455 research outputs found
Transfer Entropy as a Log-likelihood Ratio
Transfer entropy, an information-theoretic measure of time-directed
information transfer between joint processes, has steadily gained popularity in
the analysis of complex stochastic dynamics in diverse fields, including the
neurosciences, ecology, climatology and econometrics. We show that for a broad
class of predictive models, the log-likelihood ratio test statistic for the
null hypothesis of zero transfer entropy is a consistent estimator for the
transfer entropy itself. For finite Markov chains, furthermore, no explicit
model is required. In the general case, an asymptotic chi-squared distribution
is established for the transfer entropy estimator. The result generalises the
equivalence in the Gaussian case of transfer entropy and Granger causality, a
statistical notion of causal influence based on prediction via vector
autoregression, and establishes a fundamental connection between directed
information transfer and causality in the Wiener-Granger sense
Spectral Analysis of Multi-dimensional Self-similar Markov Processes
In this paper we consider a discrete scale invariant (DSI) process with scale . We consider to have some fix number of
observations in every scale, say , and to get our samples at discrete points
where is obtained by the equality
and . So we provide a discrete time scale
invariant (DT-SI) process with parameter space . We find the spectral representation of the covariance function of
such DT-SI process. By providing harmonic like representation of
multi-dimensional self-similar processes, spectral density function of them are
presented. We assume that the process is also Markov
in the wide sense and provide a discrete time scale invariant Markov (DT-SIM)
process with the above scheme of sampling. We present an example of DT-SIM
process, simple Brownian motion, by the above sampling scheme and verify our
results. Finally we find the spectral density matrix of such DT-SIM process and
show that its associated -dimensional self-similar Markov process is fully
specified by where is
the covariance function of th and th observations of the process.Comment: 16 page
Multivariate Granger Causality and Generalized Variance
Granger causality analysis is a popular method for inference on directed
interactions in complex systems of many variables. A shortcoming of the
standard framework for Granger causality is that it only allows for examination
of interactions between single (univariate) variables within a system, perhaps
conditioned on other variables. However, interactions do not necessarily take
place between single variables, but may occur among groups, or "ensembles", of
variables. In this study we establish a principled framework for Granger
causality in the context of causal interactions among two or more multivariate
sets of variables. Building on Geweke's seminal 1982 work, we offer new
justifications for one particular form of multivariate Granger causality based
on the generalized variances of residual errors. Taken together, our results
support a comprehensive and theoretically consistent extension of Granger
causality to the multivariate case. Treated individually, they highlight
several specific advantages of the generalized variance measure, which we
illustrate using applications in neuroscience as an example. We further show
how the measure can be used to define "partial" Granger causality in the
multivariate context and we also motivate reformulations of "causal density"
and "Granger autonomy". Our results are directly applicable to experimental
data and promise to reveal new types of functional relations in complex
systems, neural and otherwise.Comment: added 1 reference, minor change to discussion, typos corrected; 28
pages, 3 figures, 1 table, LaTe
A functional non-central limit theorem for jump-diffusions with periodic coefficients driven by stable Levy-noise
We prove a functional non-central limit theorem for jump-diffusions with
periodic coefficients driven by strictly stable Levy-processes with stability
index bigger than one. The limit process turns out to be a strictly stable Levy
process with an averaged jump-measure. Unlike in the situation where the
diffusion is driven by Brownian motion, there is no drift related enhancement
of diffusivity.Comment: Accepted to Journal of Theoretical Probabilit
Measured quantum probability distribution functions for Brownian motion
The quantum analog of the joint probability distributions describing a
classical stochastic process is introduced. A prescription is given for
constructing the quantum distribution associated with a sequence of
measurements. For the case of quantum Brownian motion this prescription is
illustrated with a number of explicit examples. In particular it is shown how
the prescription can be extended in the form of a general formula for the
Wigner function of a Brownian particle entangled with a heat bath.Comment: Phys. Rev. A, in pres
Sentencing Outcomes of Convicted Child Sex Offenders
This research examines the sentencing outcomes of convicted child sexual offenders from data collected over an eight year period. Multiple regression and nominal log linear regression are used to examine length of prison sentence, length of probation sentence, and whether or not the convicted offender is actually sent to prison or to probation. While many independent variables appear to be related to sentence outcome, they fall into three categories: characteristics of the offender, characteristics of the victim, and characteristics of the crime. Additionally, while many variables appear related at the bivariate level, when multivariate analysis is applied, fewer variables remain significant and these are mostly from the characteristics of the offense
Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. III: potential function in local stochastic dynamics and in steady state of Boltzmann-Gibbs type distribution function
From a logic point of view this is the third in the series to solve the
problem of absence of detailed balance. This paper will be denoted as SDS III.
The existence of a dynamical potential with both local and global meanings in
general nonequilibrium processes has been controversial. Following an earlier
explicit construction by one of us (Ao, J. Phys. {\bf A37}, L25 '04,
arXiv:0803.4356, referred to as SDS II), in the present paper we show
rigorously its existence for a generic class of situations in physical and
biological sciences. The local dynamical meaning of this potential function is
demonstrated via a special stochastic differential equation and its global
steady-state meaning via a novel and explicit form of Fokker-Planck equation,
the zero mass limit. We also give a procedure to obtain the special stochastic
differential equation for any given Fokker-Planck equation. No detailed balance
condition is required in our demonstration. For the first time we obtain here a
formula to describe the noise induced shift in drift force comparing to the
steady state distribution, a phenomenon extensively observed in numerical
studies. The comparison to two well known stochastic integration methods, Ito
and Stratonovich, are made ready. Such comparison was made elsewhere (Ao, Phys.
Life Rev. {\bf 2} (2005) 117. q-bio/0605020).Comment: latex. 13 page
A Pathwise Ergodic Theorem for Quantum Trajectories
If the time evolution of an open quantum system approaches equilibrium in the
time mean, then on any single trajectory of any of its unravelings the time
averaged state approaches the same equilibrium state with probability 1. In the
case of multiple equilibrium states the quantum trajectory converges in the
mean to a random choice from these states.Comment: 8 page
Scaling Limits for Internal Aggregation Models with Multiple Sources
We study the scaling limits of three different aggregation models on Z^d:
internal DLA, in which particles perform random walks until reaching an
unoccupied site; the rotor-router model, in which particles perform
deterministic analogues of random walks; and the divisible sandpile, in which
each site distributes its excess mass equally among its neighbors. As the
lattice spacing tends to zero, all three models are found to have the same
scaling limit, which we describe as the solution to a certain PDE free boundary
problem in R^d. In particular, internal DLA has a deterministic scaling limit.
We find that the scaling limits are quadrature domains, which have arisen
independently in many fields such as potential theory and fluid dynamics. Our
results apply both to the case of multiple point sources and to the
Diaconis-Fulton smash sum of domains.Comment: 74 pages, 4 figures, to appear in J. d'Analyse Math. Main changes in
v2: added "least action principle" (Lemma 3.2); small corrections in section
4, and corrected the proof of Lemma 5.3 (Lemma 5.4 in the new version);
expanded section 6.
Eyewitness descriptions without memory: The (f)utility of describing faces
Eyewitness descriptions provide critical information for the police and other agencies to use during investigations. While researchers have typically considered the impact of memory, little consideration has been given to the utility of facial descriptions themselves, without the additional memory demands. In Experiment 1, participants described face images to their partners, who were then required to select these faces from photographic lineups. Performance was error‐prone when the same image appeared in the lineup (73% correct), and decreased further when a different image of the same face was presented (22% correct). We found some evidence to suggest this was due, in part, to difficulties with recognizing that two different images depicted the same person. In Experiment 2, we demonstrated that descriptions of the same face given by different people showed only moderate agreement. Taken together, these results highlight the problematic nature of facial descriptions, even without memory, and their limited utility
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