A psis_loo_ss object to update.

Currently not used.

For loo_subsample.function(), these are the data, posterior draws, and other arguments to pass to the log-likelihood function.

For loo_subsample.function(), these are the data, posterior draws, and other arguments to pass to the log-likelihood function.

The subsample observations to use. The argument can take four (4) types of arguments:

• NULL to use all observations. The algorithm then just uses standard loo() or loo_approximate_posterior().

• A single integer to specify the number of observations to be subsampled.

• A vector of integers to provide the indices used to subset the data. These observations need to be subsampled with the same scheme as given by the estimator argument.

• A psis_loo_ss object to use the same observations that were used in a previous call to loo_subsample().

Vector of relative effective sample size estimates for the likelihood (exp(log_lik)) of each observation. This is related to the relative efficiency of estimating the normalizing term in self-normalizing importance sampling when using posterior draws obtained with MCMC. If MCMC draws are used and r_eff is not provided then the reported PSIS effective sample sizes and Monte Carlo error estimates will be over-optimistic. If the posterior draws are independent then r_eff=1 and can be omitted. See the relative_eff() helper functions for computing r_eff.

The number of cores to use for parallelization. This defaults to the option mc.cores which can be set for an entire R session by options(mc.cores = NUMBER). The old option loo.cores is now deprecated but will be given precedence over mc.cores until loo.cores is removed in a future release. As of version 2.0.0 the default is now 1 core if mc.cores is not set, but we recommend using as many (or close to as many) cores as possible.

• Note for Windows 10 users: it is strongly recommended to avoid using the .Rprofile file to set mc.cores (using the cores argument or setting mc.cores interactively or in a script is fine).

What type of approximation of the loo_i's should be used? The default is "plpd" (the log predictive density using the posterior expectation). There are six different methods implemented to approximate loo_i's (see the references for more details):

• "plpd": uses the lpd based on point estimates (i.e., p(y_i|\hat{θ})).

• "lpd": uses the lpds (i,e., p(y_i|y)).

• "tis": uses truncated importance sampling to approximate PSIS-LOO.

• "waic": uses waic (i.e., p(y_i|y) - p_{waic}).

• "waic_grad_marginal": uses waic approximation using first order delta method and posterior marginal variances to approximate p_{waic} (ie. p(y_i|\hat{θ})-p_waic_grad_marginal). Requires gradient of likelihood function.

• "waic_grad": uses waic approximation using first order delta method and posterior covariance to approximate p_{waic} (ie. p(y_i|\hat{θ})-p_waic_grad). Requires gradient of likelihood function.

• "waic_hess": uses waic approximation using second order delta method and posterior covariance to approximate p_{waic} (ie. p(y_i|\hat{θ})-p_waic_grad). Requires gradient and Hessian of likelihood function.

As point estimates of \hat{θ}, the posterior expectations of the parameters are used.

The number of posterior draws used when integrating over the posterior. This is used if loo_approximation is set to "lpd", "waic", or "tis".

The gradient of the log-likelihood. This is only used when loo_approximation is "waic_grad", "waic_grad_marginal", or "waic_hess". The default is NULL.

The hessian of the log-likelihood. This is only used with loo_approximation = "waic_hess". The default is NULL.