scholarly journals On the Pitman–Yor process with spike and slab base measure

Biometrika ◽  
2017 ◽  
Vol 104 (3) ◽  
pp. 681-697 ◽  
Author(s):  
A. Canale ◽  
A. Lijoi ◽  
B. Nipoti ◽  
I. Prünster
Keyword(s):  
Functional Data Analysis ◽  
Functional Data ◽  
Dirichlet Process ◽  
Prior Information ◽  
Real Data ◽  
Basal Body Temperature ◽  
Analysis Problem ◽  
Curve Estimation ◽  
Nonparametric Models ◽  
Generalized Pólya Urn

Summary For the most popular discrete nonparametric models, beyond the Dirichlet process, the prior guess at the shape of the data-generating distribution, also known as the base measure, is assumed to be diffuse. Such a specification greatly simplifies the derivation of analytical results, allowing for a straightforward implementation of Bayesian nonparametric inferential procedures. However, in several applied problems the available prior information leads naturally to the incorporation of an atom into the base measure, and then the Dirichlet process is essentially the only tractable choice for the prior. In this paper we fill this gap by considering the Pitman–Yor process with an atom in its base measure. We derive computable expressions for the distribution of the induced random partitions and for the predictive distributions. These findings allow us to devise an effective generalized Pólya urn Gibbs sampler. Applications to density estimation, clustering and curve estimation, with both simulated and real data, serve as an illustration of our results and allow comparisons with existing methodology. In particular, we tackle a functional data analysis problem concerning basal body temperature curves.

scholarly journals Detection of Anomalies in Water Networks by Functional Data Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Laura Millán-Roures ◽  
Irene Epifanio ◽  
Vicente Martínez
Keyword(s):  
Data Analysis ◽  
Outlier Detection ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Real Data ◽  
Water Networks ◽  
Archetypal Analysis ◽  
Detection Techniques ◽  
Second Stage ◽  
Two Phases

A functional data analysis (FDA) based methodology for detecting anomalous flows in urban water networks is introduced. Primary hydraulic variables are recorded in real-time by telecontrol systems, so they are functional data (FD). In the first stage, the data are validated (false data are detected) and reconstructed, since there could be not only false data, but also missing and noisy data. FDA tools are used such as tolerance bands for FD and smoothing for dense and sparse FD. In the second stage, functional outlier detection tools are used in two phases. In Phase I, the data are cleared of anomalies to ensure that data are representative of the in-control system. The objective of Phase II is system monitoring. A new functional outlier detection method is also proposed based on archetypal analysis. The methodology is applied and illustrated with real data. A simulated study is also carried out to assess the performance of the outlier detection techniques, including our proposal. The results are very promising.

scholarly journals Resampling methods for functional data

2018 ◽  
Author(s):  
Timothy McMurry ◽  
Dimitris Politis
Keyword(s):  
Data Analysis ◽  
Density Estimation ◽  
Nonparametric Regression ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Real Data ◽  
Confidence Bands ◽  
Resampling Methods ◽  
Current State ◽  
Inference Techniques

This article examines the current state of methodological and practical developments for resampling inference techniques in functional data analysis, paying special attention to situations where either the data and/or the parameters being estimated take values in a space of functions. It first provides the basic background and notation before discussing bootstrap results from nonparametric smoothing, taking into account confidence bands in density estimation as well as confidence bands in nonparametric regression and autoregression. It then considers the major results in subsampling and what is known about bootstraps, along with a few recent real-data applications of bootstrapping with functional data. Finally, it highlights possible directions for further research and exploration.

Identifying and Classifying Aberrant Response Patterns Through Functional Data Analysis

2020 ◽  
Vol 45 (6) ◽  
pp. 719-749
Author(s):  
Eduardo Doval ◽  
Pedro Delicado
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Simulated Data ◽  
Real Data ◽  
Response Patterns ◽  
Fit Indices ◽  
Person Fit ◽  
Data Set ◽  
Aberrant Response Patterns

We propose new methods for identifying and classifying aberrant response patterns (ARPs) by means of functional data analysis. These methods take the person response function (PRF) of an individual and compare it with the pattern that would correspond to a generic individual of the same ability according to the item-person response surface. ARPs correspond to atypical difference functions. The ARP classification is done with functional data clustering applied to the PRFs identified as ARP. We apply these methods to two sets of simulated data (the first is used to illustrate the ARP identification methods and the second demonstrates classification of the response patterns flagged as ARP) and a real data set (a Grade 12 science assessment test, SAT, with 32 items answered by 600 examinees). For comparative purposes, ARPs are also identified with three nonparametric person-fit indices (Ht, Modified Caution Index, and ZU3). Our results indicate that the ARP detection ability of one of our proposed methods is comparable to that of person-fit indices. Moreover, the proposed classification methods enable ARP associated with either spuriously low or spuriously high scores to be distinguished.

Model reduction in geostatistical seismic inversion with functional data analysis

Geophysics ◽  
2021 ◽  
pp. 1-48
Author(s):  
Leonardo Azevedo
Keyword(s):  
Data Analysis ◽  
Model Reduction ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Computational Cost ◽  
Real Data ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Inversion Methods ◽  
Starting Point

In subsurface modelling and characterization, predicting the spatial distribution of subsurface elastic properties is commonly achieved by seismic inversion. Stochastic seismic inversion methods, such as iterative geostatistical seismic inversion, are widely applied to this end. Global iterative geostatistical seismic inversion methods are computationally expensive as they require, at a given iteration, the stochastic sequential simulation of the entire inversion grid at once multiple times. Functional data analysis is a well-established statistical method suited to model long-term and noisy temporal series. This method allows to summarize spatiotemporal series in a set of analytical functions with a low-dimension representation. Functional data analysis has been recently extended to problems related to geosciences, but its application to geophysics is still limited. We propose the use functional data analysis as a model reduction technique during the model perturbation step in global iterative geostatistical seismic inversion. Functional data analysis is used to collapse the vertical dimension of the inversion grid. We illustrate the proposed hybrid inversion method with its application to three-dimensional synthetic and real data sets. The results show the ability of the proposed inversion methodology to predict smooth inverted subsurface models that match the observed data at a similar convergence as obtained by a global iterative geostatistical seismic inversion, but with a considerable decrease in the computational cost. While the resolution of the inverted models might not be enough for a detailed subsurface characterization, the inverted models can be used as starting point of global iterative geostatistical seismic inversion to speed-up the inversion or to test alternative geological scenarios by changing the inversion parameterization and obtaining inverted models in a relatively short time.

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

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