Von Mises' definition of random sequences reconsidered

Von Mises' Definition of Random Sequences Reconsidered

Randomness and Foundations of Probability: Von Mises’ Axiomatisation of Random Sequences

to David Blackwell

Von Mises Type Statistics for Single Site Updated Local Interaction Random Elds Running Title: Von Mises Statistics for Random Elds

Random eld models in image analysis and spatial statistics usually have local interactions. They can be simulated by Markov chains which update a single site at a time. The updating rules typically condition on only a few neighboring sites. If we want to approximate the expectation of a bounded function, can we make better use of the simulations than through the empirical estimator? We describe...

The Definition of Random Sequences

Kolmogorov has defined tile conditional complexity of an object y when the object x is already given to us as the minimal length of a binary program which by means of x computes y on a certain asymptotically optimal machine. On the basis of this definition he has proposed to consider those elements of a given large finite population to be random whose complexity is maximal. Almost all elements ...

Approximations for Von Mises

We prove Edgeworth expansions for degenerate von Mises statistics like the Beran, Watson, and Cram er-von Mises goodness-of-t statistics. Furthermore, we show that the bootstrap approximation works up to an error of order O(N ?1=2) and that Bootstrap based conndence regions attain a prescribed conndence level up to the order O(n ?1).