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Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
Sines, steps and droplets: Semiparametric Bayesian modeling of arrival time series
I describe ongoing work developing Bayesian methods for flexible modeling of
arrival time series data without binning, aiming to improve detection and
measurement of X-ray and gamma-ray pulsars, and of pulses in gamma-ray bursts.
The methods use parametric and semiparametric Poisson point process models for
the event rate, and by design have close connections to conventional
frequentist methods currently used in time-domain astronomy.Comment: 4 pages, 1 figure; to appear in the proceedings of IAU Symposium 285,
"New Horizons in Time Domain Astronomy" (proceedings eds. Elizabeth Griffin,
Bob Hanisch, and Rob Seaman), Cambridge University Press; see
http://www.physics.ox.ac.uk/IAUS285
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