predictive_interval.conformal {conformalbayes}

Jackknife(+) predictive intervals

Description

Construct finite-sample calibrated predictive intervals for Bayesian models, following the approach in Barber et al. (2021). By default, the intervals will also reflect the relative uncertainty in the Bayesian model, using the locally-weighted conformal methods of Lei et al. (2018).

Usage

## S3 method for class 'conformal'
predictive_interval(object, probs = 0.9, plus = NULL, local = TRUE, ...)

Arguments

object

A fitted model which has been passed through loo_conformal()

probs

The coverage probabilities to calculate intervals for. Empirically, the coverage rate of the constructed intervals will generally match these probabilities, but the theoretical guarantee for a probability of 1-\alpha is only for coverage of at least 1-2\alpha, and only if plus=TRUE (below).

plus

If TRUE, construct jackknife+ intervals, which have a theoretical guarantee. These require higher computational costs, which scale with both the number of training and prediction points. Defaults to TRUE when both of these numbers are less than 500.

local

If TRUE (the default), perform locally-weighted conformal inference. This will inflate the width of the predictive intervals by a constant amount across all predictions, preserving the relative amount of uncertainty captured by the model. If FALSE, all predictive intervals will have (nearly) the same width.

...

Further arguments to the posterior_predict() method for object.

Value

A matrix with the number of rows matching the number of predictions. Columns will be labeled with a percentile corresponding to probs; e.g. if probs=0.9 the columns will be ⁠5%⁠ and ⁠95%⁠.

References

Barber, R. F., Candes, E. J., Ramdas, A., & Tibshirani, R. J. (2021). Predictive inference with the jackknife+. The Annals of Statistics, 49(1), 486-507.

Lei, J., G’Sell, M., Rinaldo, A., Tibshirani, R. J., & Wasserman, L. (2018). Distribution-free predictive inference for regression. Journal of the American Statistical Association, 113(523), 1094-1111.

Examples

if (requireNamespace("rstanarm", quietly=TRUE)) suppressWarnings({
    library(rstanarm)
    # fit a simple linear regression
    m = stan_glm(mpg ~ disp + cyl, data=mtcars,
        chains=1, iter=1000,
        control=list(adapt_delta=0.999), refresh=0)

    m = loo_conformal(m)
    # make predictive intervals
    predictive_interval(m)
})