The bayesplot MCMC module provides various plotting functions for creating graphical displays of Markov chain Monte Carlo (MCMC) simulations. The MCMC plotting functions section, below, provides links to the documentation for various categories of MCMC plots. Currently the MCMC plotting functions accept posterior draws provided in one of the following formats:

• 3-D array: An array with dimensions [Iteration, Chain, Parameter] in that order.

• list: A list of matrices, where each matrix corresponds to a Markov chain. All of the matrices should have the same number of iterations (rows) and parameters (columns), and parameters should have the same names and be in the same order.

• matrix (2-D array): A matrix with one column per parameter. If using matrix there should only be a single Markov chain or all chains should already be merged (stacked).

• data frame: There are two types of data frames allowed. Either a data frame with one column per parameter (if only a single chain or all chains have already been merged), or a data frame with one column per parameter plus an additional column "Chain" that contains the chain number (an integer) corresponding to each row in the data frame.

Note: typically the user should not include warmup iterations in the object passed to bayesplot plotting functions, although for certain plots (e.g. trace plots) it can occasionally be useful to include the warmup iterations for diagnostic purposes.

## MCMC plotting functions

• Posterior distributions: Histograms and kernel density plots of parameter draws, optionally showing each Markov chain separately.

• Uncertainty intervals: Uncertainty intervals computed from parameter draws.

• Trace plots: Times series of parameter draws, optionally including with HMC/NUTS diagnostic information.

• Scatterplots: Scatterplots, heatmaps, and pairs plots of parameter draws, optionally including with HMC/NUTS diagnostic information.

• Parallel coordinates plots: Parallel coordinates plot of MCMC draws (one dimension per parameter), optionally including with HMC/NUTS diagnostic information.

• Combos: Combination plots (e.g. trace plot + histogram).

• General MCMC diagnostics: MCMC diagnostic plots including R-hat, effective sample size, autocorrelation. NUTS diagnostics: Special diagnostic plots for the No-U-Turn Sampler.

• Comparisons to "true" values: Plots comparing MCMC estimates to "true" parameter values (e.g., values used to simulate data).

## References

Gabry, J. , Simpson, D. , Vehtari, A. , Betancourt, M. and Gelman, A. (2019), Visualization in Bayesian workflow. J. R. Stat. Soc. A, 182: 389-402. doi:10.1111/rssa.12378. (journal version, arXiv preprint, code on GitHub)

Other MCMC: MCMC-combos, MCMC-diagnostics, MCMC-distributions, MCMC-intervals, MCMC-nuts, MCMC-parcoord, MCMC-recover, MCMC-scatterplots, MCMC-traces