IAT: Integrated Autocorrelation Time

In LaplacesDemon: Complete Environment for Bayesian Inference

Description

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.

Usage

IAT(x)

Arguments

x	This requried argument is a vector of samples from a chain.

Details

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.

Value

The IAT function returns the integrated autocorrelation time of a chain.

Author(s)

Statisticat, LLC. [e-mail]

References

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.

See Also

burnin, Compare, ESS, LaplacesDemon, MCSE, and PosteriorChecks.

Examples

library(LaplacesDemon)
theta <- rnorm(100)
IAT(theta)

LaplacesDemon documentation built on July 9, 2021, 5:07 p.m.