2,364 research outputs found
The Computational Structure of Spike Trains
Neurons perform computations, and convey the results of those computations
through the statistical structure of their output spike trains. Here we present
a practical method, grounded in the information-theoretic analysis of
prediction, for inferring a minimal representation of that structure and for
characterizing its complexity. Starting from spike trains, our approach finds
their causal state models (CSMs), the minimal hidden Markov models or
stochastic automata capable of generating statistically identical time series.
We then use these CSMs to objectively quantify both the generalizable structure
and the idiosyncratic randomness of the spike train. Specifically, we show that
the expected algorithmic information content (the information needed to
describe the spike train exactly) can be split into three parts describing (1)
the time-invariant structure (complexity) of the minimal spike-generating
process, which describes the spike train statistically; (2) the randomness
(internal entropy rate) of the minimal spike-generating process; and (3) a
residual pure noise term not described by the minimal spike-generating process.
We use CSMs to approximate each of these quantities. The CSMs are inferred
nonparametrically from the data, making only mild regularity assumptions, via
the causal state splitting reconstruction algorithm. The methods presented here
complement more traditional spike train analyses by describing not only spiking
probability and spike train entropy, but also the complexity of a spike train's
structure. We demonstrate our approach using both simulated spike trains and
experimental data recorded in rat barrel cortex during vibrissa stimulation.Comment: Somewhat different format from journal version but same conten
Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology
The detection and attribution of long-term patterns in hydrological time series have been important research topics for decades. A significant portion of the literature regards such patterns as âdeterministic componentsâ or âtrendsâ even though the complexity of hydrological systems does not allow easy deterministic explanations and attributions. Consequently, trend estimation techniques have been developed to make and justify statements about tendencies in the historical data, which are often used to predict future events. Testing trend hypothesis on observed time series is widespread in the hydro-meteorological literature mainly due to the interest in detecting consequences of human activities on the hydrological cycle. This analysis usually relies on the application of some null hypothesis significance tests (NHSTs) for slowly-varying and/or abrupt changes, such as Mann-Kendall, Pettitt, or similar, to summary statistics of hydrological time series (e.g., annual averages, maxima, minima, etc.). However, the reliability of this application has seldom been explored in detail. This paper discusses misuse, misinterpretation, and logical flaws of NHST for trends in the analysis of hydrological data from three different points of view: historic-logical, semantic-epistemological, and practical. Based on a review of NHST rationale, and basic statistical definitions of stationarity, nonstationarity, and ergodicity, we show that even if the empirical estimation of trends in hydrological time series is always feasible from a numerical point of view, it is uninformative and does not allow the inference of nonstationarity without assuming a priori additional information on the underlying stochastic process, according to deductive reasoning. This prevents the use of trend NHST outcomes to support nonstationary frequency analysis and modeling. We also show that the correlation structures characterizing hydrological time series might easily be underestimated, further compromising the attempt to draw conclusions about trends spanning the period of records. Moreover, even though adjusting procedures accounting for correlation have been developed, some of them are insufficient or are applied only to some tests, while some others are theoretically flawed but still widely applied. In particular, using 250 unimpacted stream flow time series across the conterminous United States (CONUS), we show that the test results can dramatically change if the sequences of annual values are reproduced starting from daily stream flow records, whose larger sizes enable a more reliable assessment of the correlation structures
Residual acceleration data on IML-1: Development of a data reduction and dissemination plan
The research performed consisted of three stages: (1) identification of sensitive IML-1 experiments and sensitivity ranges by order of magnitude estimates, numerical modeling, and investigator input; (2) research and development towards reduction, supplementation, and dissemination of residual acceleration data; and (3) implementation of the plan on existing acceleration databases
Analysing Convergence through the Distribution Dynamics Approach: Why and how?
The convergence hypothesis has stimulated a heated debate within the growth literature. The present paper compares the two most commonly adopted empirical approaches, the regression approach and the distribution dynamics approach, and argues that the former fails to uncover important features of the dynamics that might characterise the convergence process. Next, it provides an in depth description of the features and underlying assumptions of the distribution dynamics approach as well as a detailed discussion of some important aspects related to the estimate of stochastic kernels via kernel density estimators. Finally, the empirical section allows to emphasises the interpretational advantages stemming from the use of stochastic kernels to capture the evolution of the entire cross-sectional income distribution. Incidentally, through a comparison between the results obtained from alternative sets of Italian regions, it suggest that the use of administrative regions could lead to ambiguous results.Distribution Dynamics, Stochastic Kernel, Kernel Density Estimation, beta-convergence, Regions
Nonlinear stability of the ensemble Kalman filter with adaptive covariance inflation
The Ensemble Kalman filter and Ensemble square root filters are data
assimilation methods used to combine high dimensional nonlinear models with
observed data. These methods have proved to be indispensable tools in science
and engineering as they allow computationally cheap, low dimensional ensemble
state approximation for extremely high dimensional turbulent forecast models.
From a theoretical perspective, these methods are poorly understood, with the
exception of a recently established but still incomplete nonlinear stability
theory. Moreover, recent numerical and theoretical studies of catastrophic
filter divergence have indicated that stability is a genuine mathematical
concern and can not be taken for granted in implementation. In this article we
propose a simple modification of ensemble based methods which resolves these
stability issues entirely. The method involves a new type of adaptive
covariance inflation, which comes with minimal additional cost. We develop a
complete nonlinear stability theory for the adaptive method, yielding Lyapunov
functions and geometric ergodicity under weak assumptions. We present numerical
evidence which suggests the adaptive methods have improved accuracy over
standard methods and completely eliminate catastrophic filter divergence. This
enhanced stability allows for the use of extremely cheap, unstable forecast
integrators, which would otherwise lead to widespread filter malfunction.Comment: 34 pages. 4 figure
Effects of statistical dependence on multiple testing under a hidden Markov model
The performance of multiple hypothesis testing is known to be affected by the
statistical dependence among random variables involved. The mechanisms
responsible for this, however, are not well understood. We study the effects of
the dependence structure of a finite state hidden Markov model (HMM) on the
likelihood ratios critical for optimal multiple testing on the hidden states.
Various convergence results are obtained for the likelihood ratios as the
observations of the HMM form an increasing long chain. Analytic expansions of
the first and second order derivatives are obtained for the case of binary
states, explicitly showing the effects of the parameters of the HMM on the
likelihood ratios.Comment: Published in at http://dx.doi.org/10.1214/10-AOS822 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Practical implementation of nonlinear time series methods: The TISEAN package
Nonlinear time series analysis is becoming a more and more reliable tool for
the study of complicated dynamics from measurements. The concept of
low-dimensional chaos has proven to be fruitful in the understanding of many
complex phenomena despite the fact that very few natural systems have actually
been found to be low dimensional deterministic in the sense of the theory. In
order to evaluate the long term usefulness of the nonlinear time series
approach as inspired by chaos theory, it will be important that the
corresponding methods become more widely accessible. This paper, while not a
proper review on nonlinear time series analysis, tries to make a contribution
to this process by describing the actual implementation of the algorithms, and
their proper usage. Most of the methods require the choice of certain
parameters for each specific time series application. We will try to give
guidance in this respect. The scope and selection of topics in this article, as
well as the implementational choices that have been made, correspond to the
contents of the software package TISEAN which is publicly available from
http://www.mpipks-dresden.mpg.de/~tisean . In fact, this paper can be seen as
an extended manual for the TISEAN programs. It fills the gap between the
technical documentation and the existing literature, providing the necessary
entry points for a more thorough study of the theoretical background.Comment: 27 pages, 21 figures, downloadable software at
http://www.mpipks-dresden.mpg.de/~tisea
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