414,830 research outputs found
Statistical methods in cosmology
The advent of large data-set in cosmology has meant that in the past 10 or 20
years our knowledge and understanding of the Universe has changed not only
quantitatively but also, and most importantly, qualitatively. Cosmologists rely
on data where a host of useful information is enclosed, but is encoded in a
non-trivial way. The challenges in extracting this information must be overcome
to make the most of a large experimental effort. Even after having converged to
a standard cosmological model (the LCDM model) we should keep in mind that this
model is described by 10 or more physical parameters and if we want to study
deviations from it, the number of parameters is even larger. Dealing with such
a high dimensional parameter space and finding parameters constraints is a
challenge on itself. Cosmologists want to be able to compare and combine
different data sets both for testing for possible disagreements (which could
indicate new physics) and for improving parameter determinations. Finally,
cosmologists in many cases want to find out, before actually doing the
experiment, how much one would be able to learn from it. For all these reasons,
sophisiticated statistical techniques are being employed in cosmology, and it
has become crucial to know some statistical background to understand recent
literature in the field. I will introduce some statistical tools that any
cosmologist should know about in order to be able to understand recently
published results from the analysis of cosmological data sets. I will not
present a complete and rigorous introduction to statistics as there are several
good books which are reported in the references. The reader should refer to
those.Comment: 31, pages, 6 figures, notes from 2nd Trans-Regio Winter school in
Passo del Tonale. To appear in Lectures Notes in Physics, "Lectures on
cosmology: Accelerated expansion of the universe" Feb 201
Modern Statistical Methods for GLAST Event Analysis
We describe a statistical reconstruction methodology for the GLAST LAT. The
methodology incorporates in detail the statistics of the interactions of
photons and charged particles with the tungsten layers in the LAT, and uses the
scattering distributions to compute the full probability distribution over the
energy and direction of the incident photons. It uses model selection methods
to estimate the probabilities of the possible geometrical configurations of the
particles produced in the detector, and numerical marginalization over the
energy loss and scattering angles at each layer. Preliminary results show that
it can improve on the tracker-only energy estimates for muons and electrons
incident on the LAT.Comment: To appear in the proceedings of the First GLAST Symposium (held at
Stanford University, 5-8 February 2007
Using simulation studies to evaluate statistical methods
Simulation studies are computer experiments that involve creating data by
pseudorandom sampling. The key strength of simulation studies is the ability to
understand the behaviour of statistical methods because some 'truth' (usually
some parameter/s of interest) is known from the process of generating the data.
This allows us to consider properties of methods, such as bias. While widely
used, simulation studies are often poorly designed, analysed and reported. This
tutorial outlines the rationale for using simulation studies and offers
guidance for design, execution, analysis, reporting and presentation. In
particular, this tutorial provides: a structured approach for planning and
reporting simulation studies, which involves defining aims, data-generating
mechanisms, estimands, methods and performance measures ('ADEMP'); coherent
terminology for simulation studies; guidance on coding simulation studies; a
critical discussion of key performance measures and their estimation; guidance
on structuring tabular and graphical presentation of results; and new graphical
presentations. With a view to describing recent practice, we review 100
articles taken from Volume 34 of Statistics in Medicine that included at least
one simulation study and identify areas for improvement.Comment: 31 pages, 9 figures (2 in appendix), 8 tables (1 in appendix
Statistical methods for critical scenarios in aeronautics
We present numerical results obtained on the CEMRACS project Predictive SMS
proposed by Safety Line. The goal of this work was to elaborate a purely
statistical method in order to reconstruct the deceleration profile of a plane
during landing under normal operating conditions, from a database containing
around recordings. The aim of Safety Line is to use this model to detect
malfunctions of the braking system of the plane from deviations of the measured
deceleration profile of the plane to the one predicted by the model. This
yields to a multivariate nonparametric regression problem, which we chose to
tackle using a Bayesian approach based on the use of gaussian processes. We
also compare this approach with other statistical methods.Comment: 14 pages, 5 figure
- …