TracePlots

A traceplot is a graphical tool used primarily in computational statistics and Bayesian inference to assess the behavior and convergence of Markov chain Monte Carlo (MCMC) simulations. Each line in a traceplot represents the evolution of a sampled parameter value across successive iterations of the algorithm. By plotting sample indices on the horizontal axis and parameter values on the vertical axis, traceplots provide an immediate visual cue as to whether the chain has reached a stable regime and whether it mixes well.

The main purpose of a traceplot is to diagnose problems such as non‑convergence, autocorrelation, or the presence of multiple modes. If the chain has converged to its stationary distribution, the traceplot should look like a dense cloud of points without systematic trends or jumps. A noticeable drift or a clear “spike” suggests that the sampler has not yet stabilized and longer runs or different tuning may be required. In addition, traceplots allow the explorer to see whether different chains (with different initial values) share the same distribution, which is a key condition in multi‑chain diagnostics such as the potential scale reduction factor (R̂).

Traceplots are commonly generated by statistical software packages such as R (packages mcmc, rstan, coda), Python (PyMC, arviz), and Stan’s own graphical interface. Implementations often allow multiple chains to be displayed side‑by‑side or overlaid, and may provide smoothing or autocorrelation overlays to enhance interpretability. Despite their simplicity, traceplots remain an indispensable first step in validating the quality of MCMC output and ensuring that posterior estimates are reliable.