16,063 research outputs found
On the Independence Jeffreys prior for skew--symmetric models with applications
We study the Jeffreys prior of the skewness parameter of a general class of
scalar skew--symmetric models. It is shown that this prior is symmetric about
0, proper, and with tails under mild regularity conditions.
We also calculate the independence Jeffreys prior for the case with unknown
location and scale parameters. Sufficient conditions for the existence of the
corresponding posterior distribution are investigated for the case when the
sampling model belongs to the family of skew--symmetric scale mixtures of
normal distributions. The usefulness of these results is illustrated using the
skew--logistic model and two applications with real data
Bayesian variable selection for high dimensional generalized linear models: convergence rates of the fitted densities
Bayesian variable selection has gained much empirical success recently in a
variety of applications when the number of explanatory variables
is possibly much larger than the sample size . For
generalized linear models, if most of the 's have very small effects on
the response , we show that it is possible to use Bayesian variable
selection to reduce overfitting caused by the curse of dimensionality .
In this approach a suitable prior can be used to choose a few out of the many
's to model , so that the posterior will propose probability densities
that are ``often close'' to the true density in some sense. The
closeness can be described by a Hellinger distance between and that
scales at a power very close to , which is the ``finite-dimensional
rate'' corresponding to a low-dimensional situation. These findings extend some
recent work of Jiang [Technical Report 05-02 (2005) Dept. Statistics,
Northwestern Univ.] on consistency of Bayesian variable selection for binary
classification.Comment: Published in at http://dx.doi.org/10.1214/009053607000000019 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Meta-analysis of functional neuroimaging data using Bayesian nonparametric binary regression
In this work we perform a meta-analysis of neuroimaging data, consisting of
locations of peak activations identified in 162 separate studies on emotion.
Neuroimaging meta-analyses are typically performed using kernel-based methods.
However, these methods require the width of the kernel to be set a priori and
to be constant across the brain. To address these issues, we propose a fully
Bayesian nonparametric binary regression method to perform neuroimaging
meta-analyses. In our method, each location (or voxel) has a probability of
being a peak activation, and the corresponding probability function is based on
a spatially adaptive Gaussian Markov random field (GMRF). We also include
parameters in the model to robustify the procedure against miscoding of the
voxel response. Posterior inference is implemented using efficient MCMC
algorithms extended from those introduced in Holmes and Held [Bayesian Anal. 1
(2006) 145--168]. Our method allows the probability function to be locally
adaptive with respect to the covariates, that is, to be smooth in one region of
the covariate space and wiggly or even discontinuous in another. Posterior
miscoding probabilities for each of the identified voxels can also be obtained,
identifying voxels that may have been falsely classified as being activated.
Simulation studies and application to the emotion neuroimaging data indicate
that our method is superior to standard kernel-based methods.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS523 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A flexible regression model for count data
Poisson regression is a popular tool for modeling count data and is applied
in a vast array of applications from the social to the physical sciences and
beyond. Real data, however, are often over- or under-dispersed and, thus, not
conducive to Poisson regression. We propose a regression model based on the
Conway--Maxwell-Poisson (COM-Poisson) distribution to address this problem. The
COM-Poisson regression generalizes the well-known Poisson and logistic
regression models, and is suitable for fitting count data with a wide range of
dispersion levels. With a GLM approach that takes advantage of exponential
family properties, we discuss model estimation, inference, diagnostics, and
interpretation, and present a test for determining the need for a COM-Poisson
regression over a standard Poisson regression. We compare the COM-Poisson to
several alternatives and illustrate its advantages and usefulness using three
data sets with varying dispersion.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS306 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Generalized extreme value regression for binary response data: An application to B2B electronic payments system adoption
In the information system research, a question of particular interest is to
interpret and to predict the probability of a firm to adopt a new technology
such that market promotions are targeted to only those firms that were more
likely to adopt the technology. Typically, there exists significant difference
between the observed number of ``adopters'' and ``nonadopters,'' which is
usually coded as binary response. A critical issue involved in modeling such
binary response data is the appropriate choice of link functions in a
regression model. In this paper we introduce a new flexible skewed link
function for modeling binary response data based on the generalized extreme
value (GEV) distribution. We show how the proposed GEV links provide more
flexible and improved skewed link regression models than the existing skewed
links, especially when dealing with imbalance between the observed number of
0's and 1's in a data. The flexibility of the proposed model is illustrated
through simulated data sets and a billing data set of the electronic payments
system adoption from a Fortune 100 company in 2005.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS354 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The Overlooked Potential of Generalized Linear Models in Astronomy - I: Binomial Regression
Revealing hidden patterns in astronomical data is often the path to
fundamental scientific breakthroughs; meanwhile the complexity of scientific
inquiry increases as more subtle relationships are sought. Contemporary data
analysis problems often elude the capabilities of classical statistical
techniques, suggesting the use of cutting edge statistical methods. In this
light, astronomers have overlooked a whole family of statistical techniques for
exploratory data analysis and robust regression, the so-called Generalized
Linear Models (GLMs). In this paper -- the first in a series aimed at
illustrating the power of these methods in astronomical applications -- we
elucidate the potential of a particular class of GLMs for handling
binary/binomial data, the so-called logit and probit regression techniques,
from both a maximum likelihood and a Bayesian perspective. As a case in point,
we present the use of these GLMs to explore the conditions of star formation
activity and metal enrichment in primordial minihaloes from cosmological
hydro-simulations including detailed chemistry, gas physics, and stellar
feedback. We predict that for a dark mini-halo with metallicity , an increase of in the gas
molecular fraction, increases the probability of star formation occurrence by a
factor of 75%. Finally, we highlight the use of receiver operating
characteristic curves as a diagnostic for binary classifiers, and ultimately we
use these to demonstrate the competitive predictive performance of GLMs against
the popular technique of artificial neural networks.Comment: 20 pages, 10 figures, 3 tables, accepted for publication in Astronomy
and Computin
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