Terminates an MCMC run when the difference between the means of individual runs
and the mean of the sample pooled from all runs ceases to be significant.
This convergence criterion evaluates whether the mean of the sample pooled
from multiple runs lies outside the confidence interval of width 1 - `prob`
constructed for the mean of each individual run. Accordingly, it can only be
calculated when two or more independent runs are performed.
The number of samples to be removed as burnin before calculating the test
statistic is determined using the `burninMethod`. If the `"ESS"` (default) or
`"SEM"` options are chosen, different burnin lengths are tested, increasing
from 0 to 50% (for `"ESS"`) or 100% (for `"SEM"`) of the length of the trace in
increments of 10 samples. The `"ESS"` option calculates effective sample sizes
(ESS) for all monitored parameters after removing the number of samples
corresponding to each candidate burnin length. The best burnin length for a
given parameter is the one that maximizes its ESS value. The `"SEM"` option
instead calculates the standard error of the mean (SEM), and the best burnin
length for a given parameter is the one that minimizes its SEM value. In both
cases, the final burnin length is set to the maximum of the parameter-specific
burnin lengths.
Alternatively, the user may set `burninMethod` to `"fixed"`, which discards a
constant fraction of the samples collected up to that point. This fraction can
be specified using the `burnin` argument, and is set to 0.25 by default. The
`burnin` argument has no effect if the `"ESS"` or `"SEM"` options are chosen,
and a corresponding warning is displayed if the user explicitly sets the
argument without specifying `burninMethod="fixed"`. The `"fixed"` option is
appropriate for analyses with very long parameter traces and large numbers of
monitored variables, for which the automatic burnin determination may be too
computationally demanding.
See also the tutorial on [convergence assessment](https://revbayes.github.io/tutorials/convergence/).
# Binomial example: estimate success probability given 7 successes out of 20 trials
r ~ dnExp(10)
p := Probability(ifelse(r < 1, r, 1))
n <- 20
k ~ dnBinomial(n, p)
k.clamp(7)
mymodel = model(k)
moves = VectorMoves()
moves.append( mvSlide(r, delta=0.1, weight=1) )
paramFile = "parameters.log"
monitors = VectorMonitors()
monitors.append( mnModel(filename=paramFile, printgen=100, p) )
# Stop when stationarity has been attained at confidence level gamma = 0.25
stopping_rules[1] = srStationarity(prob = 0.25, file = paramFile, freq = 1000)
# Create the MCMC object
# Set nruns = 2 to ensure the stationarity statistic is applicable
mymcmc = mcmc(mymodel, monitors, moves, nruns = 2)
# Begin the MCMC run
mymcmc.run(rules = stopping_rules)