8,198 research outputs found
A new framework for extracting coarse-grained models from time series with multiscale structure
In many applications it is desirable to infer coarse-grained models from
observational data. The observed process often corresponds only to a few
selected degrees of freedom of a high-dimensional dynamical system with
multiple time scales. In this work we consider the inference problem of
identifying an appropriate coarse-grained model from a single time series of a
multiscale system. It is known that estimators such as the maximum likelihood
estimator or the quadratic variation of the path estimator can be strongly
biased in this setting. Here we present a novel parametric inference
methodology for problems with linear parameter dependency that does not suffer
from this drawback. Furthermore, we demonstrate through a wide spectrum of
examples that our methodology can be used to derive appropriate coarse-grained
models from time series of partial observations of a multiscale system in an
effective and systematic fashion
Detecting single-trial EEG evoked potential using a wavelet domain linear mixed model: application to error potentials classification
Objective. The main goal of this work is to develop a model for multi-sensor
signals such as MEG or EEG signals, that accounts for the inter-trial
variability, suitable for corresponding binary classification problems. An
important constraint is that the model be simple enough to handle small size
and unbalanced datasets, as often encountered in BCI type experiments.
Approach. The method involves linear mixed effects statistical model, wavelet
transform and spatial filtering, and aims at the characterization of localized
discriminant features in multi-sensor signals. After discrete wavelet transform
and spatial filtering, a projection onto the relevant wavelet and spatial
channels subspaces is used for dimension reduction. The projected signals are
then decomposed as the sum of a signal of interest (i.e. discriminant) and
background noise, using a very simple Gaussian linear mixed model. Main
results. Thanks to the simplicity of the model, the corresponding parameter
estimation problem is simplified. Robust estimates of class-covariance matrices
are obtained from small sample sizes and an effective Bayes plug-in classifier
is derived. The approach is applied to the detection of error potentials in
multichannel EEG data, in a very unbalanced situation (detection of rare
events). Classification results prove the relevance of the proposed approach in
such a context. Significance. The combination of linear mixed model, wavelet
transform and spatial filtering for EEG classification is, to the best of our
knowledge, an original approach, which is proven to be effective. This paper
improves on earlier results on similar problems, and the three main ingredients
all play an important role
Fully-Automatic Multiresolution Idealization for Filtered Ion Channel Recordings: Flickering Event Detection
We propose a new model-free segmentation method, JULES, which combines recent
statistical multiresolution techniques with local deconvolution for
idealization of ion channel recordings. The multiresolution criterion takes
into account scales down to the sampling rate enabling the detection of
flickering events, i.e., events on small temporal scales, even below the filter
frequency. For such small scales the deconvolution step allows for a precise
determination of dwell times and, in particular, of amplitude levels, a task
which is not possible with common thresholding methods. This is confirmed
theoretically and in a comprehensive simulation study. In addition, JULES can
be applied as a preprocessing method for a refined hidden Markov analysis. Our
new methodolodgy allows us to show that gramicidin A flickering events have the
same amplitude as the slow gating events. JULES is available as an R function
jules in the package clampSeg
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