Extract log probability (target)

The $lp() method extracts lp__, the target log density evaluated by Stan, up to an additive constant. For variational inference, Laplace approximation, and Pathfinder, the log density of the corresponding approximating distribution is available via $lp_approx().

See the Increment log density and Distribution Statements sections of the Stan Reference Manual for details on when normalizing constants are dropped from log probability calculations.

Usage

lp()

lp_approx()

Value

A numeric vector with length equal to the number of (post-warmup) draws or length equal to 1 for optimization.

Details

The target includes all contributions to the log probability, which can come from the transformed parameters and model blocks, including certain user-defined functions. The exact target represented by lp__ depends on the inference method:

• For MCMC sampling, variational inference, Pathfinder, and diagnostic mode, lp__ is the log density on Stan's unconstrained space and includes the Jacobian adjustments for constrained parameters.

• For optimization and Laplace approximation, whether the Jacobian adjustments are included depends on the jacobian argument.

For MCMC, lp__ can be used to diagnose sampling efficiency; for approximation methods, it can be used to evaluate the approximation.

For variational inference lp_approx__ is the log density of the variational approximation to lp__ (also on the unconstrained space). It is exposed in the variational method for performing the checks described in Yao et al. (2018) and implemented in the loo package.

For Laplace approximation lp_approx__ is CmdStan's log_q__: the unnormalized log density of the normal approximation on the unconstrained space. It can be used to perform the same checks as in the case of the variational method described in Yao et al. (2018).

For Pathfinder lp_approx__ is the log density of the approximating distribution on the unconstrained space.

References

Yao, Y., Vehtari, A., Simpson, D., and Gelman, A. (2018). Yes, but did it work?: Evaluating variational inference. Proceedings of the 35th International Conference on Machine Learning, PMLR 80:5581–5590.

Examples

# \dontrun{
fit_mcmc <- cmdstanr_example("logistic")
head(fit_mcmc$lp())
#> [1] -67.37350 -68.09788 -64.11029 -65.24980 -65.11933 -66.92787

fit_optim <- cmdstanr_example("logistic", method = "optimize")
fit_optim$lp()
#> [1] -63.9218

fit_vb <- cmdstanr_example("logistic", method = "variational")
plot(fit_vb$lp(), fit_vb$lp_approx())


fit_pathfinder <- cmdstanr_example("logistic", method = "pathfinder")
plot(fit_pathfinder$lp(), fit_pathfinder$lp_approx())

# }