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On the fractional record values

100%

Bieniek M. , Szynal D.

tom Vol. 24, Fasc. 1

27--46

We define the record-values process which may be considered as the collection of record values with non-integer or fractional indices. The alternative con-struction from the sample as well as the basic properties of the defined process are shown.

On some method for diagnosing convergence in MCMC setups via atoms and renewal sets

75%

Romaniuk M.

Control and Cybernetics

2007

tom Vol. 36, no 4

985-1008

MCMC setups are among the best known methods for conducting computer simulations necessary in statistics, physics, biology, etc. However, to obtain appropriate solutions, additional convergence diagnosis must be applied for trajectory generated by Markov Chain. In the paper 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. The discussed method has some appealing properties, like high degree of diagnosis automation. Apart from theoretical lemmas, the example of application is also provided.