Skip to main content
Duke University Libraries
DukeSpace Scholarship by Duke Authors
  • Login
  • Ask
  • Menu
  • Login
  • Ask a Librarian
  • Search & Find
  • Using the Library
  • Research Support
  • Course Support
  • Libraries
  • About
View Item 
  •   DukeSpace
  • Theses and Dissertations
  • Duke Dissertations
  • View Item
  •   DukeSpace
  • Theses and Dissertations
  • Duke Dissertations
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Using Data Augmentation and Stochastic Differential Equations in Spatio Temporal Modeling

Thumbnail
View / Download
2.3 Mb
Date
2008-12-12
Author
Puggioni, Gavino
Advisor
Gelfand, Alan
Repository Usage Stats
442
views
600
downloads
Abstract

One of the biggest challenges in spatiotemporal modeling is indeed how to manage the large amount of missing information. Data augmentation techniques are frequently used to infer about missing values, unobserved or latent processes, approximation of continuous time processes that are discretely observed.

The literature treating the inference when modeling using stochastic differential equations (SDE) that are partially observed has been growing in recent years. Many attempts have been made to tackle this problem, from very different perspectives. The goal of this thesis is not a comparison of the different methods. The focus is, instead, on Bayesian inference for the SDE in a spatial context, using a data augmentation approach. While other methods can be less computationally intensive or more accurate in some cases, the main advantage of the Bayesian approach based on model augmentation is the general scope of applicability. In Chapter 2 we propose some methods to model space time data as noisy realizations of an underlying system of nonlinear SDEs. The parameters of this system are realizations of spatially correlated Gaussian processes. Models that are formulated in this fashion are complex and present several challenges in their estimation. Standard methods degenerate when the the level of refinement in the discretization gets larger. The innovation algorithm overcomes such problems. We present an extension of the innvoation scheme for the case of high-dimensional parameter spaces. Our algorithm, although presented in spatial SDE examples, can be actually applied in any general multivariate SDE setting.

In Chapter 3 we discuss additional insights regarding SDE with a spatial interpretation: spatial dependence is enforced through the driving Brownian motion.

In Chapter 4 we discuss some possible refinement on the SDE parameter estimation. Such refinements, that involve second order SDE approximations, have actually a more general scope than spatiotemporal modeling and can be applied in a variety of settings.

In the last chapter we propose some methodology ideas for fitting space-time models to data that are collected in a wireless sensor network when suppression and failure in transmission are considered. In this case also we make use of data augmentation techniques but in conjunction with linear constraints on the missing values.

Type
Dissertation
Department
Statistics and Decision Sciences
Subject
Statistics
Permalink
https://hdl.handle.net/10161/905
Citation
Puggioni, Gavino (2008). Using Data Augmentation and Stochastic Differential Equations in Spatio Temporal Modeling. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/905.
Collections
  • Duke Dissertations
More Info
Show full item record
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.

Rights for Collection: Duke Dissertations


Works are deposited here by their authors, and represent their research and opinions, not that of Duke University. Some materials and descriptions may include offensive content. More info

Make Your Work Available Here

How to Deposit

Browse

All of DukeSpaceCommunities & CollectionsAuthorsTitlesTypesBy Issue DateDepartmentsAffiliations of Duke Author(s)SubjectsBy Submit DateThis CollectionAuthorsTitlesTypesBy Issue DateDepartmentsAffiliations of Duke Author(s)SubjectsBy Submit Date

My Account

LoginRegister

Statistics

View Usage Statistics
Duke University Libraries

Contact Us

411 Chapel Drive
Durham, NC 27708
(919) 660-5870
Perkins Library Service Desk

Digital Repositories at Duke

  • Report a problem with the repositories
  • About digital repositories at Duke
  • Accessibility Policy
  • Deaccession and DMCA Takedown Policy

TwitterFacebookYouTubeFlickrInstagramBlogs

Sign Up for Our Newsletter
  • Re-use & Attribution / Privacy
  • Harmful Language Statement
  • Support the Libraries
Duke University