510 research outputs found
Sufficient burn-in for Gibbs samplers for a hierarchical random effects model
We consider Gibbs and block Gibbs samplers for a Bayesian hierarchical
version of the one-way random effects model. Drift and minorization conditions
are established for the underlying Markov chains. The drift and minorization
are used in conjunction with results from J. S. Rosenthal [J. Amer. Statist.
Assoc. 90 (1995) 558-566] and G. O. Roberts and R. L. Tweedie [Stochastic
Process. Appl. 80 (1999) 211-229] to construct analytical upper bounds on the
distance to stationarity. These lead to upper bounds on the amount of burn-in
that is required to get the chain within a prespecified (total variation)
distance of the stationary distribution. The results are illustrated with a
numerical example
Evaluation of Formal posterior distributions via Markov chain arguments
We consider evaluation of proper posterior distributions obtained from
improper prior distributions. Our context is estimating a bounded function
of a parameter when the loss is quadratic. If the posterior mean of
is admissible for all bounded , the posterior is strongly
admissible. We give sufficient conditions for strong admissibility. These
conditions involve the recurrence of a Markov chain associated with the
estimation problem. We develop general sufficient conditions for recurrence of
general state space Markov chains that are also of independent interest. Our
main example concerns the -dimensional multivariate normal distribution with
mean vector when the prior distribution has the form on the parameter space . Conditions on for strong
admissibility of the posterior are provided.Comment: Published in at http://dx.doi.org/10.1214/07-AOS542 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Evaluating default priors with a generalization of Eaton's Markov chain
We consider evaluating improper priors in a formal Bayes setting according to the consequences of their use. Let Φ be a class of functions on the parameter space and consider estimating elements of Φ under quadratic loss. If the formal Bayes estimator of every function in Φ is admissible, then the prior is strongly admissible with respect to Φ. Eaton’s method for establishing strong admissibility is based on studying the stability properties of a particular Markov chain associated with the inferential setting. In previous work, this was handled differently depending upon whether ϕ ∈ Φ was bounded or unbounded. We consider a new Markov chain which allows us to unify and generalize existing approaches while simultaneously broadening the scope of their potential applicability. We use our general theory to investigate strong admissibility conditions for location models when the prior is Lebesgue measure and for the p-dimensional multivariate Normal distribution with unknown mean vector θ and a prior of the form ν(‖θ‖²)dθ
Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics
Finite-dimensional reductions of the 2D dispersionless Toda hierarchy,
constrained by the ``string equation'' are studied. These include solutions
determined by polynomial, rational or logarithmic functions, which are of
interest in relation to the ``Laplacian growth'' problem governing interface
dynamics. The consistency of such reductions is proved, and the Hamiltonian
structure of the reduced dynamics is derived. The Poisson structure of the
rationally reduced dispersionless Toda hierarchies is also derivedComment: 18 pages LaTex, accepted to J.Math.Phys, Significantly updated
version of the previous submissio
Gravitational Lensing by Rotating Naked Singularities
We model massive compact objects in galactic nuclei as stationary,
axially-symmetric naked singularities in the Einstein-massless scalar field
theory and study the resulting gravitational lensing. In the weak deflection
limit we study analytically the position of the two weak field images, the
corresponding signed and absolute magnifications as well as the centroid up to
post-Newtonian order. We show that there are a static post-Newtonian
corrections to the signed magnification and their sum as well as to the
critical curves, which are function of the scalar charge. The shift of the
critical curves as a function of the lens angular momentum is found, and it is
shown that they decrease slightingly for the weakly naked and vastly for the
strongly naked singularities with the increase of the scalar charge. The
point-like caustics drift away from the optical axis and do not depend on the
scalar charge. In the strong deflection limit approximation we compute
numerically the position of the relativistic images and their separability for
weakly naked singularities. All of the lensing quantities are compared to
particular cases as Schwarzschild and Kerr black holes as well as
Janis--Newman--Winicour naked singularities.Comment: 35 pages, 30 figure
Diffusion-Limited Aggregation on Curved Surfaces
We develop a general theory of transport-limited aggregation phenomena
occurring on curved surfaces, based on stochastic iterated conformal maps and
conformal projections to the complex plane. To illustrate the theory, we use
stereographic projections to simulate diffusion-limited-aggregation (DLA) on
surfaces of constant Gaussian curvature, including the sphere () and
pseudo-sphere (), which approximate "bumps" and "saddles" in smooth
surfaces, respectively. Although curvature affects the global morphology of the
aggregates, the fractal dimension (in the curved metric) is remarkably
insensitive to curvature, as long as the particle size is much smaller than the
radius of curvature. We conjecture that all aggregates grown by conformally
invariant transport on curved surfaces have the same fractal dimension as DLA
in the plane. Our simulations suggest, however, that the multifractal
dimensions increase from hyperbolic () geometry, which
we attribute to curvature-dependent screening of tip branching.Comment: 4 pages, 3 fig
Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit
In the present work we study numerically quasi-equatorial lensing by the
charged, stationary, axially-symmetric Kerr-Sen dilaton-axion black hole in the
strong deflection limit. In this approximation we compute the magnification and
the positions of the relativistic images. The most outstanding effect is that
the Kerr-Sen black hole caustics drift away from the optical axis and shift in
clockwise direction with respect to the Kerr caustics. The intersections of the
critical curves on the equatorial plane as a function of the black hole angular
momentum are found, and it is shown that they decrease with the increase of the
parameter . All of the lensing quantities are compared to particular
cases as Schwarzschild, Kerr and Gibbons-Maeda black holes.Comment: 31 pages, 17 figures; V2 references added, some typos corrected, V3
references added, language corrections, V4 table added, minor technical
correction
«Grey zone» of heart failure
The review is devoted to modern understanding of heart failure with mid-range ejection fraction. The formation of the paradigm of «two phenotypes» of heart failure began around the end of the last century. As a result of a number of large epidemiological studies on heart failure with preserved ejection fraction, so-called «grey zone» of ejection fraction values was formed in the range of about 40-50%. This situation arose because of the lack of clearly established level of normal ejection fraction and underlines imperfection of this parameter as the only classification criterion. But no more convenient «tool» for research work was offered. In the past decade, «grey zone» of heart failure has been actively explored by clinical epidemiologists and clinicians. Should we classify these patients as one of the existing phenotypes of heart failure or present them as a new, separate phenotype? Both the first and second decisions require information about the population «portrait» of subgroup, about their response to treatment, and presumptive pathophysiological mechanisms of heart failure. In 2016 European society of cardiology guidelines for the diagnosis and treatment of acute and chronic heart failure, heart failure with mid-range ejection fraction was determined as a separate subgroup to stimulate the search for such data. At the moment mid-range ejection fraction is known to be recorded in about 10-20% of patients with heart failure. They have substantial comorbidities as patients with preserved ejection fraction but the prevalence of ischemic heart disease in this subgroup makes it similar to heart failure with reduced ejection fraction. The response to treatment with beta-blockers and aldosterone antagonists is similar to that of heart failure with reduced ejection fraction. It is important that the mortality rates in all three groups of patients are approximately the same. This circumstance underlines the importance of further searche. Perhaps the research of «grey zone» of the syndrome will help to better understand pathophysiology of the existing heart failure phenotypes and confirm the validity of their identification based on ejection fraction
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