1,576 research outputs found
H\"ormander Type Functional Calculus and Square Function Estimates
We investigate H\"ormander spectral multiplier theorems as they hold on for many self-adjoint elliptic differential
operators including the standard Laplacian on A strengthened
matricial extension is considered, which coincides with a completely bounded
map between operator spaces in the case that is a Hilbert space. We show
that the validity of the matricial H\"ormander theorem can be characterized in
terms of square function estimates for imaginary powers , for
resolvents and for the analytic semigroup We
deduce H\"ormander spectral multiplier theorems for semigroups satisfying
generalized Gaussian estimates
Small area estimation of the homeless in Los Angeles: An application of cost-sensitive stochastic gradient boosting
In many metropolitan areas efforts are made to count the homeless to ensure
proper provision of social services. Some areas are very large, which makes
spatial sampling a viable alternative to an enumeration of the entire terrain.
Counts are observed in sampled regions but must be imputed in unvisited areas.
Along with the imputation process, the costs of underestimating and
overestimating may be different. For example, if precise estimation in areas
with large homeless c ounts is critical, then underestimation should be
penalized more than overestimation in the loss function. We analyze data from
the 2004--2005 Los Angeles County homeless study using an augmentation of
stochastic gradient boosting that can weight overestimates and underestimates
asymmetrically. We discuss our choice to utilize stochastic gradient boosting
over other function estimation procedures. In-sample fitted and out-of-sample
imputed values, as well as relationships between the response and predictors,
are analyzed for various cost functions. Practical usage and policy
implications of these results are discussed briefly.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS328 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Paley-Littlewood decomposition for sectorial operators and interpolation spaces
We prove Paley-Littlewood decompositions for the scales of fractional powers
of -sectorial operators on a Banach space which correspond to
Triebel-Lizorkin spaces and the scale of Besov spaces if is the classical
Laplace operator on We use the -calculus,
spectral multiplier theorems and generalized square functions on Banach spaces
and apply our results to Laplace-type operators on manifolds and graphs,
Schr\"odinger operators and Hermite expansion.We also give variants of these
results for bisectorial operators and for generators of groups with a bounded
-calculus on strips.Comment: 2nd version to appear in Mathematische Nachrichten, Mathematical News
/ Mathematische Nachrichten, Wiley-VCH Verlag, 201
Extension of ERIM multispectral data processing capabilities through improved data handling techniques
The improvement and extension of the capabilities of the Environmental Research Institute of Michigan processing facility in handling multispectral data are discussed. Improvements consisted of implementing hardware modifications which permitted more rapid access to the recorded data through improved numbering and indexing of such data. In addition, techniques are discussed for handling data from sources other than the ERIM M-5 and M-7 scanner systems
Spectral multiplier theorems and averaged R-boundedness
Let be a -sectorial operator with a bounded
-calculus for some e.g. a
Laplace type operator on where is a
manifold or a graph. We show that has a H{\"o}rmander functional calculus
if and only if certain operator families derived from the resolvent the semigroup the wave operators or the
imaginary powers of are -bounded in an -averaged sense. If
is an space with -boundedness reduces
to well-known estimates of square sums.Comment: Error in the title correcte
Bayesian Learning for a Class of Priors with Prescribed Marginals
We present Bayesian updating of an imprecise probability measure, represented by a class of precise multidimensional probability measures. Choice and analysis of our class are motivated by expert interviews that we conducted with modelers in the context of climatic change. From the interviews we deduce that generically, experts hold a much more informed opinion on the marginals of uncertain parameters rather than on their correlations. Accordingly, we specify the class by prescribing precise measures for the marginals while letting the correlation structure subject to complete ignorance. For sake of transparency, our discussion focuses on the tutorial example of a linear two-dimensional Gaussian model. We operationalize Bayesian learning for that class by various updating rules, starting with (a modified version of) the generalized Bayes' rule and the maximum likelihood update rule (after Gilboa and Schmeidler). Over a large range of potential observations, the generalized Bayes' rule would provide non-informative results. We restrict this counter-intuitive and unnecessary growth of uncertainty by two means, the discussion of which refers to any kind of imprecise model, not only to our class. First, we find our class of priors too inclusive and, hence, require certain additional properties of prior measures in terms of smoothness of probability density functions. Second, we argue that both updating rules are dissatisfying, the generalized Bayes' rule being too conservative, i.e., too inclusive, the maximum likelihood rule being too exclusive. Instead, we introduce two new ways of Bayesian updating of imprecise probabilities: a ``weighted maximum likelihood method'' and a ``semi-classical method.'' The former bases Bayesian updating on the whole set of priors, however, with weighted influence of its members. By referring to the whole set, the weighted maximum likelihood method allows for more robust inferences than the standard maximum likelihood method and, hence, is better to justify than the latter.Furthermore, the semi-classical method is more objective than the weighted maximum likelihood method as it does not require the subjective definition of a weighting function. Both new methods reveal much more informative results than the generalized Bayes' rule, what we demonstrate for the example of a stylized insurance model
MIDAS prototype Multispectral Interactive Digital Analysis System for large area earth resources surveys. Volume 2: Charge coupled device investigation
MIDAS is a third-generation, fast, low cost, multispectral recognition system able to keep pace with the large quantity and high rates of data acquisition from large regions with present and projected sensors. MIDAS, for example, can process a complete ERTS frame in forty seconds and provide a color map of sixteen constituent categories in a few minutes. A principal objective of the MIDAS Program is to provide a system well interfaced with the human operator and thus to obtain large overall reductions in turn-around time and significant gains in throughput. The need for advanced onboard spacecraft processing of remotely sensed data is stated and approaches to this problem are described which are feasible through the use of charge coupled devices. Tentative mechanizations for the required processing operations are given in large block form. These initial designs can serve as a guide to circuit/system designers
Singular integral operators on tent spaces
We extend the recent results concerning boundedness of the maximal regularity
operator on tent spaces. This leads us to develop a singular integral operator
theory on tent spaces. Such operators have operator-valued kernels. A seemingly
appropriate condition on the kernel is time-space decay measured by
off-diagonal estimates with various exponents.Comment: modification of the introduction and references added as suggested by
the refere
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