3,039 research outputs found
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Haymarket to the Heights: The Movement of Cleveland\u27s Orthodox Synagogues From Their Initial Meeting Places to the Heights
This document traces the movement, growth and demise of the small neighborhood synagogues, or shuls, established by newly-arrived Eastern European Jews in the Haymarket area as they migrated to the eastern suburbs.https://engagedscholarship.csuohio.edu/clevmembks/1022/thumbnail.jp
Beechwood, The Book
From the forward by Darrell A.Young: The city fathers have been called visionaries. The city has been studied by architects, planners, engineers and the like from all over the country. What is it about Beachwood that has attracted so much attention?
To be certain, there is something magical that has taken place over the last 80 years in Beachwood and Jeffrey Morris has finally documented the historical blueprint from which we can study and learn. This book is the first opportunity to understand our heritage and to delve into the intellect that forged this wonderful community.https://engagedscholarship.csuohio.edu/clevmembks/1009/thumbnail.jp
Haymarket to the Heights: The Movement of Cleveland\u27s Orthodox Synagogues From Their Initial Meeting Places to the Heights
This document traces the movement, growth and demise of the small neighborhood synagogues, or shuls, established by newly-arrived Eastern European Jews in the Haymarket area as they migrated to the eastern suburbs.https://engagedscholarship.csuohio.edu/clevmembks/1022/thumbnail.jp
Automated analysis of quantitative image data using isomorphic functional mixed models, with application to proteomics data
Image data are increasingly encountered and are of growing importance in many
areas of science. Much of these data are quantitative image data, which are
characterized by intensities that represent some measurement of interest in the
scanned images. The data typically consist of multiple images on the same
domain and the goal of the research is to combine the quantitative information
across images to make inference about populations or interventions. In this
paper we present a unified analysis framework for the analysis of quantitative
image data using a Bayesian functional mixed model approach. This framework is
flexible enough to handle complex, irregular images with many local features,
and can model the simultaneous effects of multiple factors on the image
intensities and account for the correlation between images induced by the
design. We introduce a general isomorphic modeling approach to fitting the
functional mixed model, of which the wavelet-based functional mixed model is
one special case. With suitable modeling choices, this approach leads to
efficient calculations and can result in flexible modeling and adaptive
smoothing of the salient features in the data. The proposed method has the
following advantages: it can be run automatically, it produces inferential
plots indicating which regions of the image are associated with each factor, it
simultaneously considers the practical and statistical significance of
findings, and it controls the false discovery rate.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS407 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Novel Bayesian method for simultaneous detection of activation signatures and background connectivity for task fMRI data
In this paper, we introduce a new Bayesian approach for analyzing task fMRI
data that simultaneously detects activation signatures and background
connectivity. Our modeling involves a new hybrid tensor spatial-temporal basis
strategy that enables scalable computing yet captures nearby and distant
intervoxel correlation and long-memory temporal correlation. The spatial basis
involves a composite hybrid transform with two levels: the first accounts for
within-ROI correlation, and second between-ROI distant correlation. We
demonstrate in simulations how our basis space regression modeling strategy
increases sensitivity for identifying activation signatures, partly driven by
the induced background connectivity that itself can be summarized to reveal
biological insights. This strategy leads to computationally scalable fully
Bayesian inference at the voxel or ROI level that adjusts for multiple testing.
We apply this model to Human Connectome Project data to reveal insights into
brain activation patterns and background connectivity related to working memory
tasks
Ordinal Probit Functional Regression Models with Application to Computer-Use Behavior in Rhesus Monkeys
Research in functional regression has made great strides in expanding to
non-Gaussian functional outcomes, however the exploration of ordinal functional
outcomes remains limited. Motivated by a study of computer-use behavior in
rhesus macaques (\emph{Macaca mulatta}), we introduce the Ordinal Probit
Functional Regression Model or OPFRM to perform ordinal function-on-scalar
regression. The OPFRM is flexibly formulated to allow for the choice of
different basis functions including penalized B-splines, wavelets, and
O'Sullivan splines. We demonstrate the operating characteristics of the model
in simulation using a variety of underlying covariance patterns showing the
model performs reasonably well in estimation under multiple basis functions. We
also present and compare two approaches for conducting posterior inference
showing that joint credible intervals tend to out perform point-wise credible.
Finally, in application, we determine demographic factors associated with the
monkeys' computer use over the course of a year and provide a brief analysis of
the findings
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