Shortest Probability Interval (SPI)

Compute the Shortest Probability Interval (SPI) of posterior distributions. The SPI is a more computationally stable HDI. The implementation is based on the algorithm from the SPIn package.

Usage

spi(x, ...)

# S3 method for numeric
spi(x, ci = 0.95, verbose = TRUE, ...)

# S3 method for stanreg
spi(
  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 brmsfit
spi(
  x,
  ci = 0.95,
  effects = c("fixed", "random", "all"),
  component = c("conditional", "zi", "zero_inflated", "all"),
  parameters = NULL,
  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, methods("hdi")) and not all of those are documented in the 'Usage' section, because methods for other classes mostly resemble the arguments of the .numeric or .data.framemethods.
...: Currently not used.
ci: Value or vector of probability of the (credible) interval - CI (between 0 and 1) to be estimated. Default to .95 (95%).
verbose: Toggle off warnings.
effects: Should results for fixed effects, random effects or both be returned? Only applies to mixed models. May be abbreviated.
component: Should results for all parameters, parameters for the conditional model or the zero-inflated part of the model be returned? May be abbreviated. Only applies to brms-models.
parameters: Regular expression pattern that describes the parameters that should be returned. Meta-parameters (like lp__ or prior_) are filtered by default, so only parameters that typically appear in the summary() are returned. Use parameters to select specific parameters for the output.

Value

A data frame with following columns:

Parameter The model parameter(s), if x is a model-object. If x 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.

Details

The SPI is an alternative method to the HDI (hdi()) to quantify uncertainty of (posterior) distributions. The SPI is said to be more stable than the HDI, because, the "HDI can be noisy (that is, have a high Monte Carlo error)" (Liu et al. 2015). Furthermore, the HDI is sensitive to additional assumptions, in particular assumptions related to the different estimation methods, which can make the HDI less accurate or reliable (see also discussion here).

Note

The code to compute the SPI was adapted from the SPIn package, and slightly modified to be more robust for Stan models. Thus, credits go to Ying Liu for the original SPI algorithm and R implementation.

References

Liu, Y., Gelman, A., & Zheng, T. (2015). Simulation-efficient shortest probability intervals. Statistics and Computing, 25(4), 809–819. https://doi.org/10.1007/s11222-015-9563-8

Examples

library(bayestestR)

posterior <- rnorm(1000)
spi(posterior)
#> 95% SPI: [-1.69, 2.01]
spi(posterior, ci = c(0.80, 0.89, 0.95))
#> Shortest Probability Interval
#> 
#> 80% SPI       |       89% SPI |       95% SPI
#> ---------------------------------------------
#> [-1.20, 1.18] | [-1.60, 1.40] | [-1.69, 2.01]

df <- data.frame(replicate(4, rnorm(100)))
spi(df)
#> Shortest Probability Interval
#> 
#> Parameter |       95% SPI
#> -------------------------
#> X1        | [-1.68, 1.90]
#> X2        | [-1.75, 1.95]
#> X3        | [-2.39, 1.68]
#> X4        | [-1.73, 2.01]
spi(df, ci = c(0.80, 0.89, 0.95))
#> Shortest Probability Interval
#> 
#> Parameter |       80% SPI |       89% SPI |       95% SPI
#> ---------------------------------------------------------
#> X1        | [-1.45, 0.76] | [-1.52, 1.45] | [-1.68, 1.90]
#> X2        | [-0.76, 1.61] | [-1.50, 1.61] | [-1.75, 1.95]
#> X3        | [-1.22, 0.86] | [-1.24, 1.68] | [-2.39, 1.68]
#> X4        | [-0.73, 1.35] | [-1.65, 1.35] | [-1.73, 2.01]
# \dontrun{
library(rstanarm)
model <- stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0)
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
spi(model)
#> Shortest Probability Interval 
#> 
#> Parameter   |        95% SPI
#> ----------------------------
#> (Intercept) | [30.62, 47.80]
#> wt          | [-6.54, -4.28]
#> gear        | [-1.64,  1.61]
# }