# MCMC-scatterplots

##### Scatterplots of MCMC draws

Scatterplots, hexagonal heatmaps, and pairs plots from MCMC draws. See the
**Plot Descriptions** section, below, for details.

##### Usage

```
mcmc_scatter(x, pars = character(), regex_pars = character(),
transformations = list(), ..., size = 2.5, alpha = 0.8, np = NULL,
np_style = scatter_style_np())
```mcmc_hex(x, pars = character(), regex_pars = character(),
transformations = list(), ..., binwidth = NULL)

mcmc_pairs(x, pars = character(), regex_pars = character(),
transformations = list(), ..., diag_fun = c("hist", "dens"),
off_diag_fun = c("scatter", "hex"), diag_args = list(),
off_diag_args = list(), condition = pairs_condition(), lp = NULL,
np = NULL, np_style = pairs_style_np(), max_treedepth = NULL,
grid_args = list(), save_gg_objects = TRUE)

scatter_style_np(div_color = "red", div_shape = 16, div_size = 2.5,
div_alpha = 1)

pairs_style_np(div_color = "red", div_shape = 4, div_size = 1,
div_alpha = 1, td_color = "yellow2", td_shape = 3, td_size = 1,
td_alpha = 1)

pairs_condition(chains = NULL, draws = NULL, nuts = NULL)

##### Arguments

- x
A 3-D array, matrix, list of matrices, or data frame of MCMC draws. The MCMC-overview page provides details on how to specify each these allowed inputs.

- pars
An optional character vector of parameter names. For

`mcmc_scatter`

and`mcmc_hex`

only two parameters can be selected. To plot more than two parameters use`mcmc_pairs`

.- regex_pars
An optional regular expression to use for parameter selection. Can be specified instead of

`pars`

or in addition to`pars`

.- transformations
Optionally, transformations to apply to parameters before plotting. If

`transformations`

is a function or a single string naming a function then that function will be used to transform all parameters. To apply transformations to particular parameters, the`transformations`

argument can be a named list with length equal to the number of parameters to be transformed. Currently only univariate transformations of scalar parameters can be specified (multivariate transformations will be implemented in a future release). If`transformations`

is a list, the name of each list element should be a parameter name and the content of each list element should be a function (or any item to match as a function via`match.fun`

, e.g. a string naming a function). If a function is specified by its name as a string (e.g.`"log"`

), then it can be used to construct a new parameter label for the appropriate parameter (e.g.`"log(sigma)"`

). If a function itself is specified (e.g.`log`

or`function(x) log(x)`

) then`"t"`

is used in the new parameter label to indicate that the parameter is transformed (e.g.`"t(sigma)"`

).Note: due to partial argument matching

`transformations`

can be abbreviated for convenience in interactive use (e.g.,`transform`

,`trans`

, etc.).- ...
Currently ignored.

- size, alpha
For

`mcmc_scatter`

, passed to`geom_point`

to control the appearance of the points.- np
Optionally, a data frame of NUTS sampler parameters, either created by

`nuts_params`

or in the same form as the object returned by`nuts_params`

. The colors, shapes, and sizes of the superimposed points can be customized using the`np_style`

argument.- np_style
If

`np`

is specified,`np_style`

can be a call to the`scatter_style_np`

helper function (for`mcmc_scatter`

) or the`pairs_style_np`

helper function (for`mcmc_pars`

) to specify arguments controlling the appearance of superimposed points representing NUTS diagnostic information. (Note: for`pairs_style_np`

the`size`

arguments are interpreted as scaling factors).- binwidth
For

`mcmc_hex`

, an optional numeric vector of*length two*passed to`geom_hex`

to override the default binwidth in both the vertical and horizontal directions.- diag_fun, off_diag_fun
For

`mcmc_pairs`

, the plotting function to use for the plots along the diagonal and for the off-diagonal plots, respectively. Currently`diag_fun`

can be`"hist"`

for histogram or`"dens"`

for density, and`off_diag_fun`

can be`"scatter"`

for scatterplot or`"hex"`

for a hexagonal heatmap.- diag_args, off_diag_args
For

`mcmc_pairs`

, optional named lists of arguments to pass to the functions implied by the`diag_fun`

and`off_diag_fun`

arguments, respectively. For example, if`off_diag_fun`

is`"scatter"`

then`off_diag_args`

could include optional arguments to`mcmc_scatter`

like`size`

and`alpha`

.- condition
For

`mcmc_pairs`

, a call to the`pairs_condition`

helper function, which is used to specify a criterion for determining which chains (or iterations) are shown in the plots above the diagonal and which are shown in the plots below the diagonal. The histograms (or density plots) along the diagonal are always made using all chains and iterations, but the scatterplots (or hex plots) above and below the diagonal show different combinations of chains/iterations depending on`condition`

. The default is a call to`pairs_condition`

with none of its arguments specified. In this case half of the chains (or roughly half if there are an odd number) will be used in the plots above the diagonal and the rest in the plots below the diagonal. The`chains`

,`draws`

, and`nuts`

arguments to`pairs_condition`

, which are documented below, can be used to change this default.- lp
For

`mcmc_pairs`

, 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`

.- max_treedepth
For

`mcmc_pairs`

, an integer representing the maximum treedepth allowed when fitting the model (if fit using NUTS). This is only needed for detecting which transitions (if any) hit the maximum treedepth.- grid_args, save_gg_objects
For

`mcmc_pairs`

, arguments to pass to`bayesplot_grid`

. For example, since`mcmc_pairs`

returns more than a single ggplot object, using`ggtitle`

afterwards will not work. But you you can still add a title to the plot using`grid_args = list(top="My title")`

.- div_color, div_shape, div_size, div_alpha, td_color, td_shape, td_size, td_alpha
Optional arguments to the

`scatter_style_np`

or`pairs_style_np`

helper functions that are eventually passed to`geom_point`

.The default values are displayed in the**Usage**section above.- chains, draws, nuts
Optional arguments to the

`pairs_condition`

helper function, which is used to specify the`condition`

argument for`mcmc_pairs`

.The

`chains`

argument can be used to select some subset of the chains. If`chains`

is an integer vector then the behavior is the same as the default (half the chains above the diagonal and half below) except using only the specified subset of chains. Alternatively,`chains`

can be a list of two integer vectors with the first specifying the chains to be shown in the plots above the diagonal and the second for below the diagonal.The

`draws`

argument to`pairs_condition`

can be used to directly specify which realizations are plotted above and below the diagonal.`draws`

can be a single proportion, which is interpreted as the proportion of realizations (among all chains) to plot in the lower panel starting with the first realization in each chain, with the complement (from the end of each chain) plotted in the upper panel. Alternatively`draws`

can be a logical vector with length equal to the product of the number of iterations and the number of chains, in which case realizations corresponding to`FALSE`

and`TRUE`

will be plotted in the lower and upper panels, respectively.For models fit using NUTS, the

`nuts`

argument to`pairs_condition`

can be used. It takes a (possibly abbreviated) string to select among`"accept_stat__"`

,`"stepsize__"`

,`"treedepth__"`

,`"n_leapfrog__"`

,`"divergent__"`

,`"energy__"`

, and`"lp__"`

. These are the sampler parameters associated with`NUTS`

(and`"lp__"`

is the log-posterior up to an additive constant). In this case, plots below the diagonal will contain realizations that are below the median of the indicated variable (or are zero in the case of`"divergent__"`

), and plots above the diagonal will contain realizations that are greater than or equal to the median of the indicated variable (or are one in the case of`"divergent__"`

). If`"lp__"`

is used then the`lp`

argument to`mcmc_pairs`

must also be specified. For the other NUTS parameters the`np`

argument to`mcmc_pairs`

must also be specified.

##### Value

`mcmc_scatter`

and `mcmc_hex`

return a ggplot object that
can be further customized using the ggplot2 package.

`mcmc_pairs`

returns many ggplot objects organized into a grid via
`bayesplot_grid`

.

##### Plot Descriptions

`mcmc_scatter`

Bivariate scatterplot of posterior draws. If using a very large number of posterior draws then

`mcmc_hex`

may be preferable to avoid overplotting. For models fit using`NUTS`

the`np`

, and`np_style`

arguments can be used to add additional information in the plot (in this case the approximate location of divergences).`mcmc_hex`

Hexagonal heatmap of 2-D bin counts. This plot is useful in cases where the posterior sample size is large enough that

`mcmc_scatter`

suffers from overplotting.`mcmc_pairs`

A square plot matrix with univariate marginal distributions along the diagonal (as histograms or kernel density plots) and bivariate distributions off the diagonal (as scatterplots or hex heatmaps).

For the off-diagonal plots, the default is to split the chains so that (roughly) half are displayed above the diagonal and half are below (all chains are always merged together for the plots along the diagonal). Other possibilities are available by setting the

`condition`

argument.Additionally, extra diagnostic information for models fit using

`NUTS`

can be added to the pairs plot using the`lp`

,`np`

, and`np_style`

arguments. If`np`

is specified (and`condition`

is*not*`"divergent__"`

), then points (red, by default) will be superimposed onto the off-diagonal plots indicating which (if any) iterations encountered a divergent transition. Also, if both`np`

and`max_treedepth`

are specified then points (yellow, by default) will be superimposed to indicate a transition that hit the maximum treedepth rather than terminated its evolution normally. The`np_style`

argument can be used with the`pairs_style_np`

convenience function to change the appearance of these overlaid points. See the**Examples**section.

##### References

Gabry, J., Simpson, D., Vehtari, A., Betancourt, M., and Gelman,
A. (2018). Visualization in Bayesian workflow. *Journal of the Royal
Statistical Society Series A*, accepted for publication. arXiv preprint:
http://arxiv.org/abs/1709.01449.

##### See Also

Other MCMC: `MCMC-combos`

,
`MCMC-diagnostics`

,
`MCMC-distributions`

,
`MCMC-intervals`

, `MCMC-nuts`

,
`MCMC-overview`

, `MCMC-parcoord`

,
`MCMC-recover`

, `MCMC-traces`

##### Examples

```
# NOT RUN {
library("ggplot2")
# some parameter draws to use for demonstration
x <- example_mcmc_draws(params = 6)
dimnames(x)
# scatterplot of alpha vs log(sigma)
color_scheme_set("teal")
(p <- mcmc_scatter(x, pars = c("alpha", "sigma"),
transform = list(sigma = "log")))
p +
labs(
title = "Insert your own headline-grabbing title",
subtitle = "with a provocative subtitle",
caption = "and a controversial caption",
x = expression(alpha),
y = expression(log(sigma))
)
# add ellipse
p + stat_ellipse(level = 0.9, color = "gray20", size = 1)
# add contour
color_scheme_set("red")
p2 <- mcmc_scatter(x, pars = c("alpha", "sigma"), size = 3.5, alpha = 0.25)
p2 + stat_density_2d(color = "black", size = .5)
# can also add lines/smooths
color_scheme_set("pink")
(p3 <- mcmc_scatter(x, pars = c("alpha", "beta[3]"), alpha = 0.25, size = 3))
p3 + geom_smooth(method = "lm", se = FALSE, color = "gray20",
size = .75, linetype = 2)
# }
# NOT RUN {
# hexagonal heatmap
color_scheme_set("brightblue")
(p <- mcmc_hex(x, pars = c("sigma", "alpha"), transform = list(sigma = "log")))
p + plot_bg(fill = "gray95")
p + plot_bg(fill = "gray95") + panel_bg(fill = "gray70")
# }
# NOT RUN {
color_scheme_set("purple")
# pairs plots
# default of condition=NULL implies splitting chains between upper and lower panels
mcmc_pairs(x, pars = "alpha", regex_pars = "beta\\[[1,4]\\]",
off_diag_args = list(size = 1, alpha = 0.5))
# change to density plots instead of histograms and hex plots instead of
# scatterplots
mcmc_pairs(x, pars = "alpha", regex_pars = "beta\\[[1,4]\\]",
diag_fun = "dens", off_diag_fun = "hex")
# plot chain 1 above diagonal and chains 2, 3, and 4 below
color_scheme_set("brightblue")
mcmc_pairs(x, pars = "alpha", regex_pars = "beta\\[[1,4]\\]",
diag_fun = "dens", off_diag_fun = "hex",
condition = pairs_condition(chains = list(1, 2:4)))
# }
# NOT RUN {
# }
# NOT RUN {
### Adding NUTS diagnostics to scatterplots and pairs plots
# examples using rstanarm package
library(rstanarm)
# for demonstration purposes, intentionally fit a model that
# will (almost certainly) have some divergences
fit <- stan_glm(
mpg ~ ., data = mtcars,
iter = 1000,
# this combo of prior and adapt_delta should lead to some divergences
prior = hs(),
adapt_delta = 0.9
)
posterior <- as.array(fit)
np <- nuts_params(fit)
# mcmc_scatter with divergences highlighted
color_scheme_set("brightblue")
mcmc_scatter(posterior, pars = c("wt", "sigma"), np = np)
color_scheme_set("darkgray")
div_style <- scatter_style_np(div_color = "green", div_shape = 4, div_size = 4)
mcmc_scatter(posterior, pars = c("sigma", "(Intercept)"),
np = np, np_style = div_style)
# split the draws according to above/below median accept_stat__
# and show approximate location of divergences (red points)
color_scheme_set("brightblue")
mcmc_pairs(
posterior,
pars = c("wt", "cyl", "sigma"),
off_diag_args = list(size = 1, alpha = 1/3),
condition = pairs_condition(nuts = "accept_stat__"),
np = np
)
# more customizations:
# - transform sigma to log(sigma)
# - median log-posterior as 'condition'
# - hex instead of scatter for off-diagonal plots
# - show points where max treedepth hit in blue
color_scheme_set("darkgray")
mcmc_pairs(
posterior,
pars = c("wt", "cyl", "sigma"),
transform = list(sigma = "log"),
off_diag_fun = "hex",
condition = pairs_condition(nuts = "lp__"),
lp = log_posterior(fit),
np = np,
np_style = pairs_style_np(div_color = "firebrick",
td_color = "blue",
td_size = 2),
# for demonstration purposes, set max_treedepth to a value that will
# result in at least a few max treedepth warnings
max_treedepth = with(np, -1 + max(Value[Parameter == "treedepth__"]))
)
# }
# NOT RUN {
# }
```

*Documentation reproduced from package bayesplot, version 1.6.0, License: GPL (>= 3)*