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

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

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

The History of Jewish Cemeteries In Cleveland and Cuyahoga County

This book documents the history of the sixteen Jewish cemeteries in Cleveland and Cuyahoga County, using primary sources such as recorded deed transfers, records of incorporation, and plat maps to trace ownership from the time of acquisition to today. It facilitates an understanding of the correlation between each cemetery and its governance with a synagogue or benevolent organization.https://engagedscholarship.csuohio.edu/clevmembks/1068/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