IAT {LaplacesDemon} | R Documentation |

## Integrated Autocorrelation Time

### 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 `IAT`

s 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. software@bayesian-inference.com

### 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*version 16.1.6 Index]