Markov chain diagnostics & reproducibility

Bayesian Modeling with RJAGS

Alicia Johnson

Associate Professor, Macalester College

Markov chain output

Questions to consider

What does a "good" Markov chain look like?
How accurate is the Markov chain approximation of the posterior?
For how many iterations should we run the Markov chain?

Diagnostic: trace plots

Good: stability!

Bad: instability

Diagnostic: multiple chains

# COMPILE the model
sleep_jags <- jags.model(..., n.chains = 1)

Diagnostic: multiple chains

# COMPILE the model
sleep_jags <- jags.model(..., n.chains = 2)

Diagnostic: multiple chains

# COMPILE the model
sleep_jags <- jags.model(..., n.chains = 4)

Diagnostic: multiple chains

# COMPILE the model
sleep_jags <- jags.model(..., n.chains = 4)

summary(sleep_sim)

1. Empirical mean and standard deviation for each variable,
   plus standard error of the mean:

   Mean    SD Naive SE Time-series SE
m 29.10 8.968   0.2836         0.2820
s 40.07 7.887   0.2494         0.4227

2. Quantiles for each variable:

   2.5%   25%   50%   75% 97.5%
m 11.42 23.27 28.85 34.76 46.76
s 28.31 34.65 38.93 43.91 57.56

Estimate of the posterior mean of $m$ = 29.10 ms
(Naive) standard error of this estimate = 0.2836 ms
SD / $\sqrt{\text{number of iterations}}$

Diagnostic: standard error

Estimated mean = 29.10 ms
(Naive) standard error = 0.2836 ms

$29.10 \pm 2*0.2836$

Markov chain work flow

Define, compile, simulate the model
Examine the following diagnostics:
- Trace plots
- Multiple chain output
- Standard errors
Finalize the simulation

Finalizing the Markov chain: Reproducibility

sleep_jags <- jags.model(textConnection(sleep_model), 
    data = list(Y = sleep_study$diff_3),
    inits = list(.RNG.name = "base::Wichmann-Hill",
                 .RNG.seed = 1989))

Let's practice!

Bayesian Modeling with RJAGS