242,227 research outputs found
Testing Properties of Multiple Distributions with Few Samples
We propose a new setting for testing properties of distributions while
receiving samples from several distributions, but few samples per distribution.
Given samples from distributions, , we design
testers for the following problems: (1) Uniformity Testing: Testing whether all
the 's are uniform or -far from being uniform in
-distance (2) Identity Testing: Testing whether all the 's are
equal to an explicitly given distribution or -far from in
-distance, and (3) Closeness Testing: Testing whether all the 's
are equal to a distribution which we have sample access to, or
-far from in -distance. By assuming an additional natural
condition about the source distributions, we provide sample optimal testers for
all of these problems.Comment: ITCS 202
Modeling Persistent Trends in Distributions
We present a nonparametric framework to model a short sequence of probability
distributions that vary both due to underlying effects of sequential
progression and confounding noise. To distinguish between these two types of
variation and estimate the sequential-progression effects, our approach
leverages an assumption that these effects follow a persistent trend. This work
is motivated by the recent rise of single-cell RNA-sequencing experiments over
a brief time course, which aim to identify genes relevant to the progression of
a particular biological process across diverse cell populations. While
classical statistical tools focus on scalar-response regression or
order-agnostic differences between distributions, it is desirable in this
setting to consider both the full distributions as well as the structure
imposed by their ordering. We introduce a new regression model for ordinal
covariates where responses are univariate distributions and the underlying
relationship reflects consistent changes in the distributions over increasing
levels of the covariate. This concept is formalized as a "trend" in
distributions, which we define as an evolution that is linear under the
Wasserstein metric. Implemented via a fast alternating projections algorithm,
our method exhibits numerous strengths in simulations and analyses of
single-cell gene expression data.Comment: To appear in: Journal of the American Statistical Associatio
Probability and Statistics for Particle Physicists
Lectures presented at the 1st CERN Asia-Europe-Pacific School of High-Energy
Physics, Fukuoka, Japan, 14-27 October 2012. A pedagogical selection of topics
in probability and statistics is presented. Choice and emphasis are driven by
the author's personal experience, predominantly in the context of physics
analyses using experimental data from high-energy physics detectors.Comment: Updated version of lectures given at the First Asia-Europe-Pacific
School of High-Energy Physics, Fukuoka, Japan, 14-27 October 2012. Published
as a CERN Yellow Report (CERN-2014-001) and KEK report
(KEK-Proceedings-2013-8), K. Kawagoe and M. Mulders (eds.), 2014, p. 219.
Total 28 pages, 36 figure
Young Massive Clusters: Their Population Properties, Formation and Evolution, and Their Relation to the Ancient Globular Clusters
This review summarises the main properties of Young Massive Clusters (YMCs),
including their population properties, particularly focusing on extragalactic
cluster samples. We discuss potential biases and caveats that can affect the
construction of cluster samples and how incompleteness effects can result in
erroneous conclusions regarding the long term survival of clusters. In addition
to the luminosity, mass and age distributions of the clusters, we discuss the
size distribution and profile evolution of the clusters. We also briefly
discuss the stellar populations within YMCs. The final part of the review
focusses on the connections between YMCs and the ancient globular clusters,
whether or not they are related objects and how we can use what we know about
YMC formation and evolution to understand how GCs formed in the early universe
and how they relate to galaxy formation/evolution.Comment: 33 pages. To appear in EES2015 - Stellar Clusters: benchmarks of
stellar physics and galactic evolution - eds. E. Moraux, Y. Lebreton and C.
Charbonne
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