Workshop: Time Series Analysis in Neuroscience
April 14th, 2009, 12-5pm
Columbia University

BACKGROUND

This workshop is part of the Department of Statistics special focus series on Statistical Methods in Neuroscience.

The goal of this workshop is to highlight the role that time series analysis plays in neuroscience research. Talks will deal specifically with time series problems that arise in fMRI, EEG and neuro-spiking research. The workshop will take place on April 14, between 12-5pm in Alfred Lerner Hall Room 555 on the Morningside Campus of Columbia University.

Schedule

Admission is free, however we ask that you register in advance. Please register by noon on Friday, April 10.

Registration closed

INVITED SPEAKERS

Srikesh Arunajadai, Department of Biostatistics, Columbia University Abstract

Uri Eden, Department of Mathematics and Statistics, Boston University Abstract

Ian McKeague, Department of Biostatistics, Columbia University Abstract

Kamiar Rahnama Rad, Department of Statistics, Columbia University Abstract

Lucy Robinson, Department of Statistics, Columbia University

Victor Solo, School of Electrical Engineering and Telecommunications, The University of New South Wales Abstract

David Stoffer, Department of Statistics, University of Pittsburgh and Statistics Program, Division of Mathematical Sciences, Directorate for Mathematical and Physical Sciences, NSF Abstract

SPONSORED BY

The Department of Statistics at Columbia University.

ORGANIZERS

Richard Davis, Martin Lindquist and Liam Paninski.

ABSTRACTS


Quadratic System Identification: A Statistical Framework for the Paired-Pulse Paradigm
Srikesh G. Arunajadai
Department of Biostatistics
Columbia University

System Identication refers to the problem of identifying a model or de- scription of a system based on a stretch of input and the corresponding output from the system. The paired-pulse paradigm or the conditioning test pulse paradigm is often used in neurophysiology experiments. In this work we provide a statistical framework for the conditioning test pulse paradigm which also serves as a system identication tool for quadratic or second order Volterra systems. A nonparametric spectral domain based methodology is proposed for the quadratic system identication. It is shown that by carrying out the analysis in the spectral domain one needs to perform only a single set of double pulse experiments as opposed to multiple sets of experiments in the time domain. Simulation studies are performed to assess the performance of the methodology and to study the conditions under which the methods are expected to perform well. The methodology is also extended to estimate the latency of the system. The method is applied to study voluntary movements of the wrist using Electroencephalogram (EEG) signals from the primary motor cortex.
This is joint work with Prof. David Brillinger (Statistics, University of California, Berkeley), Prof. Jay Rosenberg (Neuroscience, University of Glas- gow) and Prof. Bernie Conway (Bioengineering, University of Strathclyde, Glasgow).

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Exact and approximate point process filters applied to spike train decoding
Uri Eden
Department of Mathematics and Statistics
Boston University

Although it is well known that neurons receive, process and transmit information via sequences of sudden stereotyped electrical events, called action potentials or spikes, most analyses of neural data ignore the highly localized nature of these events. In this talk, we discuss a point process modeling framework for neural systems that allows us to perform inference, assess goodness-of-fit, and estimate a state variable from neural spiking observations.
We develop a state space estimation and inference framework by constructing state models that describe the stochastic evolution of the signals to estimate, and conditional intensity models that define the probability distribution of observing a particular sequence of spike times for a neuron or ensemble. We can then develop discrete or continuous time expressions for the conditional density of the state given the observations using a recursive Bayesian framework combined with the Chapman-Kolmogorov equation or the forward Kolmogorov equation respectively. This allows us to derive a toolbox of estimation algorithms and adaptive filters to address questions of static and dynamic encoding and decoding. In our analysis of these filtering algorithms, we draw analogies to well-studied linear estimation algorithms for continuous valued processes, such as the Kalman filter and its discrete and continuous time extensions. We will discuss the application of these modeling and estimation methods to neural data from a variety of systems including spatially specific firing activity in the rat hippocampus and movement related activity in primate motor cortex.

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Logistic Regression with Brownian-like Predictors
Ian W. McKeague
Department of Biostatistics
Columbia University

This article introduces a new type of logistic regression model involving functional predictors of binary responses, along with an extension of the ap- proach to generalized linear models. The predictors are trajectories that have certain sample-path properties in common with Brownian motion. Time points are treated as parameters of interest, and condence intervals developed under prospective and retrospective (case-control) sampling designs. In an applica- tion to fMRI data, signals from individual subjects are used to nd the portion of the time course that is most predictive of the response. This allows the identication of sensitive time points, specic to a brain region and associated with a certain task, that can be used to distinguish between responses. A second application concerns gene expression data in a case-control study involving breast cancer, where the aim is to identify genetic loci along a chromosome that best discriminate between cases and controls.

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Efficient, adaptive estimation of two-dimensional firing rate surfaces via Gaussian process methods
Kamiar Rahnama Rad
Department of Statistics
Columbia University

Estimating spatiotemporal point process rate maps arises in a number of contexts. Spatial examples include the estimation of 'place fields' in the hippocampus, 'grid fields' in entorhinal cortex, and position- or velocity-fields in motor cortex. Spatiotemporal examples include the estimation of tuning curves that change as a function of time; purely temporal examples include the tracking of firing rates that change as a function of both intra- and inter-trial times during a behavioral task. We discuss a Bayesian nonparametric approach to the two-dimensional point process rate estimation problem which is applicable in both the spatial and spatiotemporal settings and show that this approach is in a sense a generalization of the temporal state-space methods for point process smoothing. In the end we will describe several applications of our method to both simulated and real spike train data.

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Geometric Optimization, Sampled Granger Causality and Point Processes with Coincidences; with Applications.
Professor Victor Solo
School of Electrical Engineering
University of New South Wales, Sydney, AUSTRALIA

We discuss briefly three cases in which neuro-science application has thrown up new problems in statistical signal processing.

Firstly we develop a sparse PCA based on penalized optimization on a Stiefel manifold using geodesic steepest descent. We sketch an application to fMRI.

Next we discuss problems with Granger casuality when the data is sampled more slowly than the signals of interest. Application to neuro-imaging is sketched.

Finally in the neural coding area there is much interest in analyzing multivariate point processes with coincidences. But the standard Jacod likelihood explicitly excludes coincidences. We sketch briefly the construction of a new likelihood for multivariate point processes that allows coincidences.

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Grant opportunities at NSF with a view towards neuroscience.
Professor David Stoffer
Department of Statistics
University of Pittsburgh

Statistics Program,
Division of Mathematical Sciences,
Directorate for Mathematical and Physical Sciences,
National Science Foundation

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