151,615 research outputs found
Empirical likelihood for single-index varying-coefficient models
In this paper, we develop statistical inference techniques for the unknown
coefficient functions and single-index parameters in single-index
varying-coefficient models. We first estimate the nonparametric component via
the local linear fitting, then construct an estimated empirical likelihood
ratio function and hence obtain a maximum empirical likelihood estimator for
the parametric component. Our estimator for parametric component is
asymptotically efficient, and the estimator of nonparametric component has an
optimal convergence rate. Our results provide ways to construct the confidence
region for the involved unknown parameter. We also develop an adjusted
empirical likelihood ratio for constructing the confidence regions of
parameters of interest. A simulation study is conducted to evaluate the finite
sample behaviors of the proposed methods.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ365 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
The Substellar Mass Function: A Bayesian Approach
We report our efforts to constrain the form of the low-mass star and brown
dwarf mass function via Bayesian inference. Recent surveys of M, L, and T
dwarfs in the local solar neighborhood are an essential component of our study.
Uncertainties in the age distribution of local field stars make reliable
inference complicated. We adopt a wide range of plausible assumptions about the
rate of galactic star formation and show that their deviations from a uniform
rate produce little effect on the resulting luminosity function for a given
mass function. We use a Bayesian statistical formalism to evaluate the
probability of commonly used mass functions in light of recent discoveries. We
consider three functional forms of the mass function, include a two-segment
power law, a single power law with a low-mass cutoff, and a log-normal
distribution. Our results show that, at a 60% confidence level, the power-law
index, , for the low-mass arm of a two-segment power law has a value
between -0.5 and 0.5 for objects with masses between and . The best-fit index is at the 60% confidence
level for a single-segment mass function. Current data require this function
extend to at least with no restrictions placed on a lower mass
cutoff. Inferences of the parameter values for a log-normal mass function are
virtually unaffected by recent estimates of the local space density of L and T
dwarfs. We find no preference among these three forms using this method. We
discuss current and future capabilities that may eventually discriminate
between mass-function models and refine estimates of their associated parameter
values.Comment: 40 pages, 15 figures, 3 tables, accepted for publication in The
Astrophysical Journa
Gaussian process single-index models as emulators for computer experiments
A single-index model (SIM) provides for parsimonious multi-dimensional
nonlinear regression by combining parametric (linear) projection with
univariate nonparametric (non-linear) regression models. We show that a
particular Gaussian process (GP) formulation is simple to work with and ideal
as an emulator for some types of computer experiment as it can outperform the
canonical separable GP regression model commonly used in this setting. Our
contribution focuses on drastically simplifying, re-interpreting, and then
generalizing a recently proposed fully Bayesian GP-SIM combination, and then
illustrating its favorable performance on synthetic data and a real-data
computer experiment. Two R packages, both released on CRAN, have been augmented
to facilitate inference under our proposed model(s).Comment: 23 pages, 9 figures, 1 tabl
Large-sample estimation and inference in multivariate single-index models
By optimizing index functions against different outcomes, we propose a multivariate single-index model (SIM) for development of medical indices that simultaneously work with multiple outcomes. Fitting of a multivariate SIM is not fundamentally different from fitting a univariate SIM, as the former can be written as a sum of multiple univariate SIMs with appropriate indicator functions. What have not been carefully studied are the theoretical properties of the parameter estimators. Because of the lack of asymptotic results, no formal inference procedure has been made available for multivariate SIMs. In this paper, we examine the asymptotic properties of the multivariate SIM parameter estimators. We show that, under mild regularity conditions, estimators for the multivariate SIM parameters are indee
New insight on galaxy structure from GALPHAT I. Motivation, methodology, and benchmarks for Sersic models
We introduce a new galaxy image decomposition tool, GALPHAT (GALaxy
PHotometric ATtributes), to provide full posterior probability distributions
and reliable confidence intervals for all model parameters. GALPHAT is designed
to yield a high speed and accurate likelihood computation, using grid
interpolation and Fourier rotation. We benchmark this approach using an
ensemble of simulated Sersic model galaxies over a wide range of observational
conditions: the signal-to-noise ratio S/N, the ratio of galaxy size to the PSF
and the image size, and errors in the assumed PSF; and a range of structural
parameters: the half-light radius and the Sersic index . We
characterise the strength of parameter covariance in Sersic model, which
increases with S/N and , and the results strongly motivate the need for the
full posterior probability distribution in galaxy morphology analyses and later
inferences.
The test results for simulated galaxies successfully demonstrate that, with a
careful choice of Markov chain Monte Carlo algorithms and fast model image
generation, GALPHAT is a powerful analysis tool for reliably inferring
morphological parameters from a large ensemble of galaxies over a wide range of
different observational conditions. (abridged)Comment: Submitted to MNRAS. The submitted version with high resolution
figures can be downloaded from
http://www.astro.umass.edu/~iyoon/GALPHAT/galphat1.pd
Nested Hierarchical Dirichlet Processes
We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical
topic modeling. The nHDP is a generalization of the nested Chinese restaurant
process (nCRP) that allows each word to follow its own path to a topic node
according to a document-specific distribution on a shared tree. This alleviates
the rigid, single-path formulation of the nCRP, allowing a document to more
easily express thematic borrowings as a random effect. We derive a stochastic
variational inference algorithm for the model, in addition to a greedy subtree
selection method for each document, which allows for efficient inference using
massive collections of text documents. We demonstrate our algorithm on 1.8
million documents from The New York Times and 3.3 million documents from
Wikipedia.Comment: To appear in IEEE Transactions on Pattern Analysis and Machine
Intelligence, Special Issue on Bayesian Nonparametric
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