12,930 research outputs found
Fletcher-Turek Model Averaged Profile Likelihood Confidence Intervals
We evaluate the model averaged profile likelihood confidence intervals
proposed by Fletcher and Turek (2011) in a simple situation in which there are
two linear regression models over which we average. We obtain exact expressions
for the coverage and the scaled expected length of the intervals and use these
to compute these quantities in particular situations. We show that the
Fletcher-Turek confidence intervals can have coverage well below the nominal
coverage and expected length greater than that of the standard confidence
interval with coverage equal to the same minimum coverage. In these situations,
the Fletcher-Turek confidence intervals are unfortunately not better than the
standard confidence interval used after model selection but ignoring the model
selection process
A quartet of fermionic expressions for Virasoro characters via half-lattice paths
We derive new fermionic expressions for the characters of the Virasoro
minimal models by analysing the recently introduced half-lattice
paths. These fermionic expressions display a quasiparticle formulation
characteristic of the and integrable perturbations.
We find that they arise by imposing a simple restriction on the RSOS
quasiparticle states of the unitary models . In fact, four fermionic
expressions are obtained for each generating function of half-lattice paths of
finite length , and these lead to four distinct expressions for most
characters . These are direct analogues of Melzer's
expressions for , and their proof entails revisiting, reworking and
refining a proof of Melzer's identities which used combinatorial transforms on
lattice paths.
We also derive a bosonic version of the generating functions of length
half-lattice paths, this expression being notable in that it involves
-trinomial coefficients. Taking the limit shows that the
generating functions for infinite length half-lattice paths are indeed the
Virasoro characters .Comment: 29 pages. v2: minor improvements, references adde
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