11,798 research outputs found
Geometry of the random interlacement
We consider the geometry of random interlacements on the -dimensional
lattice. We use ideas from stochastic dimension theory developed in
\cite{benjamini2004geometry} to prove the following: Given that two vertices
belong to the interlacement set, it is possible to find a path between
and contained in the trace left by at most
trajectories from the underlying Poisson point process. Moreover, this result
is sharp in the sense that there are pairs of points in the interlacement set
which cannot be connected by a path using the traces of at most trajectories
Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models
This tutorial provides a gentle introduction to the particle
Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear
state-space models together with a software implementation in the statistical
programming language R. We employ a step-by-step approach to develop an
implementation of the PMH algorithm (and the particle filter within) together
with the reader. This final implementation is also available as the package
pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some
intuition as to how the algorithm operates and discuss some solutions to
problems that might occur in practice. To illustrate the use of PMH, we
consider parameter inference in a linear Gaussian state-space model with
synthetic data and a nonlinear stochastic volatility model with real-world
data.Comment: 41 pages, 7 figures. In press for Journal of Statistical Software.
Source code for R, Python and MATLAB available at:
https://github.com/compops/pmh-tutoria
Do not log-transform count data
1. Ecological count data (e.g., number of individuals or species) are often log-transformed to satisfy parametric test assumptions.
2. Apart from the fact that generalized linear models are better suited in dealing with count data, a log-transformation of counts has the additional quandary in how to deal with zero observations. With just one zero observation (if this observation represents a sampling unit), the whole dataset needs to be fudged by adding a value (usually 1) before transformation. 
3. Simulating data from a negative binomial distribution, we compared the outcome of fitting models that were transformed in various ways (log, square-root) with results from fitting models using Poisson and negative binomial models to untransformed count data. 
4. We found that the transformations performed poorly, except when the dispersion was small and the mean counts were large.  The Poisson and negative binomial models consistently performed well, with little bias
Non-local gyrokinetic model of linear ion-temperature-gradient modes
A theory of non-local linear ion-temperature-gradient (ITG) drift modes while
retaining non-adiabatic electrons is presented, extending the previous work [S.
Moradi, et al {\em Phys. Plasmas} {\bf 18}, 062106 (2011)]. A dispersion
relation is derived to quantify the effects of the fractional velocity operator
in the Fokker-Planck equation modified by temperature gradients and
non-adiabatic electrons on the real frequency and growth rate. Solving the
dispersion relation, it is shown here that as the plasma becomes more
turbulent, it deviates from a Maxwellian distribution and becomes L\'{e}vy
distributed. The resulting L\'{e}vy distribution of the plasma may thus
significantly alter the transport. The relative effect of the fractional
derivative is larger on the real frequency than on the growth rate of the ITG
mode.Comment: 14pages 1 Figure submitted to Phys. Rev.
Particle Metropolis-Hastings using gradient and Hessian information
Particle Metropolis-Hastings (PMH) allows for Bayesian parameter inference in
nonlinear state space models by combining Markov chain Monte Carlo (MCMC) and
particle filtering. The latter is used to estimate the intractable likelihood.
In its original formulation, PMH makes use of a marginal MCMC proposal for the
parameters, typically a Gaussian random walk. However, this can lead to a poor
exploration of the parameter space and an inefficient use of the generated
particles.
We propose a number of alternative versions of PMH that incorporate gradient
and Hessian information about the posterior into the proposal. This information
is more or less obtained as a byproduct of the likelihood estimation. Indeed,
we show how to estimate the required information using a fixed-lag particle
smoother, with a computational cost growing linearly in the number of
particles. We conclude that the proposed methods can: (i) decrease the length
of the burn-in phase, (ii) increase the mixing of the Markov chain at the
stationary phase, and (iii) make the proposal distribution scale invariant
which simplifies tuning.Comment: 27 pages, 5 figures, 2 tables. The final publication is available at
Springer via: http://dx.doi.org/10.1007/s11222-014-9510-
Quasi-Newton particle Metropolis-Hastings
Particle Metropolis-Hastings enables Bayesian parameter inference in general
nonlinear state space models (SSMs). However, in many implementations a random
walk proposal is used and this can result in poor mixing if not tuned correctly
using tedious pilot runs. Therefore, we consider a new proposal inspired by
quasi-Newton algorithms that may achieve similar (or better) mixing with less
tuning. An advantage compared to other Hessian based proposals, is that it only
requires estimates of the gradient of the log-posterior. A possible application
is parameter inference in the challenging class of SSMs with intractable
likelihoods. We exemplify this application and the benefits of the new proposal
by modelling log-returns of future contracts on coffee by a stochastic
volatility model with -stable observations.Comment: 23 pages, 5 figures. Accepted for the 17th IFAC Symposium on System
Identification (SYSID), Beijing, China, October 201
Maximum likelihood estimation for social network dynamics
A model for network panel data is discussed, based on the assumption that the
observed data are discrete observations of a continuous-time Markov process on
the space of all directed graphs on a given node set, in which changes in tie
variables are independent conditional on the current graph. The model for tie
changes is parametric and designed for applications to social network analysis,
where the network dynamics can be interpreted as being generated by choices
made by the social actors represented by the nodes of the graph. An algorithm
for calculating the Maximum Likelihood estimator is presented, based on data
augmentation and stochastic approximation. An application to an evolving
friendship network is given and a small simulation study is presented which
suggests that for small data sets the Maximum Likelihood estimator is more
efficient than the earlier proposed Method of Moments estimator.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS313 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On the Accuracy of Equivalent Antenna Representations
The accuracy of two equivalent antenna representations, near-field sources
and far-field sources, are evaluated for an antenna installed on a simplified
platform in a series of case studies using different configurations of
equivalent antenna representations. The accuracy is evaluated in terms of
installed far-fields and surface currents on the platform. The results show
large variations between configurations. The root-mean-square installed
far-field error is 4.4% for the most accurate equivalent representation. When
using far-field sources, the design parameters have a large influence of the
achieved accuracy. There is also a varying accuracy depending on the type of
numerical method used. Based on the results, some recommendations on the choice
of sub-domain for the equivalent antenna representation are given. In
industrial antenna applications, the accuracy in determining e.g. installed
far-fields and antenna isolation on large platforms are critical. Equivalent
representations can reduce the fine-detail complexity of antennas and thus give
an efficient numerical descriptions to be used in large-scale simulations. The
results in this paper can be used as a guideline by antenna designers or system
engineers when using equivalent sources
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