2,070 research outputs found
Surrogate time series
Before we apply nonlinear techniques, for example those inspired by chaos
theory, to dynamical phenomena occurring in nature, it is necessary to first
ask if the use of such advanced techniques is justified "by the data". While
many processes in nature seem very unlikely a priori to be linear, the possible
nonlinear nature might not be evident in specific aspects of their dynamics.
The method of surrogate data has become a very popular tool to address such a
question. However, while it was meant to provide a statistically rigorous,
foolproof framework, some limitations and caveats have shown up in its
practical use. In this paper, recent efforts to understand the caveats, avoid
the pitfalls, and to overcome some of the limitations, are reviewed and
augmented by new material. In particular, we will discuss specific as well as
more general approaches to constrained randomisation, providing a full range of
examples. New algorithms will be introduced for unevenly sampled and
multivariate data and for surrogate spike trains. The main limitation, which
lies in the interpretability of the test results, will be illustrated through
instructive case studies. We will also discuss some implementational aspects of
the realisation of these methods in the TISEAN
(http://www.mpipks-dresden.mpg.de/~tisean) software package.Comment: 28 pages, 23 figures, software at
http://www.mpipks-dresden.mpg.de/~tisea
Practical Statistics for the LHC
This document is a pedagogical introduction to statistics for particle
physics. Emphasis is placed on the terminology, concepts, and methods being
used at the Large Hadron Collider. The document addresses both the statistical
tests applied to a model of the data and the modeling itself.Comment: presented at the 2011 European School of High-Energy Physics, Cheile
Gradistei, Romania, 7-20 September 2011 I expect to release updated versions
of this document in the futur
Determination of the CMSSM Parameters using Neural Networks
In most (weakly interacting) extensions of the Standard Model the relation
mapping the parameter values onto experimentally measurable quantities can be
computed (with some uncertainties), but the inverse relation is usually not
known. In this paper we demonstrate the ability of artificial neural networks
to find this unknown relation, by determining the unknown parameters of the
constrained minimal supersymmetric extension of the Standard Model (CMSSM) from
quantities that can be measured at the LHC. We expect that the method works
also for many other new physics models. We compare its performance with the
results of a straightforward \chi^2 minimization. We simulate LHC signals at a
center of mass energy of 14 TeV at the hadron level. In this proof-of-concept
study we do not explicitly simulate Standard Model backgrounds, but apply cuts
that have been shown to enhance the signal-to-background ratio. We analyze four
different benchmark points that lie just beyond current lower limits on
superparticle masses, each of which leads to around 1000 events after cuts for
an integrated luminosity of 10 fb^{-1}. We use up to 84 observables, most of
which are counting observables; we do not attempt to directly reconstruct
(differences of) masses from kinematic edges or kinks of distributions. We
nevertheless find that m_0 and m_{1/2} can be determined reliably, with errors
as small as 1% in some cases. With 500 fb^{-1} of data tan\beta as well as A_0
can also be determined quite accurately. For comparable computational effort
the \chi^2 minimization yielded much worse results.Comment: 46 pages, 10 figures, 4 tables; added short paragraph in Section 5
about the goodness of the fit, version to appear in Phys. Rev.
Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part one: Sunspot dynamics
In this study, the nonlinear analysis of the sunspot index is embedded in the
non-extensive statistical theory of Tsallis. The triplet of Tsallis, as well as
the correlation dimension and the Lyapunov exponent spectrum were estimated for
the SVD components of the sunspot index timeseries. Also the multifractal
scaling exponent spectrum, the generalized Renyi dimension spectrum and the
spectrum of the structure function exponents were estimated experimentally and
theoretically by using the entropy principle included in Tsallis non extensive
statistical theory, following Arimitsu and Arimitsu. Our analysis showed
clearly the following: a) a phase transition process in the solar dynamics from
high dimensional non Gaussian SOC state to a low dimensional non Gaussian
chaotic state, b) strong intermittent solar turbulence and anomalous
(multifractal) diffusion solar process, which is strengthened as the solar
dynamics makes phase transition to low dimensional chaos in accordance to
Ruzmaikin, Zeleny and Milovanov studies c) faithful agreement of Tsallis non
equilibrium statistical theory with the experimental estimations of i)
non-Gaussian probability distribution function, ii) multifractal scaling
exponent spectrum and generalized Renyi dimension spectrum, iii) exponent
spectrum of the structure functions estimated for the sunspot index and its
underlying non equilibrium solar dynamics.Comment: 40 pages, 11 figure
Selection of sequence motifs and generative Hopfield-Potts models for protein familiesilies
Statistical models for families of evolutionary related proteins have
recently gained interest: in particular pairwise Potts models, as those
inferred by the Direct-Coupling Analysis, have been able to extract information
about the three-dimensional structure of folded proteins, and about the effect
of amino-acid substitutions in proteins. These models are typically requested
to reproduce the one- and two-point statistics of the amino-acid usage in a
protein family, {\em i.e.}~to capture the so-called residue conservation and
covariation statistics of proteins of common evolutionary origin. Pairwise
Potts models are the maximum-entropy models achieving this. While being
successful, these models depend on huge numbers of {\em ad hoc} introduced
parameters, which have to be estimated from finite amount of data and whose
biophysical interpretation remains unclear. Here we propose an approach to
parameter reduction, which is based on selecting collective sequence motifs. It
naturally leads to the formulation of statistical sequence models in terms of
Hopfield-Potts models. These models can be accurately inferred using a mapping
to restricted Boltzmann machines and persistent contrastive divergence. We show
that, when applied to protein data, even 20-40 patterns are sufficient to
obtain statistically close-to-generative models. The Hopfield patterns form
interpretable sequence motifs and may be used to clusterize amino-acid
sequences into functional sub-families. However, the distributed collective
nature of these motifs intrinsically limits the ability of Hopfield-Potts
models in predicting contact maps, showing the necessity of developing models
going beyond the Hopfield-Potts models discussed here.Comment: 26 pages, 16 figures, to app. in PR
Fitting the Phenomenological MSSM
We perform a global Bayesian fit of the phenomenological minimal
supersymmetric standard model (pMSSM) to current indirect collider and dark
matter data. The pMSSM contains the most relevant 25 weak-scale MSSM
parameters, which are simultaneously fit using `nested sampling' Monte Carlo
techniques in more than 15 years of CPU time. We calculate the Bayesian
evidence for the pMSSM and constrain its parameters and observables in the
context of two widely different, but reasonable, priors to determine which
inferences are robust. We make inferences about sparticle masses, the sign of
the parameter, the amount of fine tuning, dark matter properties and the
prospects for direct dark matter detection without assuming a restrictive
high-scale supersymmetry breaking model. We find the inferred lightest CP-even
Higgs boson mass as an example of an approximately prior independent
observable. This analysis constitutes the first statistically convergent pMSSM
global fit to all current data.Comment: Added references, paragraph on fine-tunin
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