12,705 research outputs found
Practical Statistics for Particle Physics
This is the write-up of a set of lectures given at the Asia Europe Pacific
School of High Energy Physics in Quy Nhon, Vietnam in September 2018, to an
audience of PhD students in all branches of particle physics They cover the
different meanings of 'probability', particularly frequentist and Bayesian, the
binomial, Poisson and Gaussian distributions, hypothesis testing, estimation,
errors (including asymmetric and systematic errors) and goodness of fit.
Several different methods used in setting upper limits are explained, followed
by a discussion on why 5 sigma are conventionally required for a 'discovery'
Asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels
Variational methods for parameter estimation are an active research area,
potentially offering computationally tractable heuristics with theoretical
performance bounds. We build on recent work that applies such methods to
network data, and establish asymptotic normality rates for parameter estimates
of stochastic blockmodel data, by either maximum likelihood or variational
estimation. The result also applies to various sub-models of the stochastic
blockmodel found in the literature.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1124 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Bayesian modelling of clusters of galaxies from multi-frequency pointed Sunyaev--Zel'dovich observations
We present a Bayesian approach to modelling galaxy clusters using
multi-frequency pointed observations from telescopes that exploit the
Sunyaev--Zel'dovich effect. We use the recently developed MultiNest technique
(Feroz, Hobson & Bridges, 2008) to explore the high-dimensional parameter
spaces and also to calculate the Bayesian evidence. This permits robust
parameter estimation as well as model comparison. Tests on simulated Arcminute
Microkelvin Imager observations of a cluster, in the presence of primary CMB
signal, radio point sources (detected as well as an unresolved background) and
receiver noise, show that our algorithm is able to analyse jointly the data
from six frequency channels, sample the posterior space of the model and
calculate the Bayesian evidence very efficiently on a single processor. We also
illustrate the robustness of our detection process by applying it to a field
with radio sources and primordial CMB but no cluster, and show that indeed no
cluster is identified. The extension of our methodology to the detection and
modelling of multiple clusters in multi-frequency SZ survey data will be
described in a future work.Comment: 12 pages, 7 figures, submitted to MNRA
Deep Learning for Single Image Super-Resolution: A Brief Review
Single image super-resolution (SISR) is a notoriously challenging ill-posed
problem, which aims to obtain a high-resolution (HR) output from one of its
low-resolution (LR) versions. To solve the SISR problem, recently powerful deep
learning algorithms have been employed and achieved the state-of-the-art
performance. In this survey, we review representative deep learning-based SISR
methods, and group them into two categories according to their major
contributions to two essential aspects of SISR: the exploration of efficient
neural network architectures for SISR, and the development of effective
optimization objectives for deep SISR learning. For each category, a baseline
is firstly established and several critical limitations of the baseline are
summarized. Then representative works on overcoming these limitations are
presented based on their original contents as well as our critical
understandings and analyses, and relevant comparisons are conducted from a
variety of perspectives. Finally we conclude this review with some vital
current challenges and future trends in SISR leveraging deep learning
algorithms.Comment: Accepted by IEEE Transactions on Multimedia (TMM
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