15,185 research outputs found
A detailed statistical analysis of the mass profiles of galaxy clusters
The distribution of mass in the halos of galaxies and galaxy clusters has
been probed observationally, theoretically, and in numerical simulations. Yet
there is still confusion about which of several suggested parameterized models
is the better representation, and whether these models are universal. We use
the temperature and density profiles of the intracluster medium as measured by
X-ray observations of 11 relaxed galaxy clusters to investigate mass models for
the halo using a thorough Bayesian statistical analysis. We make careful
comparisons between two- and three-parameter models, including the issue of a
universal third parameter. We find that, of the two-parameter models, the NFW
is the best representation, but we also find moderate statistical evidence that
a generalized three-parameter NFW model with a freely varying inner slope is
preferred, despite penalizing against the extra degree of freedom. There is a
strong indication that this inner slope needs to be determined for each cluster
individually, i.e. some clusters have central cores and others have steep
cusps. The mass-concentration relation of our sample is in reasonable agreement
with predictions based on numerical simulations.Comment: 10 pages, 5 figures, accepted by ApJ. Matches accepted versio
Inferring the intensity of Poisson processes at the limit of the detector sensitivity (with a case study on gravitational wave burst search)
We consider the issue of reporting the result of search experiment in the
most unbiased and efficient way, i.e. in a way which allows an easy
interpretation and combination of results and which do not depend on whether
the experimenters believe or not to having found the searched-for effect. Since
this work uses the language of Bayesian theory, to which most physicists are
not used, we find that it could be useful to practitioners to have in a single
paper a simple presentation of Bayesian inference, together with an example of
application of it in search of rare processes.Comment: 36 pages, 11 figures, Latex files using cernart.cls (included). This
paper and related work are also available at
http://www-zeus.roma1.infn.it/~agostini/prob+stat.htm
Bayesian Model Selection in Complex Linear Systems, as Illustrated in Genetic Association Studies
Motivated by examples from genetic association studies, this paper considers
the model selection problem in a general complex linear model system and in a
Bayesian framework. We discuss formulating model selection problems and
incorporating context-dependent {\it a priori} information through different
levels of prior specifications. We also derive analytic Bayes factors and their
approximations to facilitate model selection and discuss their theoretical and
computational properties. We demonstrate our Bayesian approach based on an
implemented Markov Chain Monte Carlo (MCMC) algorithm in simulations and a real
data application of mapping tissue-specific eQTLs. Our novel results on Bayes
factors provide a general framework to perform efficient model comparisons in
complex linear model systems
Interplay between distribution of live cells and growth dynamics of solid tumours
Experiments show that simple diffusion of nutrients and waste molecules is not sufficient to explain the typical multilayered structure of solid tumours, where an outer rim of proliferating cells surrounds a layer of quiescent but viable cells and a central necrotic region. These experiments challenge models of tumour growth based exclusively on diffusion. Here we propose a model of tumour growth that incorporates the volume dynamics and the distribution of cells within the viable cell rim. The model is suggested by in silico experiments and is validated using in vitro data. The results correlate with in vivo data as well, and the model can be used to support experimental and clinical oncology
Bayesian evidence and predictivity of the inflationary paradigm
In this paper we consider the issue of paradigm evaluation by applying Bayes'
theorem along the following nested hierarchy of progressively more complex
structures: i) parameter estimation (within a model), ii) model selection and
comparison (within a paradigm), iii) paradigm evaluation. In such a hierarchy
the Bayesian evidence works both as the posterior's normalization at a given
level and as the likelihood function at the next level up. Whilst raising no
objections to the standard application of the procedure at the two lowest
levels, we argue that it should receive a considerable modification when
evaluating paradigms, when testability and fitting data are equally important.
By considering toy models we illustrate how models and paradigms that are
difficult to falsify are always favoured by the Bayes factor. We argue that the
evidence for a paradigm should not only be high for a given dataset, but
exceptional with respect to what it would have been, had the data been
different. With this motivation we propose a measure which we term
predictivity, as well as a prior to be incorporated into the Bayesian
framework, penalising unpredictivity as much as not fitting data. We apply this
measure to inflation seen as a whole, and to a scenario where a specific
inflationary model is hypothetically deemed as the only one viable as a result
of information alien to cosmology (e.g. Solar System gravity experiments, or
particle physics input). We conclude that cosmic inflation is currently hard to
falsify, but that this could change were external/additional information to
cosmology to select one of its many models. We also compare this state of
affairs to bimetric varying speed of light cosmology.Comment: Final version with corrections adde
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