentROPE
the percentage of posterior samples falling into the ROPE

- PercentMID
the percentage of posterior samples falling at or beyond the MID

- CI
the width of the credible interval used

- CIType
the type of credible interval used (e.g., highest density interval)

- ROPE
a label describing the values included in the ROPE

- MID
a label describing the values included in the MID

## References

Kruschke, J. K. (2018). doi:10.1177/2515245918771304 “Rejecting or accepting parameter values in Bayesian estimation”

## Examples

```
bsummary(rnorm(1000))
#> M Mdn LL UL PercentROPE PercentMID CI CIType
#> 1: 0.04189949 0.01399722 -2.532469 2.450347 NA NA 0.99 HDI
#> ROPE MID
#> 1: <NA> <NA>
bsummary(rnorm(1000), ROPE = c(-.5, .5), MID = c(-1, 1))
#> M Mdn LL UL PercentROPE PercentMID CI CIType
#> 1: 0.00439252 0.004145693 -2.482015 2.239139 38.1 31.1 0.99 HDI
#> ROPE MID
#> 1: [-0.5, 0.5] [-Inf, -1] | [1, Inf]
```