13,307 research outputs found
Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal experiments under asymmetric loss
Local asymptotic minimax risk bounds in a locally asymptotically mixture of
normal family of distributions have been investigated under asymmetric loss
functions and the asymptotic distribution of the optimal estimator that attains
the bound has been obtained.Comment: Published at http://dx.doi.org/10.1214/074921706000000527 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Scaling and universality in coupled driven diffusive models
Inspired by the physics of magnetohydrodynamics (MHD) a simplified coupled
Burgers-like model in one dimension (1d), a generalization of the Burgers model
to coupled degrees of freedom, is proposed to describe 1dMHD. In addition to
MHD, this model serves as a 1d reduced model for driven binary fluid mixtures.
Here we have performed a comprehensive study of the universal properties of the
generalized d-dimensional version of the reduced model. We employ both
analytical and numerical approaches. In particular, we determine the scaling
exponents and the amplitude-ratios of the relevant two-point time-dependent
correlation functions in the model. We demonstrate that these quantities vary
continuously with the amplitude of the noise cross-correlation. Further our
numerical studies corroborate the continuous dependence of long wavelength and
long time-scale physics of the model on the amplitude of the noise
cross-correlations, as found in our analytical studies. We construct and
simulate lattice-gas models of coupled degrees of freedom in 1d, belonging to
the universality class of our coupled Burgers-like model, which display similar
behavior. We use a variety of numerical (Monte-Carlo and Pseudospectral
methods) and analytical (Dynamic Renormalization Group, Self-Consistent
Mode-Coupling Theory and Functional Renormalization Group) approaches for our
work. The results from our different approaches complement one another.
Possible realizations of our results in various nonequilibrium models are
discussed.Comment: To appear in JSTAT (2009); 52 pages in JSTAT format. Some figure
files have been replace
A Theory of Decision-Making
In a separate article, it has been stated:
The kinds of theories which social scientists have been able to construct have largely been dependent on the level or the degree of inference which the researchers have been able to draw from observations or experimental designs (which may or may not reflect the empirical world), and the assumptions upon which these inferences rest (Basu and Kenyon, 1972.425).
Notably, in the past three decades the eventual success of a theory has been tested on this basis. A major underlying premise in the ideographic science has been that cause and effect represent the methodological level of inquiry, however singularizing (as opposed to nomothetic generalizing science) the social experience may be. These relationships are either asymetric, assming an independent-dependent variable dichotomy, or symmetric, i.e. constructing theory on the basis of an interdependent, reciprocal causation Inference. These analytic frames have attempted to explain what Darkheim has called soclal facts. However, the problems of limitation of such a search In the development and finally application of a social theory using causal inferences as methodological guidelines have cam to light, specifically In the area of policy-planning and decision making.
It is the purpose of this paper to attempt to extend theory (specifically that applying to policy-planning and decision-making) from these limitations. The author win propose a theory of decision-making and will suggest its applications
Fixed-Energy Sandpiles Belong Generically to Directed Percolation
Fixed-energy sandpiles with stochastic update rules are known to exhibit a
nonequilibrium phase transition from an active phase into infinitely many
absorbing states. Examples include the conserved Manna model, the conserved
lattice gas, and the conserved threshold transfer process. It is believed that
the transitions in these models belong to an autonomous universality class of
nonequilibrium phase transitions, the so-called Manna class. Contrarily, the
present numerical study of selected (1+1)-dimensional models in this class
suggests that their critical behavior converges to directed percolation after
very long time, questioning the existence of an independent Manna class.Comment: article (4 pages, 9 eps figures) + Supplement (8 pages, 9 eps
figures); Phys. Rev. Lett. 201
Approximation of corner polyhedra with families of intersection cuts
We study the problem of approximating the corner polyhedron using
intersection cuts derived from families of lattice-free sets in .
In particular, we look at the problem of characterizing families that
approximate the corner polyhedron up to a constant factor, which depends only
on and not the data or dimension of the corner polyhedron. The literature
already contains several results in this direction. In this paper, we use the
maximum number of facets of lattice-free sets in a family as a measure of its
complexity and precisely characterize the level of complexity of a family
required for constant factor approximations. As one of the main results, we
show that, for each natural number , a corner polyhedron with basic
integer variables and an arbitrary number of continuous non-basic variables is
approximated up to a constant factor by intersection cuts from lattice-free
sets with at most facets if and that no such approximation is
possible if . When the approximation factor is allowed to
depend on the denominator of the fractional vertex of the linear relaxation of
the corner polyhedron, we show that the threshold is versus .
The tools introduced for proving such results are of independent interest for
studying intersection cuts
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