@misc{Romaniuk_Maciej_Convergence_2008,
 author={Romaniuk, Maciej},
 copyright={Creative Commons Attribution BY 4.0 license},
 address={Warszawa},
 journal={Raport Badawczy = Research Report},
 howpublished={online},
 year={2008},
 publisher={Instytut Badań Systemowych. Polska Akademia Nauk},
 publisher={Systems Research Institute. Polish Academy of Sciences},
 language={eng},
 abstract={MCMC setups are one of the best known methods for conducting computer simulations useful in such areas as statistics, physics, biology, etc. However, to obtain appropriate solutions, the additional convergence diagnosis must be applied for Markov Chain trajectory generated by the algorithm. We present the method for dealing with this problem based on features of so called “ secondary” chain ( the chain with specially selected state space). The secondary chain is created from the initial chain by picking only some observations connected with atoms or renewal sets. In this paper we focus on finding the moment when the simulated chain is close enough to the stationary distribution of the Markov chain. The discussed method has some appealing properties, like high degree of diagnosis automation. Apart from theoretical lemmas and a more heuristic approach, the examples of application are also provided.},
 title={Convergence diagnosisto stationary distribution in MCMC methods via atoms and renewal sets},
 type={Text},
 URL={http://www.rcin.org.pl/Content/217400/PDF/RB-2008-69.pdf},
}