CI consistency

[mattansb]

Generally speaking there are 3 types of ideas for obtaining credible intervals:

• Highest Density Interval(s) / Region(s) (HDI/HDR) : Interval or intervals that contain the values that have the $(1-\alpha)$% most probable values by their density.
• Quantile / Equal-Tailed Intervals (QI/ETI): Interval where each bound is found seperately: the lower/upper bound is that value that has $\alpha/2$% below/above it.
• Shortest Probability / Highest Density Continuous Interval (SPI/HDCI): The interval with the minimum width that contains $(1-\alpha)$% posterior mass.
  • When the posterior density is uni-modal, SPI/HDCI is equal to the HDI/HDR.
  • When the posterior is symmetric, SPI/HDCI is equal to the QI/ETI.

We currently have 3 function for computing credible intervals¹:

• eti() - returns the QI/ETI based on the MCMC ecdf.
• hdi() - returns the SPI/HDCI based on the MCMC ecdf.
• spi() - returns the SPI/HDCI based on the density estimation from the MCMC samples.

This seems inconsistent and confusing. Personally I'm not a fan of the HDI/HDR that can return multiple intervals, nor of the density based SPI/HDCI (why add a step?), but something should probably be done regarding the naming of these functions? (scroll up and down here >>)

• Maybe merge hdi()/spi() into one function?
• Maybe also add one and two dimensional HDI/HDR?

Footnotes

1. We also have bci(), but if I'm not mistaken that is more appropriate for bootstrap based confidence intervals? ↩

[strengejacke]

@DominiqueMakowski thoughts?

[bwiernik]

I would be in favor of:

1. Merging hdi() and spi() (removing spi() or making it an alias)
2. Making the choice of the sample- or density-based HPI algorithm an argument in hdi(). The SPIn algorithm has potential benefit over the sample-based algorithm in terms of reduced Monte Carlo error, so I think it's good to keep. No strong preference on which is default.
3. Adding an argument to allow computing of non-continuous HDI regions (true HDI vs HDCI). Okay for continuous = TRUE to be default.

[mattansb]

Yes, I like this. Then we would have:

• HDI/HDR : hdi(..., continuous = FALSE)
• SPI/HDCI: hdi(..., continuous = TRUE) (default) with two method (density, empirical).
• QI/ETI: eti(...)