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Applied Statistics

Mark Fiecas

Selected Works

Articles 1 - 6 of 6

Full-Text Articles in Physical Sciences and Mathematics

Modeling The Evolution Of Dynamic Brain Processes During An Associative Learning Experiment, Mark Fiecas, Hernando Ombao Dec 2015

Modeling The Evolution Of Dynamic Brain Processes During An Associative Learning Experiment, Mark Fiecas, Hernando Ombao

Mark Fiecas

Our goal is to use local field potentials (LFPs) to rigorously study changes in neuronal activity in the hippocampus and the nucleus accumbens over the course of an associative learning experiment. We show that the spectral properties of the LFPs changed during the experiment. While many statistical models take into account nonstationarity within a single trial of the experiment, the evolution of brain dynamics across trials is often ignored. In this paper, we developed a novel time series model that captures both sources of nonstationarity. Under the proposed model we rigorously define the spectral density matrix so that it evolves …

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Spectral Density Shrinkage For High-Dimensional Time Series, Mark Fiecas, Rainer Von Sachs Dec 2013

Spectral Density Shrinkage For High-Dimensional Time Series, Mark Fiecas, Rainer Von Sachs

Mark Fiecas

Time series data obtained from neurophysiological signals is often high-dimensional and the length of the time series is often short relative to the number of dimensions. Thus, it is difficult or sometimes impossible to compute statistics that are based on the spectral density matrix because these matrices are numerically unstable. In this work, we discuss the importance of regularization for spectral analysis of high-dimensional time series and propose shrinkage estimation for estimating high-dimensional spectral density matrices. The shrinkage estimator is derived from a penalized log-likelihood, and the optimal penalty parameter has a closed-form solution, which can be estimated using the …

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Hierarchical Vector Auto-Regressive Models And Their Applications To Multi-Subject Effective Connectivity, Cristina Gorrostieta, Mark Fiecas, Hernando Ombao, Erin Burke, Steven Cramer Oct 2013

Hierarchical Vector Auto-Regressive Models And Their Applications To Multi-Subject Effective Connectivity, Cristina Gorrostieta, Mark Fiecas, Hernando Ombao, Erin Burke, Steven Cramer

Mark Fiecas

Vector auto-regressive (VAR) models typically form the basis for constructing directed graphical models for investigating connectivity in a brain network with brain regions of interest (ROIs) as nodes. There are limitations in the standard VAR models. The number of parameters in the VAR model increases quadratically with the number of ROIs and linearly with the order of the model and thus due to the large number of parameters, the model could pose serious estimation problems. Moreover, when applied to imaging data, the standard VAR model does not account for variability in the connectivity structure across all subjects. In this paper, …

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A Case-Control Study Of Physical Activity Patterns And Risk Of Non-Fatal Myocardial Infarction, Jian Gong, Hannia Campos, Mark Fiecas, Stephen Mcgarvey, Robert Goldberg, Caroline Richardson, Ana Baylin Dec 2012

A Case-Control Study Of Physical Activity Patterns And Risk Of Non-Fatal Myocardial Infarction, Jian Gong, Hannia Campos, Mark Fiecas, Stephen Mcgarvey, Robert Goldberg, Caroline Richardson, Ana Baylin

Mark Fiecas

Background The interactive effects of different types of physical activity on cardiovascular disease (CVD) risk have not been fully considered in previous studies. We aimed to identify physical activity patterns that take into account combinations of physical activities and examine the association between derived physical activity patterns and risk of acute myocardial infarction (AMI). Methods We examined the relationship between physical activity patterns, identified by principal component analysis (PCA), and AMI risk in a case-control study of myocardial infarction in Costa Rica (N=4172), 1994-2004. The component scores derived from PCA and total METS were used in natural cubic spline models …

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Quantifying Temporal Correlations: A Test-Retest Evaluation Of Functional Connectivity In Resting-State Fmri, Mark Fiecas, Hernando Ombao, Dan Van Lunen, Richard Baumgartner, Alexandre Coimbra, Dai Feng Dec 2012

Quantifying Temporal Correlations: A Test-Retest Evaluation Of Functional Connectivity In Resting-State Fmri, Mark Fiecas, Hernando Ombao, Dan Van Lunen, Richard Baumgartner, Alexandre Coimbra, Dai Feng

Mark Fiecas

There have been many interpretations of functional connectivity and proposed measures of temporal correlations between BOLD signals across different brain areas. These interpretations yield from many studies on functional connectivity using resting-state fMRI data that have emerged in recent years. However, not all of these studies used the same metrics for quantifying the temporal correlations between brain regions. In this paper, we use a public-domain test–retest resting-state fMRI data set to perform a systematic investigation of the stability of the metrics that are often used in resting-state functional connectivity (FC) studies. The fMRI data set was collected across three different …

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The Generalized Shrinkage Estimator For The Analysis Of Functional Connectivity Of Brain Signals, Mark Fiecas, Hernando Ombao Dec 2010

The Generalized Shrinkage Estimator For The Analysis Of Functional Connectivity Of Brain Signals, Mark Fiecas, Hernando Ombao

Mark Fiecas

We develop a new statistical method for estimating functional connectivity between neurophysiological signals represented by a multivariate time series. We use partial coherence as the measure of functional connectivity. Partial coherence identifies the frequency bands that drive the direct linear association between any pair of channels. To estimate partial coherence, one would first need an estimate of the spectral density matrix of the multivariate time series. Parametric estimators of the spectral density matrix provide good frequency resolution but could be sensitive when the parametric model is misspecified. Smoothing-based nonparametric estimators are robust to model misspecification and are consistent but may …

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