19,985 research outputs found
Second order ancillary: A differential view from continuity
Second order approximate ancillaries have evolved as the primary ingredient
for recent likelihood development in statistical inference. This uses quantile
functions rather than the equivalent distribution functions, and the intrinsic
ancillary contour is given explicitly as the plug-in estimate of the vector
quantile function. The derivation uses a Taylor expansion of the full quantile
function, and the linear term gives a tangent to the observed ancillary
contour. For the scalar parameter case, there is a vector field that integrates
to give the ancillary contours, but for the vector case, there are multiple
vector fields and the Frobenius conditions for mutual consistency may not hold.
We demonstrate, however, that the conditions hold in a restricted way and that
this verifies the second order ancillary contours in moderate deviations. The
methodology can generate an appropriate exact ancillary when such exists or an
approximate ancillary for the numerical or Monte Carlo calculation of
-values and confidence quantiles. Examples are given, including nonlinear
regression and several enigmatic examples from the literature.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ248 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Higher Accuracy for Bayesian and Frequentist Inference: Large Sample Theory for Small Sample Likelihood
Recent likelihood theory produces -values that have remarkable accuracy
and wide applicability. The calculations use familiar tools such as maximum
likelihood values (MLEs), observed information and parameter rescaling. The
usual evaluation of such -values is by simulations, and such simulations do
verify that the global distribution of the -values is uniform(0, 1), to high
accuracy in repeated sampling. The derivation of the -values, however,
asserts a stronger statement, that they have a uniform(0, 1) distribution
conditionally, given identified precision information provided by the data. We
take a simple regression example that involves exact precision information and
use large sample techniques to extract highly accurate information as to the
statistical position of the data point with respect to the parameter:
specifically, we examine various -values and Bayesian posterior survivor
-values for validity. With observed data we numerically evaluate the various
-values and -values, and we also record the related general formulas. We
then assess the numerical values for accuracy using Markov chain Monte Carlo
(McMC) methods. We also propose some third-order likelihood-based procedures
for obtaining means and variances of Bayesian posterior distributions, again
followed by McMC assessment. Finally we propose some adaptive McMC methods to
improve the simulation acceptance rates. All these methods are based on
asymptotic analysis that derives from the effect of additional data. And the
methods use simple calculations based on familiar maximizing values and related
informations. The example illustrates the general formulas and the ease of
calculations, while the McMC assessments demonstrate the numerical validity of
the -values as percentage position of a data point. The example, however, is
very simple and transparent, and thus gives little indication that in a wide
generality of models the formulas do accurately separate information for almost
any parameter of interest, and then do give accurate -value determinations
from that information. As illustration an enigmatic problem in the literature
is discussed and simulations are recorded; various examples in the literature
are cited.Comment: Published in at http://dx.doi.org/10.1214/07-STS240 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Mass segregation trends in SDSS galaxy groups
It has been shown that galaxy properties depend strongly on their host
environment. In order to understand the relevant physical processes driving
galaxy evolution it is important to study the observed properties of galaxies
in different environments. Mass segregation in bound galaxy structures is an
important indicator of evolutionary history and dynamical friction timescales.
Using group catalogues derived from the Sloan Digital Sky Survey Data Release 7
(SDSS DR7) we investigate mass segregation trends in galaxy groups at low
redshift. We investigate average galaxy stellar mass as a function of
group-centric radius and find evidence for weak mass segregation in SDSS
groups. The magnitude of the mass segregation depends on both galaxy stellar
mass limits and group halo mass. We show that the inclusion of low mass
galaxies tends to strengthen mass segregation trends, and that the strength of
mass segregation tends to decrease with increasing group halo mass. We find the
same trends if we use the fraction of massive galaxies as a function of
group-centric radius as an alternative probe of mass segregation. The magnitude
of mass segregation that we measure, particularly in high-mass haloes,
indicates that dynamical friction is not acting efficiently.Comment: 6 pages, 2 figures, accepted for publication in MNRAS Letter
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MobGeoSen: facilitating personal geosensor data collection and visualization using mobile phones
Mobile sensing and mapping applications are becoming more prevalent because sensing hardware is becoming more portable and more affordable. However, most of the hardware uses small numbers of fixed sensors that report and share multiple sets of environmental data which raises privacy concerns. Instead, these systems can be decentralized and managed by individuals in their public and private spaces. This paper describes a robust system called MobGeoSens which enables individuals to monitor their local environment (e.g. pollution and temperature) and their private spaces (e.g. activities and health) by using mobile phones in their day to day life
Rejoinder to "Is Bayes Posterior just Quick and Dirty Confidence?"
Rejoinder to "Is Bayes Posterior just Quick and Dirty Confidence?" by D. A.
S. Fraser [arXiv:1112.5582]Comment: Published in at http://dx.doi.org/10.1214/11-STS352REJ the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Teaching Excellence: A Reaction to the Smith Commission Report and its Effects
This paper has been written partially in response to the Smith Commission Report, and partially in response to the reactions the report has elicited already. The Smith Commission Report voiced many valid concerns about teaching excellence; however, many of the so-called "innovations" that have been developed in answer to Stuart Smith's call for teaching excellence are, in fact, little different from those techniques implemented under the auspices of the Ontario Universities Program for Institutional Development (OUPID) in the 1960's and early 1970's. This being the case, the authors feel that the most likely result will be a similar lack of success. It is, therefore, our suggestion that an attempt ought to be made to change the infrastructure of the university sys- tem so that it supports good teaching and research with equal measure. This, above all else, should lead to real improvements in the quality of teaching
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