Tuesday, Aug 5: 10:30 AM - 12:20 PM
Contributed Posters
Music City Center
Main Sponsor
Section on Bayesian Statistical Science
Presentations
This work seeks to investigate the impact of aging on functional connectivity across different cognitive control scenarios, particularly emphasizing the identification of brain regions significantly associated with early aging. By conceptualizing functional connectivity within each cognitive control scenario as a graph, with brain regions as nodes, the statistical challenge revolves around devising a regression framework to predict a binary scalar outcome (aging or normal) using multiple graph predictors. To address this challenge, we propose the Bayesian Multiplex Graph Classifier (BMGC). Accounting for multiplex graph topology, our method models edge coefficients at each graph layer using bilinear interactions between the latent effects associated with the two nodes connected by the edge. This approach also employs a variable selection framework on node-specific latent effects from all graph layers to identify influential nodes linked to observed outcomes. Crucially, the proposed framework is computationally efficient and quantifies the uncertainty in node identification, coefficient estimation, and binary outcome prediction.
Keywords
Bayesian statistics
Multiplex graph classification
Variable selection
Functional brain connectivity
One common type of outcome in Language Sample Analysis (LSA) is the sum of ordinal variables, which can be difficult to model. Classical approaches often assume outcomes are independent with additional distributional assumptions. Common choices include linear regression, which assumes outcomes are continuous, and logistic regression, which assumes outcomes follow a binomial distribution. However, linear regression assumes equal intervals between outcome categories, while logistic regression ignores the dependence among ordinal outcomes. Both models may fail to reflect the inherent ordering and differences in the data. Therefore, we proposed a variation of a cumulative ordinal model. Extra flexibility was introduced by allowing the probit link function to have a covariate-specific standard deviation. Additionally, we adopted a Bayesian and hierarchical framework that facilitates parameter estimation and enables direct probabilistic inference about parameters of interest. The proposed model improved fit over logistic and linear regressions on a LSA dataset collected from a study to understand how cognitive and language challenges interfere with expository abilities.
Keywords
Bayesian
Ordinal Regression
Scale Data
We present a Bayesian mixture model to cluster longitudinal pain score trajectories of breast cancer patients. Pain scores are integer-valued scores, ranging on a scale from 0 to 10, and are routinely reported at medical visits by patients throughout the course of their treatment. We focus on modeling and clustering patients' pain score trajectories from their initial cancer diagnosis throughout their treatment to better understand distinct "risk profiles" over time with the hope of tailored pain treatment interventions. We build a mixture model using Gaussian process regressions of pain scores on times, where each cluster likelihood is parameterized by latent, continuous-time pain trajectories and ordered cut points. We study model sensitivity to the choice of the number of mixtures and stability of the identified clusters through simulation studies and posterior predictive checks. We then fit the model to Duke breast cancer patient data and discuss clinical insights gained from cluster-associated patient demographics.
Keywords
Mixture model
Trajectory clustering
Bayesian modeling
Pain scores data
Clinical statistics
The skew normal distribution is a continuous probability distribution that generalizes the normal distribution to allow for non-zero skewness. In this poster presentation, we want to estimate parameters of the skew normal distribution by Bayesian technique and compare the results to the one from maximum likelihood estimation.
Keywords
Skew Normal Distribution
Bayesian Estimation
Maximum Likelihood Estimation
We introduce the Bayesian Varying Coefficient Multiple Index Model (BVCMIM), a novel statistical approach designed to estimate the longitudinal effects of environmental chemical exposure mixtures on human health outcomes. Traditional methods in environmental health often focus on single chemical exposures or rely on linear models that may not capture the complex, non-linear, and non-additive relationships inherent in chemical mixtures. BVCMIM overcomes these limitations by allowing for the estimation of non-linear relationships between exposure indices and health outcomes, while also accounting for interactions among different chemical exposures over time. The model incorporates the use of horseshoe priors for sparsity, ensuring that only the most relevant exposures are included in the analysis, and applies Hamiltonian Monte Carlo for uncertainty quantification. Through a series of simulations, we demonstrate that BVCMIM provides robust and interpretable estimates of both baseline and longitudinal health effects, even in scenarios with intricate chemical interactions.
Keywords
Bayesian Inference
Longitudinal Data Analysis
Chemical Exposure Mixture Analysis
Machine Learning
Co-Author
Roman Jandarov, University of Cincinnati
First Author
Wei Jia, University of Cincinnati
Presenting Author
Wei Jia, University of Cincinnati
Scale mixtures of normal distributions are a popular family of hierarchical Bayesian models that compromise interpretability, flexibility, and tractability. Recent work has demonstrated that generalized gamma mixtures of normals admit efficient algorithms that allow inference, uncertainty quantification, and hyper-parameter tuning in large, sparse, ill-determined inverse problems. We demonstrate parameter choices that produce popular prior families (Gaussian, Laplace, Student-t), and relate the distinguishability of priors to level sets of low-order moments in the parameter space using the KL and KS distances for power and significance respectively. We test the empirical validity of the hierarchical priors in a series of large imaging data sets. As case studies, we consider benchmark remote sensing, MRI, and image segmentation data sets. We report plausible ranges of parameters under standard representations (Fourier, wavelet, etc.). We find that, relative to the data sets tested, previous computational work has focused on an overly narrow subset of the space of available priors.
Keywords
Bayesian hierarchical models
Sparse inference
Image data
Scale mixture models
Compressed sensing
Model validation
Co-Author(s)
Yash Dave, University of California, Berkeley
Brandon Marks, University of California, Berkeley
Zixun Wang, University of California, Berkeley
Hannah Chung, University of California, Berkeley
First Author
Alexander Strang, University of California, Berkeley
Presenting Author
Yash Dave, University of California, Berkeley
Instrument calibration is essential for space-based instruments to ensure accurate measurements of physical quantities, such as photon flux from astronomical sources. This process involves in-flight adjustments to address discrepancies arising from instrument-specific variations. To enhance calibration reliability, we propose a Bayesian hierarchical spectral model that leverages domain-specific priors and integrates information across different spectra, instruments, and sources. By analyzing measurements of the same set of objects from multiple instruments, the model estimates posterior uncertainties for calibration parameters and infers about structural parameters with statistical significance. Using a log-normal approximation for photon counts, our approach provides a principled alternative to empirical methods, improving the calibration of new equipment.
Keywords
bayesian hierarchical model
shrinkage estimator
high energy spectral model
With immunotherapy drug development, meta-analyses have been used to assess adverse events in large sample sizes. However, toxicity profiles vary across adverse event categories by disease type and treatment. There is increasing interest in identifying high-risk groups for closer toxicity monitoring, but this effort is hindered by sparsely observed outcomes and a high number of potential risk factors for different types of adverse events. Traditional meta-analysis methods, such as fixed and random effects models, fail to address this issue and often yield biased estimates for rare events. We frame the problem as a Bayesian variable selection approach to identify high-risk groups and use the horseshoe prior to address sparsity in linking adverse event probabilities to study-level covariates. While earlier Bayesian horseshoe prior models exist, they have limitations and may not fully utilize available information. Building on the horseshoe prior model, we propose a Bayesian feature selection model that selects both main and interaction effects, using main effects selection to help form a hierarchical structure that facilitates interaction selection.
Keywords
Bayesian feature selection
Meta-analyses
Horseshoe prior
Categorical data analysis
Current spatial point process modeling of crime data primarily relies on Euclidean distances, while criminal incidents such as robbery or vehicle crime only occur on the streets of cities. This study utilizes the recently proposed Log-Gaussian Cox Processes (LGCPs) on metric graphs to analyze crime data from the UK. The purpose is to study the effect of explanatory variables such as population density, education levels, and socioeconomic factors and to find hotspots of crime. We also compare the LGCPs on the networks with LGCPs defined in Euclidean space to investigate the effect of taking the network structure into account.
Keywords
Metric Graphs
Log-Gaussian Cox Processes
Crime Hotspot Analysis
Network-Based Modeling
Analyzing data that is inherently spatiotemporal can be difficult when our objective becomes estimating observations on a spatial and/or temporal domain that differs from the domain of our original data. The Spatiotemporal Change of Support (STCOS) model aims to solve this problem. Often, the data used in a STCOS model is assumed to follow a Gaussian distribution. However, when presented with non-Gaussian data, this assumption is unrealistic and unreliable. This research aims to extend the STCOS model to a non-Gaussian setting. We propose a Bayesian hierarchical model and implement a Markov Chain Monte Carlo Gibbs sampler to develop a Skew-Gaussian STCOS model that accounts for skewness in the data.
Keywords
Bayesian Inference
Skew-Gaussian
Gibbs sampling
Spatiotemporal
The martingale posterior framework, recently proposed by Fong et al., is based on a sequence of one step ahead predictive distributions. It leads to computationally efficient inference in parametric and nonparametric settings. The predictive distributions implicitly provide a joint model for an infinite sequence of data. The observed data, arbitrarily considered to be Y1 through Yn, form the beginning of the sequence and the tail of the sequence is missing. Filling in the missing data allows one to summarize Y1 through Y∞ (or through YN, N large in practice). A typical summary, such as the mean, is regarded as a parameter.
In cases where the martingale posterior model does not match a de Finetti model, the joint distribution over the Y's is not exchangeable, and so the indices { 1, ..., n } of the data affect the analysis. We investigate methods of symmetrizing inference in these models. In some settings, re-indexing the observed data to { a1 < ... < an } and sending a1 to infinity is analytically tractable, and we recover classical Bayesian models with known priors. Additionally, we investigate the effect of nesting the nonexchangeable models within exchangeable models.
Keywords
Martingale posterior
Bayesian nonpamametrics
Nonexchangeable models
Predictive inference
Bayesian uncertainty