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Physical Sciences and Mathematics Commons

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Statistics and Probability

Theses/Dissertations

2019

Functional Data Analysis

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Full-Text Articles in Physical Sciences and Mathematics

A Statistical Model For The Influence Of Temperature On Bike Demand In Bike-Sharing Systems, Tobias Tietze May 2019

A Statistical Model For The Influence Of Temperature On Bike Demand In Bike-Sharing Systems, Tobias Tietze

Theses and Dissertations

Efficient fleet management is essential for bike-sharing systems. Thus, it is important to understand the impact of environmental factors on bike demand. This thesis proposes a method to analyze the influence of temperature on bike demand. Hourly temperature data are approximated by smoothed curves and modeled by functional principal components. Bike check-out times, which can be seen as realizations of a doubly stochastic process, are modeled using multiplicative component models on the underlying intensity functions. The respective component scores are then related via a multivariate regression model. An analysis of data from the Divvy system of the City of Chicago …


A Statistical Model For The Influence Of Temperature On Bike Demand In Bike-Sharing Systems, Tobias Tietze May 2019

A Statistical Model For The Influence Of Temperature On Bike Demand In Bike-Sharing Systems, Tobias Tietze

Theses and Dissertations

Efficient fleet management is essential for bike-sharing systems. Thus, it is important to understand the impact of environmental factors on bike demand. This thesis proposes a method to analyze the influence of temperature on bike demand. Hourly temperature data are approximated by smoothed curves and modeled by functional principal components. Bike check-out times, which can be seen as realizations of a doubly stochastic process, are modeled using multiplicative component models on the underlying intensity functions. The respective component scores are then related via a multivariate regression model. An analysis of data from the Divvy system of the City of Chicago …


Applications Of Bayesian Functional Data Analysis, Hao Shen Jan 2019

Applications Of Bayesian Functional Data Analysis, Hao Shen

Graduate Research Theses & Dissertations

Functional Data Analysis (FDA) is a set of statistical methods that can deal with the data which represent curves or functions. In this dissertation, we consider two extensions of FDA to two types of data, circadian data and multidimensional data. The first part of the dissertation is concerned with the analysis of circadian data. We estimate circadian functions by using Bayesian smoothing splines under the generalized linear model, and extract two measures from each estimated function, magnitude and roughness. Based on extracted measures, we cluster individual functions into normal group and abnormal group by utilizing a density based clustering method. …