1,088 research outputs found
Markov Chain Monte Carlo: Can We Trust the Third Significant Figure?
Current reporting of results based on Markov chain Monte Carlo computations
could be improved. In particular, a measure of the accuracy of the resulting
estimates is rarely reported. Thus we have little ability to objectively assess
the quality of the reported estimates. We address this issue in that we discuss
why Monte Carlo standard errors are important, how they can be easily
calculated in Markov chain Monte Carlo and how they can be used to decide when
to stop the simulation. We compare their use to a popular alternative in the
context of two examples.Comment: Published in at http://dx.doi.org/10.1214/08-STS257 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Congruence schemes
A new category of algebro-geometric objects is defined. This construction is
a vast generalization of existing F1-theories, as it contains the the theory of
monoid schemes on the one hand and classical algebraic theory, e.g.
Grothendieck schemes, on the the other. It also gives a handy description of
Berkovich subdomains and thus contains Berkovich's approach to abstract
skeletons. Further it complements the theory of monoid schemes in view of
number theoretic applications as congruence schemes encode number theoretical
information as opposed to combinatorial data which are seen by monoid schemes
Permanence criteria for semi-free profinite groups
We introduce the condition of a profinite group being semi-free, which is
more general than being free and more restrictive than being quasi-free. In
particular, every projective semi-free profinite group is free. We prove that
the usual permanence properties of free groups carry over to semi-free groups.
Using this, we conclude that if k is a separably closed field, then many field
extensions of k((x,y)) have free absolute Galois groups.Comment: 24 page
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