Raftery.Diagnostic {LaplacesDemon}  R Documentation 
Raftery and Lewis's diagnostic
Description
Raftery and Lewis (1992) introduced an MCMC diagnostic that estimates the number of iterations needed for a given level of precision in posterior samples, as well as estimating burnin, when quantiles are the posterior summaries of interest.
Usage
Raftery.Diagnostic(x, q=0.025, r=0.005, s=0.95, eps=0.001)
Arguments
x 
This required argument accepts an object of class

q 
This is the quantile to be estimated. 
r 
This is the desired margin of error of the estimate, also called the accuracy. 
s 
This is the probability of obtaining an estimate in the interval (qr, q+r). 
eps 
This is the precision required for the estimate of time to convergence. 
Details
In this MCMC diagnostic, a posterior quantile q
of interest is
specified. Next, an acceptable tolerance r
is specified for
q
, which means that it is desired to measure q
with an
accuracy of +/ r
. Finally, the user selects a probability
s
, which is the probability of being within the interval
(qr, q+r)
. The Raftery.Diagnostic
then estimates the
number N
of iterations and the number M
of burnin
iterations that are necessary to satisfy the specified conditions
regarding quantile q
.
The diagnostic was designed to test a short, initial update, in which the chains were called pilot chains, and the application was later suggested for iterative use after any update as a general method for pursuing convergence (Raftery and Lewis, 1996).
Results of the Raftery.Diagnostic
differ depending on the
chosen quantile q
. Estimates are conservative, so more
iterations are suggested than necessary.
Value
The Raftery.Diagnostic
function returns an object of class
raftery
that is list. A print method is available for objects
of this class. The list has the following components:
tspar 
These are the timeseries parameters of the posterior
samples in 
params 
This is a vector containing the parameters 
Niters 
This is the number of iterations in the posterior
samples in 
resmatrix 
This is a 3dimensional array containing the
results: 
Note
The Raftery.Diagnostic
function was adapted from the
raftery.diag
function in the coda package, which was adapted
from the FORTRAN program ‘gibbsit’, written by Steven Lewis.
References
Raftery, A.E. and Lewis, S.M. (1992). "How Many Iterations in the Gibbs Sampler?" In Bayesian Statistics, 4 (J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith, eds.). Oxford, U.K.: Oxford University Press, p. 763–773.
Raftery, A.E. and Lewis, S.M. (1992). "One Long Run with Diagnostics: Implementation Strategies for Markov chain Monte Carlo". Statistical Science, 7, p. 493–497.
Raftery, A.E. and Lewis, S.M. (1996). "Implementing MCMC". In Practical Markov Chain Monte Carlo (W.R. Gilks, D.J. Spiegelhalter and S. Richardson, eds.). Chapman and Hall: Baton Rouge, FL.
See Also
burnin
,
LaplacesDemon
,
print.raftery
, and
Thin
.
Examples
#library(LaplacesDemon)
###After updating with LaplacesDemon, do:
#rd < Raftery.Diagnostic(Fit)
#print(rd)