3,757 research outputs found
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
Random numbers from the tails of probability distributions using the transformation method
The speed of many one-line transformation methods for the production of, for
example, Levy alpha-stable random numbers, which generalize Gaussian ones, and
Mittag-Leffler random numbers, which generalize exponential ones, is very high
and satisfactory for most purposes. However, for the class of decreasing
probability densities fast rejection implementations like the Ziggurat by
Marsaglia and Tsang promise a significant speed-up if it is possible to
complement them with a method that samples the tails of the infinite support.
This requires the fast generation of random numbers greater or smaller than a
certain value. We present a method to achieve this, and also to generate random
numbers within any arbitrary interval. We demonstrate the method showing the
properties of the transform maps of the above mentioned distributions as
examples of stable and geometric stable random numbers used for the stochastic
solution of the space-time fractional diffusion equation.Comment: 17 pages, 7 figures, submitted to a peer-reviewed journa
Limited Feedback-based Block Diagonalization for the MIMO Broadcast Channel
Block diagonalization is a linear precoding technique for the multiple
antenna broadcast (downlink) channel that involves transmission of multiple
data streams to each receiver such that no multi-user interference is
experienced at any of the receivers. This low-complexity scheme operates only a
few dB away from capacity but requires very accurate channel knowledge at the
transmitter. We consider a limited feedback system where each receiver knows
its channel perfectly, but the transmitter is only provided with a finite
number of channel feedback bits from each receiver. Using a random quantization
argument, we quantify the throughput loss due to imperfect channel knowledge as
a function of the feedback level. The quality of channel knowledge must improve
proportional to the SNR in order to prevent interference-limitations, and we
show that scaling the number of feedback bits linearly with the system SNR is
sufficient to maintain a bounded rate loss. Finally, we compare our
quantization strategy to an analog feedback scheme and show the superiority of
quantized feedback.Comment: 20 pages, 4 figures, submitted to IEEE JSAC November 200
Model Selection and Adaptive Markov chain Monte Carlo for Bayesian Cointegrated VAR model
This paper develops a matrix-variate adaptive Markov chain Monte Carlo (MCMC)
methodology for Bayesian Cointegrated Vector Auto Regressions (CVAR). We
replace the popular approach to sampling Bayesian CVAR models, involving griddy
Gibbs, with an automated efficient alternative, based on the Adaptive
Metropolis algorithm of Roberts and Rosenthal, (2009). Developing the adaptive
MCMC framework for Bayesian CVAR models allows for efficient estimation of
posterior parameters in significantly higher dimensional CVAR series than
previously possible with existing griddy Gibbs samplers. For a n-dimensional
CVAR series, the matrix-variate posterior is in dimension , with
significant correlation present between the blocks of matrix random variables.
We also treat the rank of the CVAR model as a random variable and perform joint
inference on the rank and model parameters. This is achieved with a Bayesian
posterior distribution defined over both the rank and the CVAR model
parameters, and inference is made via Bayes Factor analysis of rank.
Practically the adaptive sampler also aids in the development of automated
Bayesian cointegration models for algorithmic trading systems considering
instruments made up of several assets, such as currency baskets. Previously the
literature on financial applications of CVAR trading models typically only
considers pairs trading (n=2) due to the computational cost of the griddy
Gibbs. We are able to extend under our adaptive framework to and
demonstrate an example with n = 10, resulting in a posterior distribution with
parameters up to dimension 310. By also considering the rank as a random
quantity we can ensure our resulting trading models are able to adjust to
potentially time varying market conditions in a coherent statistical framework.Comment: to appear journal Bayesian Analysi
- …