This paper introduces and evaluates methods for estimating out-of-sample prediction accuracy from Bayesian models using leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC). The authors propose an efficient computation of LOO using Pareto-smoothed importance sampling (PSIS), a new procedure that regularizes importance weights. They demonstrate that PSIS-LOO is more robust in finite cases with weak priors or influential observations compared to WAIC. The paper also provides diagnostics to assess the reliability of these approximations and discusses the trade-offs between different methods. The computations are implemented in an R package called *1oo* and demonstrated using models fit with the Bayesian inference package Stan. The examples provided illustrate the performance of the methods in various scenarios, including hierarchical models, linear regression, nonlinear regression, logistic regression, and multilevel regression.This paper introduces and evaluates methods for estimating out-of-sample prediction accuracy from Bayesian models using leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC). The authors propose an efficient computation of LOO using Pareto-smoothed importance sampling (PSIS), a new procedure that regularizes importance weights. They demonstrate that PSIS-LOO is more robust in finite cases with weak priors or influential observations compared to WAIC. The paper also provides diagnostics to assess the reliability of these approximations and discusses the trade-offs between different methods. The computations are implemented in an R package called *1oo* and demonstrated using models fit with the Bayesian inference package Stan. The examples provided illustrate the performance of the methods in various scenarios, including hierarchical models, linear regression, nonlinear regression, logistic regression, and multilevel regression.