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Submitted by pscully on Mon, 01/12/2009 - 17:46.
01/15/2009 - 16:10
01/15/2009 - 17:30
STA/BST 290: Xuanlong Nguyen
Nonparametric and distributed decision-making models with applications to functional and spatial data analysis
THURSDAY, January 15th, 2009 at 4.10pm, MSB 1147 (Colloquium Room)
Refreshments: 3.30pm, MSB 4110 (Statistics Lounge)
(Dept. Statistical Science,
Title: Nonparametric and distributed decision-making models with applications to functional and spatial data analysis
Abstract: I will present two statistical methods for modeling and decision-making with functional and spatial data. The first method is concerned with a class of nonparametric labeling processes for clustering and partitioning curves and surfaces. The labeling process provides a flexible prior for a hierarchical latent variable model, which posits that a collection of curves can be described in terms of a number of typical canonical behaviors, whereas the canonical curve allocation is driven by the latent labeling process.
The spatial dependence of labels
is driven by the use of a latent Gaussian process, while label sharing across
curve collection is enabled by the use of a Dirichlet process. Model fitting is
challenging, and a variational Bayesian inference method is proposed to obtain a
surrogate "Gibbs posterior" update embedded within an MCMC algorithm. In the
variational methodology, posterior inference can be implicitly viewed as
optimization over the space of posterior distributions. This view allows us to
modify the underlying optimization (e.g., the loss function and/or the
The second method addresses the issue of efficient statistical inference that arises in a distributed data collection and processing system. This problem is motivated by an application of distributed detection in a wireless sensor network. In this application the goal is to infer about the local decision rules at individual sensors, as well as the global decision at the base station, so as to minimize a predictive error criterion (e.g., 0-1 loss). I will present a theory of equivalent surrogate loss functions using a link between loss functions and information-theoretic divergence functionals. This theory allows us to place a range of well-known but somewhat heuristic methods in the signal processing literature on a firm statistical decision-theoretic framework. Moreover, it allows us to derive an efficient joint estimation algorithm for distributed detection by considering convex surrogate loss functions that are equivalent to the 0-1 loss.