Monday, Aug 5: 8:30 AM - 10:20 AM
5038
Contributed Papers
Oregon Convention Center
Room: CC-G132
Main Sponsor
Section on Bayesian Statistical Science
Presentations
In fMRI, as voxel sizes decrease, there is less material in them to produce a signal, leading to a decrease in the signal-to-noise ratio and contrast-to-noise ratio in each voxel. There have been many attempts to decrease the noise in an image in order to increase activation, but most lead to blurrier images. An alternative is to develop methods in spatial frequency space. Reducing noise in spatial frequency space has unique benefits. A Bayesian approach is proposed that quantifies available a priori information about spatial frequency coefficients, incorporates it with observed spatial frequency coefficients, and estimates spatial frequency coefficients values a posteriori. Inverse Fourier transform reconstructed images form marginal posterior mean estimated spatial frequency coefficients have reduced noise and increased detection power.
Keywords
Bayesian
k-space
fmri
imaging
First Author
Dan Rowe, Marquette University
Presenting Author
Dan Rowe, Marquette University
A concern when modeling ensembles of networks obtained from diverse sources is the presence of heterogeneity in the determinants of network structure; a property captured well by Dirichlet Process mixtures. Recently, work using DP mixtures of exponential family random graph models has shown that the approximate likelihood can be successfully employed for posterior inference on hidden populations, enabling broader families of such mixtures. Here, we consider hierarchical DP ERGM mixtures with both partial pooling (effects treated homogeneously across networks) and heterogeneity in included effects (allowing different effects between different mixture components). The former allows for semi-parametric estimation of given effects of interest (controlling for heterogeneity in other effects), while the latter allows for model averaging (can be used for model selection & clustering applications). The prior on the concentration parameter allows us to assign minimal prior weight to undesirable size distributions while adaptively assessing hidden population sizes. We evaluate the behavior of extended DP ERGM mixtures via simulation and display an application to heterogeneous network data.
Keywords
Networks
Exponential Family Random Graph Models
Dirichlet Process
Bayesian statistics
Hierarchical Modelling
Data Clustering
We discuss dynamic modeling of temporal paths of multiple agents through geographic networks with interest in detecting anomalous behavior of agents or subgroups of agents.The focus is sequential, monitoring incoming (noisy) time-trajectory data on huge numbers of agents on large networks in real time.Models represent geographical regions as networks of nodes as fine geographic zones.Interpretable Bayesian dynamic models are multi-scale in space, time and agents (ranging from individuals to subsets of agents defined via multiple intersecting features). Multi-scale models capture transitions over time of individual agents informed by activities at group levels. Methodology leverages decouple/recouples concepts, enabling model scalability and efficient computation.Analysis is overlaid with decision-theoretic monitoring customized to anomaly detection.Examples explore large-scale data arising from collaborative studies on real-time monitoring of human population movements in defined regions of a US city landscape.This highlights the roles and utilities of the methodology in characterizing normal dynamic patterns of trajectories at individual and group-levels, and in anomaly detection.
Keywords
anomaly detection
Bayesian dynamic models
Bayesian model monitoring
multi-scale models
network flow modeling
We propose an approach to assess stability of Gaussian directed networks with networks constructed based on data from two time points. The proposed approaches unify network construction and comparison. A penalty introduced to the calculation of conditional posterior probability mass function for network differentiation ensures convergence to the underlying truth in probability. Simulations and real data applications support the feasibility of the method and the advantage of addressing dependence in network comparisons.
Keywords
Gaussian network comparisons
Bayesian methods
Penalized conditional posterior probability
Variable selection.
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets under-utilized in determining the joint dependency structure. In this talk, we consider a Bayesian approach to model undirected graphs underlying heterogeneous multivariate observations with additional assistance from covariates. Building on product partition models, we propose a novel covariate-dependent Gaussian graphical model that allows graphs to vary with covariates so that observations whose covariates are similar share a similar undirected graph. To efficiently embed Gaussian graphical models into our proposed framework, we explore both Gaussian likelihood and pseudo-likelihood functions. Moreover, the proposed model has large prior support. We show that based on the theory of fractional likelihood, the rate of posterior contraction is minimax optimal. The efficacy of the approach is demonstrated via simulation studies and an analysis of a protein network for a breast cancer dataset assisted by mRNA gene expression as covariates.
Keywords
product partition model
Gaussian graphical model
pseudo-likelihood
G-Wishart prior
posterior contraction rate
Bayesian networks are a method of modeling conditional dependencies among variables and have a wide variety of applications. Bayesian network models place a prior distribution on the network structure, and Markov chain Monte Carlo is typically used for model fitting, which results in thousands of networks sampled from the posterior distribution. Based on these samples, we propose a method to provide a point estimate of a Bayesian network structure. First, we introduce generalized structural Hamming (GSH) loss, a function between the adjacency matrices of networks which satisfies quasi-metric properties. We also introduce a stochastic sweetening algorithm to obtain a Bayes estimate by minimizing the Monte Carlo estimate of the posterior expected GSH loss using the available samples. We provide an investigation of existing methods and our proposed methods. Our loss function and search algorithm are implemented in an R package.
Keywords
Bayesian estimation
graph estimation
loss functions
Markov chain Monte Carlo
network estimation
Object detection is a fundamental image analysis task that is relevant to many scientific disciplines. For example, astronomers detect stars and galaxies in astronomical images and biologists characterize cells and tissues in histological images. Distinguishing visually overlapping objects in images is challenging, as there is inherent ambiguity in the positions and properties of these objects. The Bayesian paradigm is well suited to this task because it provides calibrated uncertainty estimates for crowded scenes and enables scientists to incorporate prior knowledge about the imaged objects. We propose count-stratified SMC (CS-SMC), a novel Bayesian approach to object detection based on sequential Monte Carlo. Given an image, CS-SMC evaluates latent variable catalogs corresponding to various object counts and infers the posterior distribution over sets of objects. Although these sets vary in size, CS-SMC does not require transdimensional sampling, unlike existing methods for probabilistic object detection based on Markov chain Monte Carlo. We demonstrate the advantages of CS-SMC in a case study involving astronomical images of densely populated starfields.
Keywords
sequential Monte Carlo
Bayesian inference
image analysis
object detection
astronomical images
histological images