63,728 research outputs found
A Flexible Joint Longitudinal-Survival Model for Analysis of End-Stage Renal Disease Data
We propose a flexible joint longitudinal-survival framework to examine the
association between longitudinally collected biomarkers and a time-to-event
endpoint. More specifically, we use our method for analyzing the survival
outcome of end-stage renal disease patients with time-varying serum albumin
measurements. Our proposed method is robust to common parametric assumptions in
that it avoids explicit distributional assumptions on longitudinal measures and
allows for subject-specific baseline hazard in the survival component. Fully
joint estimation is performed to account for the uncertainty in the estimated
longitudinal biomarkers included in the survival model
Stochastic modelling of regional archaeomagnetic series
SUMMARY We report a new method to infer continuous time series of the
declination, inclination and intensity of the magnetic field from
archeomagnetic data. Adopting a Bayesian perspective, we need to specify a
priori knowledge about the time evolution of the magnetic field. It consists in
a time correlation function that we choose to be compatible with present
knowledge about the geomagnetic time spectra. The results are presented as
distributions of possible values for the declination, inclination or intensity.
We find that the methodology can be adapted to account for the age
uncertainties of archeological artefacts and we use Markov Chain Monte Carlo to
explore the possible dates of observations. We apply the method to intensity
datasets from Mari, Syria and to intensity and directional datasets from Paris,
France. Our reconstructions display more rapid variations than previous studies
and we find that the possible values of geomagnetic field elements are not
necessarily normally distributed. Another output of the model is better age
estimates of archeological artefacts
A Bayesian Heteroscedastic GLM with Application to fMRI Data with Motion Spikes
We propose a voxel-wise general linear model with autoregressive noise and
heteroscedastic noise innovations (GLMH) for analyzing functional magnetic
resonance imaging (fMRI) data. The model is analyzed from a Bayesian
perspective and has the benefit of automatically down-weighting time points
close to motion spikes in a data-driven manner. We develop a highly efficient
Markov Chain Monte Carlo (MCMC) algorithm that allows for Bayesian variable
selection among the regressors to model both the mean (i.e., the design matrix)
and variance. This makes it possible to include a broad range of explanatory
variables in both the mean and variance (e.g., time trends, activation stimuli,
head motion parameters and their temporal derivatives), and to compute the
posterior probability of inclusion from the MCMC output. Variable selection is
also applied to the lags in the autoregressive noise process, making it
possible to infer the lag order from the data simultaneously with all other
model parameters. We use both simulated data and real fMRI data from OpenfMRI
to illustrate the importance of proper modeling of heteroscedasticity in fMRI
data analysis. Our results show that the GLMH tends to detect more brain
activity, compared to its homoscedastic counterpart, by allowing the variance
to change over time depending on the degree of head motion
L\'{e}vy flights in inhomogeneous environments
We study the long time asymptotics of probability density functions (pdfs) of
L\'{e}vy flights in different confining potentials. For that we use two models:
Langevin - driven and (L\'{e}vy - Schr\"odinger) semigroup - driven dynamics.
It turns out that the semigroup modeling provides much stronger confining
properties than the standard Langevin one. Since contractive semigroups set a
link between L\'{e}vy flights and fractional (pseudo-differential) Hamiltonian
systems, we can use the latter to control the long - time asymptotics of the
pertinent pdfs. To do so, we need to impose suitable restrictions upon the
Hamiltonian and its potential. That provides verifiable criteria for an
invariant pdf to be actually an asymptotic pdf of the semigroup-driven
jump-type process. For computational and visualization purposes our
observations are exemplified for the Cauchy driver and its response to external
polynomial potentials (referring to L\'{e}vy oscillators), with respect to both
dynamical mechanisms.Comment: Major revisio
Modeling interest rate dynamics: an infinite-dimensional approach
We present a family of models for the term structure of interest rates which
describe the interest rate curve as a stochastic process in a Hilbert space. We
start by decomposing the deformations of the term structure into the variations
of the short rate, the long rate and the fluctuations of the curve around its
average shape. This fluctuation is then described as a solution of a stochastic
evolution equation in an infinite dimensional space. In the case where
deformations are local in maturity, this equation reduces to a stochastic PDE,
of which we give the simplest example. We discuss the properties of the
solutions and show that they capture in a parsimonious manner the essential
features of yield curve dynamics: imperfect correlation between maturities,
mean reversion of interest rates and the structure of principal components of
term structure deformations. Finally, we discuss calibration issues and show
that the model parameters have a natural interpretation in terms of empirically
observed quantities.Comment: Keywords: interest rates, stochastic PDE, term structure models,
stochastic processes in Hilbert space. Other related works may be retrieved
on http://www.eleves.ens.fr:8080/home/cont/papers.htm
Truncation effects in superdiffusive front propagation with L\'evy flights
A numerical and analytical study of the role of exponentially truncated
L\'evy flights in the superdiffusive propagation of fronts in
reaction-diffusion systems is presented. The study is based on a variation of
the Fisher-Kolmogorov equation where the diffusion operator is replaced by a
-truncated fractional derivative of order where
is the characteristic truncation length scale. For there is no
truncation and fronts exhibit exponential acceleration and algebraic decaying
tails. It is shown that for this phenomenology prevails in the
intermediate asymptotic regime where
is the diffusion constant. Outside the intermediate asymptotic regime,
i.e. for , the tail of the front exhibits the tempered decay
, the acceleration is transient, and
the front velocity, , approaches the terminal speed as , where it is assumed that
with denoting the growth rate of the
reaction kinetics. However, the convergence of this process is algebraic, , which is very slow compared to the exponential
convergence observed in the diffusive (Gaussian) case. An over-truncated regime
in which the characteristic truncation length scale is shorter than the length
scale of the decay of the initial condition, , is also identified. In
this extreme regime, fronts exhibit exponential tails, ,
and move at the constant velocity, .Comment: Accepted for publication in Phys. Rev. E (Feb. 2009
Extension of Wirtinger's Calculus to Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS
Over the last decade, kernel methods for nonlinear processing have
successfully been used in the machine learning community. The primary
mathematical tool employed in these methods is the notion of the Reproducing
Kernel Hilbert Space. However, so far, the emphasis has been on batch
techniques. It is only recently, that online techniques have been considered in
the context of adaptive signal processing tasks. Moreover, these efforts have
only been focussed on real valued data sequences. To the best of our knowledge,
no adaptive kernel-based strategy has been developed, so far, for complex
valued signals. Furthermore, although the real reproducing kernels are used in
an increasing number of machine learning problems, complex kernels have not,
yet, been used, in spite of their potential interest in applications that deal
with complex signals, with Communications being a typical example. In this
paper, we present a general framework to attack the problem of adaptive
filtering of complex signals, using either real reproducing kernels, taking
advantage of a technique called \textit{complexification} of real RKHSs, or
complex reproducing kernels, highlighting the use of the complex gaussian
kernel. In order to derive gradients of operators that need to be defined on
the associated complex RKHSs, we employ the powerful tool of Wirtinger's
Calculus, which has recently attracted attention in the signal processing
community. To this end, in this paper, the notion of Wirtinger's calculus is
extended, for the first time, to include complex RKHSs and use it to derive
several realizations of the Complex Kernel Least-Mean-Square (CKLMS) algorithm.
Experiments verify that the CKLMS offers significant performance improvements
over several linear and nonlinear algorithms, when dealing with nonlinearities.Comment: 15 pages (double column), preprint of article accepted in IEEE Trans.
Sig. Pro
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