burnin {LaplacesDemon} R Documentation

## Burn-in

### Description

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.

### Usage

burnin(x, method="BMK")


### Arguments

 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".

### Details

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.

### Value

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.

### Author(s)

Statisticat, LLC. software@bayesian-inference.com

### References

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.
library(LaplacesDemon)