62 research outputs found
Bayesian Variable Selection for Ultrahigh-dimensional Sparse Linear Models
We propose a Bayesian variable selection procedure for ultrahigh-dimensional
linear regression models. The number of regressors involved in regression,
, is allowed to grow exponentially with . Assuming the true model to be
sparse, in the sense that only a small number of regressors contribute to this
model, we propose a set of priors suitable for this regime. The model selection
procedure based on the proposed set of priors is shown to be variable selection
consistent when all the models are considered. In the
ultrahigh-dimensional setting, selection of the true model among all the
possible ones involves prohibitive computation. To cope with this, we
present a two-step model selection algorithm based on screening and Gibbs
sampling. The first step of screening discards a large set of unimportant
covariates, and retains a smaller set containing all the active covariates with
probability tending to one. In the next step, we search for the best model
among the covariates obtained in the screening step. This procedure is
computationally quite fast, simple and intuitive. We demonstrate competitive
performance of the proposed algorithm for a variety of simulated and real data
sets when compared with several frequentist, as well as Bayesian methods
Some intriguing properties of Tukey's half-space depth
For multivariate data, Tukey's half-space depth is one of the most popular
depth functions available in the literature. It is conceptually simple and
satisfies several desirable properties of depth functions. The Tukey median,
the multivariate median associated with the half-space depth, is also a
well-known measure of center for multivariate data with several interesting
properties. In this article, we derive and investigate some interesting
properties of half-space depth and its associated multivariate median. These
properties, some of which are counterintuitive, have important statistical
consequences in multivariate analysis. We also investigate a natural extension
of Tukey's half-space depth and the related median for probability
distributions on any Banach space (which may be finite- or
infinite-dimensional) and prove some results that demonstrate anomalous
behavior of half-space depth in infinite-dimensional spaces.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ322 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Robust Classification of High-Dimensional Data using Data-Adaptive Energy Distance
Classification of high-dimensional low sample size (HDLSS) data poses a
challenge in a variety of real-world situations, such as gene expression
studies, cancer research, and medical imaging. This article presents the
development and analysis of some classifiers that are specifically designed for
HDLSS data. These classifiers are free of tuning parameters and are robust, in
the sense that they are devoid of any moment conditions of the underlying data
distributions. It is shown that they yield perfect classification in the HDLSS
asymptotic regime, under some fairly general conditions. The comparative
performance of the proposed classifiers is also investigated. Our theoretical
results are supported by extensive simulation studies and real data analysis,
which demonstrate promising advantages of the proposed classification
techniques over several widely recognized methods.Comment: Accepted to be published at the European Conference on Machine
Learning and Principles and Practice of Knowledge Discovery in Databases
(ECML PKDD), 202
A rare case of breast carcinoma co-existing with axillary mantle cell lymphoma
BACKGROUND: Mantle cell lymphoma (MCL) is a rare variety of non-Hodgkin's lymphoma which originates from CD5+ B-cell population in the mantle zones of lymphoid follicles. Coexistence of such tumours in the axillary lymph nodes with invasive breast cancers without prior history of adjuvant chemotherapy or radiotherapy has not been previously reported in literature. CASE REPORT: We report a rare case of breast cancer co-existing with stage I mantle cell lymphoma of the ipsilateral axillary lymph node detected fortuitously by population screening. CONCLUSION: Though some studies have tried to prove breast carcinomas and lymphomas to share a common molecular or viral link, more research needs to be done to establish whether such a link truly exists
Sub-dimensional Mardia measures of multivariate skewness and kurtosis
The Mardia measures of multivariate skewness and kurtosis summarize the
respective characteristics of a multivariate distribution with two numbers.
However, these measures do not reflect the sub-dimensional features of the
distribution. Consequently, testing procedures based on these measures may fail
to detect skewness or kurtosis present in a sub-dimension of the multivariate
distribution. We introduce sub-dimensional Mardia measures of multivariate
skewness and kurtosis, and investigate the information they convey about all
sub-dimensional distributions of some symmetric and skewed families of
multivariate distributions. The maxima of the sub-dimensional Mardia measures
of multivariate skewness and kurtosis are considered, as these reflect the
maximum skewness and kurtosis present in the distribution, and also allow us to
identify the sub-dimension bearing the highest skewness and kurtosis.
Asymptotic distributions of the vectors of sub-dimensional Mardia measures of
multivariate skewness and kurtosis are derived, based on which testing
procedures for the presence of skewness and of deviation from Gaussian kurtosis
are developed. The performances of these tests are compared with some existing
tests in the literature on simulated and real datasets
A redefinition of Hawking temperature on the event horizon: Thermodynamical equilibrium
In this article we have used the recently introduced redefined Hawking
temperature on the event horizon and investigated whether the generalised
second law of thermodynamics (GSLT) and thermodynamic equilibrium holds for
both the event and the apparent horizons. Here we have considered FRW universe
and examined the GSLT and thermodynamic equilibrium with three examples.
Finally, we have concluded that from the thermodynamic viewpoint, the universe
bounded by the event horizon is more realistic than that by the apparent
horizon at least for some examples.Comment: 10 page
Optimization of Spectrum Sensing Parameters in Cognitive Radio Using Adaptive Genetic Algorithm, Journal of Telecommunications and Information Technology, 2017, nr 1
Quality of service parameters of cognitive radio, like, bandwidth, throughput and spectral efficiency are optimized using adaptive and demand based genetic algorithm. Simulation results show that the proposed method gives better real life solution to the cognitive radio network than other known approach
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