raftery.diag(data, q=0.025, r=0.0125, s=0.95, converge.eps=0.01)
data
| an mcmc object |
q
| the quantile to be estimated. |
r
| the desired margin of error of the estimate. |
s
| the probability of obtaining an estimate in the interval (q-r,q+r). |
converge.eps
| Precision required for estimate of time to convergence. |
raftery.diag
calculates the number of iterations required to
estimate the quantile q to within an accuracy of +/- r
with probability p. Separate calculations are performed for
each variable within each chain.
If the number of iterations in data
is too small,
an error message is printed indicating the minimum length of
pilot run. The minimum length is the required sample size for a
chain with no correlation between consecutive samples. Positive
autocorrelation will increase the required sample size above this
minimum value. An estimate I
(the "dependence factor") of the
extent to which autocorrelation inflates the required sample size
is also provided. Values of I
larger than 5 indicate strong
autocorrelation which may be due to a poor choice of starting value,
high posterior correlations or "stickyness" of the MCMC algorithm.
The number of "burn in" iterations to be discarded at the beginning of the chain is also calculated.
data
by marginalization and trunctation, but is not itself
a Markov chain. However, Z_t may behave as a Markov chain if
it is sufficiently thinned out. raftery.diag
calculates the
smallest value of thinning interval k which makes the thinned
chain Z^k_t behave as a Markov chain. The required sample size is
calculated from this thinned sequence. Since some data is `thrown away'
the sample size estimates are conservative.
Previous versions of this function displayed the value of the thinning interval k. The current version does not do so in case k is mistaken for the thinning interval which makes consecutive samples approximately independent.
The criterion for the number of "burn in" iterations m to be
discarded, is that the conditional distribution of Z^k_m
given Z_0 should be within converge.eps
of the equilibrium
distribution of the chain Z^k_t.
raftery.diag
is based on the FORTRAN program "gibbsit"
written by Steven Lewis, and available from the Statlib archive.Raftery, A.E. and Lewis, S.M. (1995). The number of iterations, convergence diagnostics and generic Metropolis algorithms. In Practical Markov Chain Monte Carlo (W.R. Gilks, D.J. Spiegelhalter and S. Richardson, eds.). London, U.K.: Chapman and Hall.