Question
Answer and Explanation
Determining if an RStan sampler was unsuccessful involves examining several diagnostic outputs and indicators. Here's a breakdown of key areas to check:
1. Divergent Transitions:
- Divergent transitions are a primary indicator of sampling problems. They occur when the Hamiltonian Monte Carlo (HMC) algorithm encounters numerical instability. RStan reports the number of divergent transitions. A high number of divergences suggests that the sampler is not exploring the posterior distribution effectively.
- How to check: Look for warnings or messages in the RStan output that mention "divergent transitions." You can also use the `rstan::get_sampler_params()` function to retrieve the number of divergent transitions for each chain.
2. R-hat (R̂) Values:
- R-hat (also known as the Gelman-Rubin statistic) measures the convergence of multiple Markov chains. Ideally, R-hat values should be close to 1. Values significantly greater than 1 (e.g., > 1.1) indicate that the chains have not converged to the same distribution, suggesting sampling issues.
- How to check: Use the `rstan::summary()` function or the `rstan::monitor()` function to obtain R-hat values for each parameter. Examine the maximum R-hat value across all parameters.
3. Effective Sample Size (N_eff):
- The effective sample size (N_eff) estimates the number of independent samples from the posterior distribution. A low N_eff relative to the total number of samples indicates high autocorrelation within the chains, which means the sampler is not exploring the space efficiently.
- How to check: Check the N_eff values in the output of `rstan::summary()` or `rstan::monitor()`. A general rule of thumb is that N_eff should be at least 10% of the total number of samples.
4. Energy Plots:
- Energy plots can help diagnose issues related to the sampler's exploration of the energy landscape. Look for "funnel" shapes or other patterns that suggest the sampler is getting stuck in certain regions of the parameter space.
- How to check: Use the `rstan::stan_plot()` function with the `type = "energy"` argument to visualize energy plots.
5. Trace Plots:
- Trace plots show the evolution of parameter values across iterations. Well-mixed chains should look like "fuzzy caterpillars" without any obvious trends or patterns. If the chains are not mixing well, it suggests that the sampler is not exploring the posterior distribution effectively.
- How to check: Use the `rstan::traceplot()` function to visualize trace plots for each parameter.
6. Warnings and Error Messages:
- Pay close attention to any warnings or error messages generated by RStan during the sampling process. These messages often provide valuable clues about potential problems.
- How to check: Carefully review the console output for any messages related to sampling issues.
7. Posterior Predictive Checks:
- Compare the simulated data from the posterior distribution with the observed data. If the simulated data does not resemble the observed data, it suggests that the model is not capturing the underlying patterns, which can be a sign of sampling or model misspecification issues.
- How to check: Implement posterior predictive checks using the `rstan::posterior_predict()` function and compare the simulated data with the observed data.
In summary, a successful RStan sampling process requires careful monitoring of various diagnostic outputs. Divergent transitions, high R-hat values, low effective sample sizes, and poorly mixed chains are all indicators of potential problems. Addressing these issues often involves adjusting the model, the sampling parameters, or both.