10,695 research outputs found
High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation
The ratio between two probability density functions is an important component
of various tasks, including selection bias correction, novelty detection and
classification. Recently, several estimators of this ratio have been proposed.
Most of these methods fail if the sample space is high-dimensional, and hence
require a dimension reduction step, the result of which can be a significant
loss of information. Here we propose a simple-to-implement, fully nonparametric
density ratio estimator that expands the ratio in terms of the eigenfunctions
of a kernel-based operator; these functions reflect the underlying geometry of
the data (e.g., submanifold structure), often leading to better estimates
without an explicit dimension reduction step. We show how our general framework
can be extended to address another important problem, the estimation of a
likelihood function in situations where that function cannot be
well-approximated by an analytical form. One is often faced with this situation
when performing statistical inference with data from the sciences, due the
complexity of the data and of the processes that generated those data. We
emphasize applications where using existing likelihood-free methods of
inference would be challenging due to the high dimensionality of the sample
space, but where our spectral series method yields a reasonable estimate of the
likelihood function. We provide theoretical guarantees and illustrate the
effectiveness of our proposed method with numerical experiments.Comment: With supplementary materia
SLIDES: A Working Model for Oil and Gas Produced Water Treatment
Presenter: Lee Schafer, Integrity Production Services, Inc., for Anticline Disposal LLC
11 slide
Prototype selection for parameter estimation in complex models
Parameter estimation in astrophysics often requires the use of complex
physical models. In this paper we study the problem of estimating the
parameters that describe star formation history (SFH) in galaxies. Here,
high-dimensional spectral data from galaxies are appropriately modeled as
linear combinations of physical components, called simple stellar populations
(SSPs), plus some nonlinear distortions. Theoretical data for each SSP is
produced for a fixed parameter vector via computer modeling. Though the
parameters that define each SSP are continuous, optimizing the signal model
over a large set of SSPs on a fine parameter grid is computationally infeasible
and inefficient. The goal of this study is to estimate the set of parameters
that describes the SFH of each galaxy. These target parameters, such as the
average ages and chemical compositions of the galaxy's stellar populations, are
derived from the SSP parameters and the component weights in the signal model.
Here, we introduce a principled approach of choosing a small basis of SSP
prototypes for SFH parameter estimation. The basic idea is to quantize the
vector space and effective support of the model components. In addition to
greater computational efficiency, we achieve better estimates of the SFH target
parameters. In simulations, our proposed quantization method obtains a
substantial improvement in estimating the target parameters over the common
method of employing a parameter grid. Sparse coding techniques are not
appropriate for this problem without proper constraints, while constrained
sparse coding methods perform poorly for parameter estimation because their
objective is signal reconstruction, not estimation of the target parameters.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS500 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Dynamics of methane ebullition from a peat monolith revealed from a dynamic flux chamber system
Methane (CH4) ebullition in northern peatlands is poorly quantified in part due to its high spatiotemporal variability. In this study, a dynamic flux chamber (DFC) system was used to continuously measure CH4 fluxes from a monolith of near‐surface Sphagnum peat at the laboratory scale to understand the complex behavior of CH4 ebullition. Coincident transmission ground penetrating radar measurements of gas content were also acquired at three depths within the monolith. A graphical method was developed to separate diffusion, steady ebullition, and episodic ebullition fluxes from the total CH4 flux recorded and to identify the timing and CH4 content of individual ebullition events. The results show that the application of the DFC had minimal disturbance on air‐peat CH4 exchange and estimated ebullition fluxes were not sensitive to the uncertainties associated with the graphical model. Steady and episodic ebullition fluxes were estimated to be averagely 36 ± 24% and 38 ± 24% of the total fluxes over the study period, respectively. The coupling between episodic CH4 ebullition and gas content within the three layers supports the existence of a threshold gas content regulating CH4 ebullition. However, the threshold at which active ebullition commenced varied between peat layers with a larger threshold (0.14 m3 m−3) observed in the deeper layers, suggesting that the peat physical structure controls gas bubble dynamics in peat. Temperature variation (23°C to 27°C) was likely only responsible for small episodic ebullition events from the upper peat layer, while large ebullition events from the deeper layers were most likely triggered by drops in atmospheric pressure
Calorons and fermion zero-modes
Calorons in the confined phase for SU(n) gauge theory, having a non-trivial
Polyakov loop, "dissolve" in n monopole constituents for large enough instanton
scale parameters. We discuss recent results for these caloron solutions and
their fermion zero-modes, as well as the implications for lattice studies and
comment on the possible influence of the constituent monopoles on the instanton
size distribution.Comment: 3 pages, 2 figures (in 7 parts); Lattice2003(topology
Statistical Communication Theory
Contains research objectives and reports on two research projects.Joint Services Electronics Programs (U. S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 36-039-AMC-03200(E)National Aeronautics and Space Administration (Grant NsG-496)National Science Foundation (Grant GK-835
Measurement-induced decoherence and Gaussian smoothing of the Wigner distribution function
We study the problem of measurement-induced decoherence using the phase-space
approach employing the Gaussian-smoothed Wigner distribution function. Our
investigation is based on the notion that measurement-induced decoherence is
represented by the transition from the Wigner distribution to the
Gaussian-smoothed Wigner distribution with the widths of the smoothing function
identified as measurement errors. We also compare the smoothed Wigner
distribution with the corresponding distribution resulting from the classical
analysis. The distributions we computed are the phase-space distributions for
simple one-dimensional dynamical systems such as a particle in a square-well
potential and a particle moving under the influence of a step potential, and
the time-frequency distributions for high-harmonic radiation emitted from an
atom irradiated by short, intense laser pulses.Comment: Accepted in Annals of Physic
Meson-loop contributions to the quark condensate from the instanton vacuum
We investigate the quark condensate of the QCD vacuum within the instanton
vacuum model. We calculate the meson-loop contributions to the dynamical quark
mass and quark condensate to -, -, and -order corrections. We find that the meson (especially pion)
loops provide substantial contributions to the dynamical quark mass and as a
result to the quark condensate. The results indicate that the
corrections should be reconsidered in the systematical way. The present results
are consistent with those from chiral perturbation theory.Comment: Final version accepted for publication in Phys. Lett. B. The title
was changed. Small corrections were adde
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