14,625 research outputs found
Multiscale time series modelling with an application to the relativistic electron intensity at the geosynchronous orbit
In this paper, a Bayesian system identification approach to multiscale time series modelling is proposed, where multiscale means that the output of the system is observed at one(coarse) resolution while the input of the system is observed at another (One) resolution.
The proposed method identifies linear models at different levels of resolution where the link between the two resolutions is realised via non-overlapping averaging process. This averaged time series at the coarse level of resolution is assumed to be a set of observations
from an implied process so that the implied process and the output of the system result in an errors-in-variables ARMAX model at the coarse level of resolution. By using a Bayesian
inference and Markov Chain Monte Carlo (MCMC) method, such a modelling framework results in different dynamical models at different levels of resolution at the same time. The
new method is also shown to have the ability to combine information across different levels of resolution. An application to the analysis of the relativistic electron intensity at the geosynchronous orbit is used to illustrate the new method
Multiscale Dictionary Learning for Estimating Conditional Distributions
Nonparametric estimation of the conditional distribution of a response given
high-dimensional features is a challenging problem. It is important to allow
not only the mean but also the variance and shape of the response density to
change flexibly with features, which are massive-dimensional. We propose a
multiscale dictionary learning model, which expresses the conditional response
density as a convex combination of dictionary densities, with the densities
used and their weights dependent on the path through a tree decomposition of
the feature space. A fast graph partitioning algorithm is applied to obtain the
tree decomposition, with Bayesian methods then used to adaptively prune and
average over different sub-trees in a soft probabilistic manner. The algorithm
scales efficiently to approximately one million features. State of the art
predictive performance is demonstrated for toy examples and two neuroscience
applications including up to a million features
Multiscale Bayesian State Space Model for Granger Causality Analysis of Brain Signal
Modelling time-varying and frequency-specific relationships between two brain
signals is becoming an essential methodological tool to answer heoretical
questions in experimental neuroscience. In this article, we propose to estimate
a frequency Granger causality statistic that may vary in time in order to
evaluate the functional connections between two brain regions during a task. We
use for that purpose an adaptive Kalman filter type of estimator of a linear
Gaussian vector autoregressive model with coefficients evolving over time. The
estimation procedure is achieved through variational Bayesian approximation and
is extended for multiple trials. This Bayesian State Space (BSS) model provides
a dynamical Granger-causality statistic that is quite natural. We propose to
extend the BSS model to include the \`{a} trous Haar decomposition. This
wavelet-based forecasting method is based on a multiscale resolution
decomposition of the signal using the redundant \`{a} trous wavelet transform
and allows us to capture short- and long-range dependencies between signals.
Equally importantly it allows us to derive the desired dynamical and
frequency-specific Granger-causality statistic. The application of these models
to intracranial local field potential data recorded during a psychological
experimental task shows the complex frequency based cross-talk between amygdala
and medial orbito-frontal cortex.
Keywords: \`{a} trous Haar wavelets; Multiple trials; Neuroscience data;
Nonstationarity; Time-frequency; Variational methods
The published version of this article is
Cekic, S., Grandjean, D., Renaud, O. (2018). Multiscale Bayesian state-space
model for Granger causality analysis of brain signal. Journal of Applied
Statistics. https://doi.org/10.1080/02664763.2018.145581
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
Multiscale Bernstein polynomials for densities
Our focus is on constructing a multiscale nonparametric prior for densities.
The Bayes density estimation literature is dominated by single scale methods,
with the exception of Polya trees, which favor overly-spiky densities even when
the truth is smooth. We propose a multiscale Bernstein polynomial family of
priors, which produce smooth realizations that do not rely on hard partitioning
of the support. At each level in an infinitely-deep binary tree, we place a
beta dictionary density; within a scale the densities are equivalent to
Bernstein polynomials. Using a stick-breaking characterization, stochastically
decreasing weights are allocated to the finer scale dictionary elements. A
slice sampler is used for posterior computation, and properties are described.
The method characterizes densities with locally-varying smoothness, and can
produce a sequence of coarse to fine density estimates. An extension for
Bayesian testing of group differences is introduced and applied to DNA
methylation array data
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