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MCMC-nuts

Diagnostic plots for the No-U-Turn-Sampler (NUTS)

Description

Diagnostic plots for the No-U-Turn-Sampler (NUTS), the default MCMC algorithm used by Stan. See the Plot Descriptions section, below.

Usage

mcmc_nuts_acceptance(x, lp, chain = NULL, ..., binwidth = NULL)

mcmc_nuts_divergence(x, lp, chain = NULL, ...)

mcmc_nuts_stepsize(x, lp, chain = NULL, ...)

mcmc_nuts_treedepth(x, lp, chain = NULL, ...)

mcmc_nuts_energy(x, ..., binwidth = NULL, alpha = 0.5, merge_chains = FALSE)

Arguments

`x`	A molten data frame of NUTS sampler parameters, either created by `nuts_params()` or in the same form as the object returned by `nuts_params()`.
`lp`	A molten data frame of draws of the log-posterior or, more commonly, of a quantity equal to the log-posterior up to a constant. `lp` should either be created via `log_posterior()` or be an object with the same form as the object returned by `log_posterior()`.
`chain`	A positive integer for selecting a particular chain. The default (`NULL`) is to merge the chains before plotting. If `chain = k` then the plot for chain `k` is overlaid (in a darker shade but with transparency) on top of the plot for all chains. The `chain` argument is not used by `mcmc_nuts_energy()`.
`...`	Currently ignored.
`binwidth`	An optional value passed to `ggplot2::geom_histogram()` to override the default binwidth.
`alpha`	For `mcmc_nuts_energy()` only, the transparency (alpha) level in `[0,1]` used for the overlaid histogram.
`merge_chains`	For `mcmc_nuts_energy()` only, should all chains be merged or displayed separately? The default is `FALSE`, i.e., to show the chains separately.

Value

A gtable object (the result of calling gridExtra::arrangeGrob()) created from several ggplot objects, except for mcmc_nuts_energy(), which returns a ggplot object.

Quick Definitions

For more details see Stan Development Team (2016) and Betancourt (2017).

accept_stat__: the average acceptance probabilities of all possible samples in the proposed tree.
divergent__: the number of leapfrog transitions with diverging error. Because NUTS terminates at the first divergence this will be either 0 or 1 for each iteration.
stepsize__: the step size used by NUTS in its Hamiltonian simulation.
treedepth__: the depth of tree used by NUTS, which is the log (base 2) of the number of leapfrog steps taken during the Hamiltonian simulation.
energy__: the value of the Hamiltonian (up to an additive constant) at each iteration.

Plot Descriptions

mcmc_nuts_acceptance()

Three plots:

Histogram of accept_stat__ with vertical lines indicating the mean (solid line) and median (dashed line).
Histogram of lp__ with vertical lines indicating the mean (solid line) and median (dashed line).
Scatterplot of accept_stat__ vs lp__.

mcmc_nuts_divergence()

Two plots:

Violin plots of lp__|divergent__=1 and lp__|divergent__=0.
Violin plots of accept_stat__|divergent__=1 and accept_stat__|divergent__=0.

mcmc_nuts_stepsize()

Two plots:

Violin plots of lp__ by chain ordered by stepsize__ value.
Violin plots of accept_stat__ by chain ordered by stepsize__ value.

mcmc_nuts_treedepth()

Three plots:

Violin plots of lp__ by value of treedepth__.
Violin plots of accept_stat__ by value of treedepth__.
Histogram of treedepth__.

mcmc_nuts_energy()

Overlaid histograms showing energy__ vs the change in energy__. See Betancourt (2016) for details.

References

Betancourt, M. (2017). A conceptual introduction to Hamiltonian Monte Carlo. https://arxiv.org/abs/1701.02434

Betancourt, M. and Girolami, M. (2013). Hamiltonian Monte Carlo for hierarchical models. https://arxiv.org/abs/1312.0906

Hoffman, M. D. and Gelman, A. (2014). The No-U-Turn Sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research. 15:1593–1623.

Stan Development Team. Stan Modeling Language Users Guide and Reference Manual. https://mc-stan.org/users/documentation/

Examples

## Not run: 
library(ggplot2)
library(rstanarm)
fit <- stan_glm(mpg ~ wt + am, data = mtcars, iter = 1000, refresh = 0)
np <- nuts_params(fit)
lp <- log_posterior(fit)

color_scheme_set("brightblue")
mcmc_nuts_acceptance(np, lp)
mcmc_nuts_acceptance(np, lp, chain = 2)

mcmc_nuts_divergence(np, lp)
mcmc_nuts_stepsize(np, lp)
mcmc_nuts_treedepth(np, lp)

color_scheme_set("red")
mcmc_nuts_energy(np)
mcmc_nuts_energy(np, merge_chains = TRUE, binwidth = .15)
mcmc_nuts_energy(np) +
 facet_wrap(~ Chain, nrow = 1) +
 coord_fixed(ratio = 150) +
 ggtitle("NUTS Energy Diagnostic")

## End(Not run)

bayesplot

Plotting for Bayesian Models

v1.8.0

GPL (>= 3)

Authors

Jonah Gabry [aut, cre], Tristan Mahr [aut], Paul-Christian Bürkner [ctb], Martin Modrák [ctb], Malcolm Barrett [ctb], Frank Weber [ctb], Eduardo Coronado Sroka [ctb], Aki Vehtari [ctb]

Initial release

2021-01-07