The `burnin`

function estimates the duration of burn-in in
iterations for one or more Markov chains. ``Burn-in'' refers to the
initial portion of a Markov chain that is not stationary and is still
affected by its initial value.

`burnin(x, method="BMK")`

x

This is a vector or matrix of posterior samples for which a the number of burn-in iterations will be estimated.

method

This argument defaults to `"BMK"`

, in which case
stationarity is estimated with the `BMK.Diagnostic`

function. Alternatively, the `Geweke.Diagnostic`

function may be used when `method="Geweke"`

or the
`KS.Diagnostic`

function may be used when
`method="KS"`

.

The `burnin`

function returns a vector equal in length to the
number of MCMC chains in `x`

, and each element indicates the
maximum iteration in burn-in.

Burn-in is a colloquial term for the initial iterations in a Markov chain prior to its convergence to the target distribution. During burn-in, the chain is not considered to have ``forgotten'' its initial value.

Burn-in is not a theoretical part of MCMC, but its use is the norm because of the need to limit the number of posterior samples due to computer memory. If burn-in were retained rather than discarded, then more posterior samples would have to be retained. If a Markov chain starts anywhere close to the center of its target distribution, then burn-in iterations do not need to be discarded.

In the `LaplacesDemon`

function, stationarity is estimated
with the `BMK.Diagnostic`

function on all thinned
posterior samples of each chain, beginning at cumulative 10% intervals
relative to the total number of samples, and the lowest number in
which all chains are stationary is considered the burn-in.

The term, ``burn-in'', originated in electronics regarding the initial testing of component failure at the factory to eliminate initial failures (Geyer, 2011). Although ``burn-in' has been the standard term for decades, some are referring to these as ``warm-up'' iterations.

Geyer, C.J. (2011). "Introduction to Markov Chain Monte Carlo". In S Brooks, A Gelman, G Jones, and M Xiao-Li (eds.), "Handbook of Markov Chain Monte Carlo", p. 3--48. Chapman and Hall, Boca Raton, FL.

`BMK.Diagnostic`

,
`deburn`

,
`Geweke.Diagnostic`

,
`KS.Diagnostic`

, and
`LaplacesDemon`

.

```
# NOT RUN {
library(LaplacesDemon)
x <- rnorm(1000)
burnin(x)
# }
```

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