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Extreme behavior of multivariate phase-type distributions
This paper investigates the limiting distributions of the componentwise maxima and minima of suitably normalized iid multivariate phase-type random vectors. In the case of maxima, a large parametric class of multivariate extreme value (MEV) distributions is obtained. The flexibility of this new class is exemplified in the bivariate setup. For minima, it is shown that the dependence structure of the Marshall-Olkin class arises in the limit
Queues and risk processes with dependencies
We study the generalization of the G/G/1 queue obtained by relaxing the
assumption of independence between inter-arrival times and service
requirements. The analysis is carried out for the class of multivariate matrix
exponential distributions introduced in [12]. In this setting, we obtain the
steady state waiting time distribution and we show that the classical relation
between the steady state waiting time and the workload distributions re- mains
valid when the independence assumption is relaxed. We also prove duality
results with the ruin functions in an ordinary and a delayed ruin process.
These extend several known dualities between queueing and risk models in the
independent case. Finally we show that there exist stochastic order relations
between the waiting times under various instances of correlation
Bose-Einstein correlations for Levy stable source distributions
The peak of the two-particle Bose-Einstein correlation functions has a very
interesting structure. It is often believed to have a multivariate Gaussian
form. We show here that for the class of stable distributions, characterized by
the index of stability , the peak has a stretched exponential
shape. The Gaussian form corresponds then to the special case of .
We give examples for the Bose-Einstein correlation functions for univariate as
well as multivariate stable distributions, and check the model against
two-particle correlation data.Comment: 30 pages, 1 figure, an important misprint in former eqs. (37-38) and
other minor misprints are corrected, citations update
SKIRT: the design of a suite of input models for Monte Carlo radiative transfer simulations
The Monte Carlo method is the most popular technique to perform radiative
transfer simulations in a general 3D geometry. The algorithms behind and
acceleration techniques for Monte Carlo radiative transfer are discussed
extensively in the literature, and many different Monte Carlo codes are
publicly available. On the contrary, the design of a suite of components that
can be used for the distribution of sources and sinks in radiative transfer
codes has received very little attention. The availability of such models, with
different degrees of complexity, has many benefits. For example, they can serve
as toy models to test new physical ingredients, or as parameterised models for
inverse radiative transfer fitting. For 3D Monte Carlo codes, this requires
algorithms to efficiently generate random positions from 3D density
distributions. We describe the design of a flexible suite of components for the
Monte Carlo radiative transfer code SKIRT. The design is based on a combination
of basic building blocks (which can be either analytical toy models or
numerical models defined on grids or a set of particles) and the extensive use
of decorators that combine and alter these building blocks to more complex
structures. For a number of decorators, e.g. those that add spiral structure or
clumpiness, we provide a detailed description of the algorithms that can be
used to generate random positions. Advantages of this decorator-based design
include code transparency, the avoidance of code duplication, and an increase
in code maintainability. Moreover, since decorators can be chained without
problems, very complex models can easily be constructed out of simple building
blocks. Finally, based on a number of test simulations, we demonstrate that our
design using customised random position generators is superior to a simpler
design based on a generic black-box random position generator.Comment: 15 pages, 4 figures, accepted for publication in Astronomy and
Computin
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
Enhancing the significance of gravitational wave bursts through signal classification
The quest to observe gravitational waves challenges our ability to
discriminate signals from detector noise. This issue is especially relevant for
transient gravitational waves searches with a robust eyes wide open approach,
the so called all- sky burst searches. Here we show how signal classification
methods inspired by broad astrophysical characteristics can be implemented in
all-sky burst searches preserving their generality. In our case study, we apply
a multivariate analyses based on artificial neural networks to classify waves
emitted in compact binary coalescences. We enhance by orders of magnitude the
significance of signals belonging to this broad astrophysical class against the
noise background. Alternatively, at a given level of mis-classification of
noise events, we can detect about 1/4 more of the total signal population. We
also show that a more general strategy of signal classification can actually be
performed, by testing the ability of artificial neural networks in
discriminating different signal classes. The possible impact on future
observations by the LIGO-Virgo network of detectors is discussed by analysing
recoloured noise from previous LIGO-Virgo data with coherent WaveBurst, one of
the flagship pipelines dedicated to all-sky searches for transient
gravitational waves
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