7,511 research outputs found
Splitting Line Patterns in Free Groups
We construct a boundary of a finite rank free group relative to a finite list
of conjugacy classes of maximal cyclic subgroups. From the cut points and
uncrossed cut pairs of this boundary we construct a simplicial tree on which
the group acts cocompactly. We show that the quotient graph of groups is the
JSJ decomposition of the group relative to the given collection of conjugacy
classes.
This provides a characterization of virtually geometric multiwords: they are
the multiwords that are built from geometric pieces. In particular, a multiword
is virtually geometric if and only if the relative boundary is planar.Comment: 22 pages, 6 figures; v2 fixed a few typos; v3 38 pages, 21 figures;
v4 30 pages, 11 figures 'Preliminaries' section expanded to make paper
self-contained and split into two sections. Some arguments refactored and
simplified. Paper streamlined; v5 56 pages, 21 figures Added examples and
improved exposition according to referee comments. To appear in Algebraic &
Geometric Topolog
Bayesian Semiparametric Hierarchical Empirical Likelihood Spatial Models
We introduce a general hierarchical Bayesian framework that incorporates a
flexible nonparametric data model specification through the use of empirical
likelihood methodology, which we term semiparametric hierarchical empirical
likelihood (SHEL) models. Although general dependence structures can be readily
accommodated, we focus on spatial modeling, a relatively underdeveloped area in
the empirical likelihood literature. Importantly, the models we develop
naturally accommodate spatial association on irregular lattices and irregularly
spaced point-referenced data. We illustrate our proposed framework by means of
a simulation study and through three real data examples. First, we develop a
spatial Fay-Herriot model in the SHEL framework and apply it to the problem of
small area estimation in the American Community Survey. Next, we illustrate the
SHEL model in the context of areal data (on an irregular lattice) through the
North Carolina sudden infant death syndrome (SIDS) dataset. Finally, we analyze
a point-referenced dataset from the North American Breeding Bird survey that
considers dove counts for the state of Missouri. In all cases, we demonstrate
superior performance of our model, in terms of mean squared prediction error,
over standard parametric analyses.Comment: 29 pages, 3 figue
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