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Pareto smoothed importance sampling (PSIS)

Source: R/loo.R
psis.brmsfit.Rd

Implementation of Pareto smoothed importance sampling (PSIS), a method for stabilizing importance ratios. The version of PSIS implemented here corresponds to the algorithm presented in Vehtari, Simpson, Gelman, Yao, and Gabry (2024). For PSIS diagnostics see the pareto-k-diagnostic page.

Usage

# S3 method for class 'brmsfit'
psis(log_ratios, newdata = NULL, resp = NULL, model_name = NULL, ...)

Arguments

log_ratios

A fitted model object of class brmsfit. Argument is named "log_ratios" to match the argument name of the loo::psis generic function.

newdata

An optional data.frame for which to evaluate predictions. If NULL (default), the original data of the model is used. NA values within factors (excluding grouping variables) are interpreted as if all dummy variables of this factor are zero. This allows, for instance, to make predictions of the grand mean when using sum coding. NA values within grouping variables are treated as a new level.

resp

Optional names of response variables. If specified, predictions are performed only for the specified response variables.

model_name

Currently ignored.

...

Further arguments passed to log_lik and loo::psis.

Value

The psis() methods return an object of class "psis", which is a named list with the following components:

log_weights

Vector or matrix of smoothed (and truncated) but unnormalized log weights. To get normalized weights use the weights() method provided for objects of class "psis".

diagnostics

A named list containing two vectors:

  • pareto_k: Estimates of the shape parameter \(k\) of the generalized Pareto distribution. See the pareto-k-diagnostic page for details.

  • n_eff: PSIS effective sample size estimates.

Objects of class "psis" also have the following attributes:

norm_const_log

Vector of precomputed values of colLogSumExps(log_weights) that are used internally by the weights method to normalize the log weights.

tail_len

Vector of tail lengths used for fitting the generalized Pareto distribution.

r_eff

If specified, the user's r_eff argument.

dims

Integer vector of length 2 containing S (posterior sample size) and N (number of observations).

method

Method used for importance sampling, here psis.

References

Vehtari, A., Gelman, A., and Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing. 27(5), 1413–1432. doi:10.1007/s11222-016-9696-4 (journal version, preprint arXiv:1507.04544).

Vehtari, A., Simpson, D., Gelman, A., Yao, Y., and Gabry, J. (2024). Pareto smoothed importance sampling. Journal of Machine Learning Research, 25(72):1-58. PDF

Examples

# \dontrun{
fit <- brm(rating ~ treat + period + carry, data = inhaler)
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 8e-06 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.08 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
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#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.034 seconds (Warm-up)
#> Chain 1:                0.03 seconds (Sampling)
#> Chain 1:                0.064 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 6e-06 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
#> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup)
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#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.032 seconds (Warm-up)
#> Chain 2:                0.029 seconds (Sampling)
#> Chain 2:                0.061 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 6e-06 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3: 
#> Chain 3: 
#> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup)
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#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.032 seconds (Warm-up)
#> Chain 3:                0.031 seconds (Sampling)
#> Chain 3:                0.063 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 5e-06 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.05 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4: 
#> Chain 4: 
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#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.032 seconds (Warm-up)
#> Chain 4:                0.029 seconds (Sampling)
#> Chain 4:                0.061 seconds (Total)
#> Chain 4: 
psis(fit)
#> Computed from 4000 by 572 log-weights matrix.
#> MCSE and ESS estimates assume MCMC draws (r_eff in [1.0, 1.2]).
#> 
#> All Pareto k estimates are good (k < 0.7).
#> See help('pareto-k-diagnostic') for details.
# }