01-diagnostics | model diagnostics #
Overview #
Diagnostics are applied to monitor whether the Markov chains have converged.
| File | Description |
|---|---|
| funnel/ | Full plots |
| trace/ | Traceplots |
| convergence-diagnostics.txt | The Gelman and Rubin ( Citation: 1992 Gelman, A. & Rubin, D. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4). 457–472. ) potential scale reduction statistic, \(\hat{R}\) , for selected parameters. \(\hat{R}\) measures the ratio of the average variance of samples within each chain to the variance of samples pooled across all chains. If the chains have converged to a common distribution, \(\hat{R} \simeq 1\) , otherwise \(\hat{R} > 1\) . We hope to see \(\hat{R} < 1.1\) . |
Subdirectories #
funnel/ | funnel plots #
Bivariate scatter plots created by plotting the posterior values of “local” parameters (a group-level effect for site \(j\) ) against a “global” scale parameter on which it depends ( \(\sigma_{\beta_0}\) ). The problem that these plots are designed to detect is discussed here. The issues presented by strong funnel-like shapes in these scatterplots can be resolved with the non-centered parameterization.
trace/ | traceplots #
The traceplot is essentially a time series plot of the Markov chains. It shows the evolution of a parameter vector over the MCMC iterations of each Markov chain. We’re hoping to see the chain exploring the same region of parameter values, with good mixing.
References #
- Gelman & Rubin (1992)
- Gelman, A. & Rubin, D. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4). 457–472.