8,732 research outputs found
Geometric and projection effects in Kramers-Moyal analysis
Kramers-Moyal coefficients provide a simple and easily visualized method with
which to analyze stochastic time series, particularly nonlinear ones. One
mechanism that can affect the estimation of the coefficients is geometric
projection effects. For some biologically-inspired examples, these effects are
predicted and explored with a non-stochastic projection operator method, and
compared with direct numerical simulation of the systems' Langevin equations.
General features and characteristics are identified, and the utility of the
Kramers-Moyal method discussed. Projections of a system are in general
non-Markovian, but here the Kramers-Moyal method remains useful, and in any
case the primary examples considered are found to be close to Markovian.Comment: Submitted to Phys. Rev.
What Is a Macrostate? Subjective Observations and Objective Dynamics
We consider the question of whether thermodynamic macrostates are objective
consequences of dynamics, or subjective reflections of our ignorance of a
physical system. We argue that they are both; more specifically, that the set
of macrostates forms the unique maximal partition of phase space which 1) is
consistent with our observations (a subjective fact about our ability to
observe the system) and 2) obeys a Markov process (an objective fact about the
system's dynamics). We review the ideas of computational mechanics, an
information-theoretic method for finding optimal causal models of stochastic
processes, and argue that macrostates coincide with the ``causal states'' of
computational mechanics. Defining a set of macrostates thus consists of an
inductive process where we start with a given set of observables, and then
refine our partition of phase space until we reach a set of states which
predict their own future, i.e. which are Markovian. Macrostates arrived at in
this way are provably optimal statistical predictors of the future values of
our observables.Comment: 15 pages, no figure
Two Procedures for Robust Monitoring of Probability Distributions of Economic Data Streams induced by Depth Functions
Data streams (streaming data) consist of transiently observed, evolving in
time, multidimensional data sequences that challenge our computational and/or
inferential capabilities. In this paper we propose user friendly approaches for
robust monitoring of selected properties of unconditional and conditional
distribution of the stream basing on depth functions. Our proposals are robust
to a small fraction of outliers and/or inliers but sensitive to a regime change
of the stream at the same time. Their implementations are available in our free
R package DepthProc.Comment: Operations Research and Decisions, vol. 25, No. 1, 201
Intermittent fluctuations in the Alcator C-Mod scrape-off layer for ohmic and high confinement mode plasmas
Plasma fluctuations in the scrape-off layer of the Alcator C-Mod tokamak in
ohmic and high confinement modes have been analyzed using gas puff imaging
data. In all cases investigated, the time series of emission from a single
spatially-resolved view into the gas puff are dominated by large-amplitude
bursts, attributed to blob-like filament structures moving radially outwards
and poloidally. There is a remarkable similarity of the fluctuation statistics
in ohmic plasmas and in edge localized mode-free and enhanced D-alpha high
confinement mode plasmas. Conditionally averaged wave forms have a two-sided
exponential shape with comparable temporal scales and asymmetry, while the
burst amplitudes and the waiting times between them are exponentially
distributed. The probability density functions and the frequency power spectral
densities are self-similar for all these confinement modes. These results are
strong evidence in support of a stochastic model describing the plasma
fluctuations in the scrape-off layer as a super-position of uncorrelated
exponential pulses. Predictions of this model are in excellent agreement with
experimental measurements in both ohmic and high confinement mode plasmas. The
stochastic model thus provides a valuable tool for predicting
fluctuation-induced plasma-wall interactions in magnetically confined fusion
plasmas.Comment: 17 pages, 10 figure
Efficient prediction for linear and nonlinear autoregressive models
Conditional expectations given past observations in stationary time series
are usually estimated directly by kernel estimators, or by plugging in kernel
estimators for transition densities. We show that, for linear and nonlinear
autoregressive models driven by independent innovations, appropriate smoothed
and weighted von Mises statistics of residuals estimate conditional
expectations at better parametric rates and are asymptotically efficient. The
proof is based on a uniform stochastic expansion for smoothed and weighted von
Mises processes of residuals. We consider, in particular, estimation of
conditional distribution functions and of conditional quantile functions.Comment: Published at http://dx.doi.org/10.1214/009053606000000812 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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