The IAT function estimates integrated autocorrelation time,
which is the computational inefficiency of a continuous chain or MCMC
sampler. IAT is also called the IACT, ACT, autocorrelation time,
autocovariance time, correlation time, or inefficiency factor. A lower
value of IAT is better. IAT is a MCMC diagnostic that is
an estimate of the number of iterations, on average, for an
independent sample to be drawn, given a continuous chain or Markov
chain. Put another way, IAT is the number of correlated samples
with the same variance-reducing power as one independent sample.
IAT is a univariate function. A multivariate form is not included.
IAT(x)This requried argument is a vector of samples from a chain.
The IAT function returns the integrated autocorrelation time of
a chain.
IAT is a MCMC diagnostic that is often used to compare
continuous chains of MCMC samplers for computational inefficiency,
where the sampler with the lowest IATs is the most efficient
sampler. Otherwise, chains may be compared within a model, such as
with the output of LaplacesDemon to learn about the
inefficiency of the continuous chain. For more information on
comparing MCMC algorithmic inefficiency, see the
Juxtapose function.
IAT is also estimated in the PosteriorChecks
function. IAT is usually applied to a stationary, continuous
chain after discarding burn-in iterations (see burnin
for more information). The IAT of a continuous chain correlates
with the variability of the mean of the chain, and relates to
Effective Sample Size (ESS) and Monte Carlo Standard
Error (MCSE).
IAT and ESS are inversely related, though not
perfectly, because each is estimated a little differently. Given
\(N\) samples and taking autocorrelation into account,
ESS estimates a reduced number of \(M\) samples.
Conversely, IAT estimates the number of autocorrelated samples,
on average, required to produce one independently drawn sample.
The IAT function is similar to the IAT function in the
Rtwalk package of Christen and Fox (2010), which is currently
unavailabe on CRAN.
Christen, J.A. and Fox, C. (2010). "A General Purpose Sampling Algorithm for Continuous Distributions (the t-walk)". Bayesian Analysis, 5(2), p. 263--282.
burnin,
Compare,
ESS,
LaplacesDemon,
MCSE, and
PosteriorChecks.
# NOT RUN {
library(LaplacesDemon)
theta <- rnorm(100)
IAT(theta)
# }
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