358,313 research outputs found
Selecting the best statistical distribution using multiple criteria
When selecting a statistical distribution to describe a set of data there are a number of criteria that can be used. Rather than select one of these criteria, we look at how multiple criteria can be combined to make the final selection. Two approaches have previously been presented in Computers and Industrial Engineering. We review these, and present a simpler method based on multiplicative aggregation. This has the advantage of being able to combine measures which are not measured on the same scale without having to use a normalisation procedure. Moreover, this method is scale-invariant, thus re-scaling the criteria values does not affect the final ranking. The method requires strictly positive criteria values measured on a ratio scale.Peer reviewe
Multi-criteria Anomaly Detection using Pareto Depth Analysis
We consider the problem of identifying patterns in a data set that exhibit
anomalous behavior, often referred to as anomaly detection. In most anomaly
detection algorithms, the dissimilarity between data samples is calculated by a
single criterion, such as Euclidean distance. However, in many cases there may
not exist a single dissimilarity measure that captures all possible anomalous
patterns. In such a case, multiple criteria can be defined, and one can test
for anomalies by scalarizing the multiple criteria using a linear combination
of them. If the importance of the different criteria are not known in advance,
the algorithm may need to be executed multiple times with different choices of
weights in the linear combination. In this paper, we introduce a novel
non-parametric multi-criteria anomaly detection method using Pareto depth
analysis (PDA). PDA uses the concept of Pareto optimality to detect anomalies
under multiple criteria without having to run an algorithm multiple times with
different choices of weights. The proposed PDA approach scales linearly in the
number of criteria and is provably better than linear combinations of the
criteria.Comment: Removed an unnecessary line from Algorithm
Cosmology with velocity dispersion counts: an alternative to measuring cluster halo masses
The evolution of galaxy cluster counts is a powerful probe of several
fundamental cosmological parameters. A number of recent studies using this
probe have claimed tension with the cosmology preferred by the analysis of the
Planck primary CMB data, in the sense that there are fewer clusters observed
than predicted based on the primary CMB cosmology. One possible resolution to
this problem is systematic errors in the absolute halo mass calibration in
cluster studies, which is required to convert the standard theoretical
prediction (the halo mass function) into counts as a function of the observable
(e.g., X-ray luminosity, Sunyaev-Zel'dovich flux, optical richness). Here we
propose an alternative strategy, which is to directly compare predicted and
observed cluster counts as a function of the one-dimensional velocity
dispersion of the cluster galaxies. We argue that the velocity dispersion of
groups/clusters can be theoretically predicted as robustly as mass but, unlike
mass, it can also be directly observed, thus circumventing the main systematic
bias in traditional cluster counts studies. With the aid of the BAHAMAS suite
of cosmological hydrodynamical simulations, we demonstrate the potential of the
velocity dispersion counts for discriminating even similar CDM models.
These predictions can be compared with the results from existing redshift
surveys such as the highly-complete Galaxy And Mass Assembly (GAMA) survey, and
upcoming wide-field spectroscopic surveys such as the Wide Area Vista
Extragalactic Survey (WAVES) and the Dark Energy Survey Instrument (DESI).Comment: 15 pages, 13 figures. Accepted for publication in MNRAS. New section
on cosmological forecasts adde
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