Related papers: Projected Bayesian Spatial Factor Models
Probabilistic Temporal Tensor Factorization (PTTF) is an effective algorithm to model the temporal tensor data. It leverages a time constraint to capture the evolving properties of tensor data. Nowadays the exploding dataset demands a large…
Particle Markov chain Monte Carlo (pMCMC) is now a popular method for performing Bayesian statistical inference on challenging state space models (SSMs) with unknown static parameters. It uses a particle filter (PF) at each iteration of an…
With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and…
Its conceptual appeal and effectiveness has made latent factor modeling an indispensable tool for multivariate analysis. Despite its popularity across many fields, there are outstanding methodological challenges that have hampered practical…
A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…
Spatial whole-brain Bayesian modeling of task-related functional magnetic resonance imaging (fMRI) is a great computational challenge. Most of the currently proposed methods therefore do inference in subregions of the brain separately or do…
The goal of Bayesian deep learning is to provide uncertainty quantification via the posterior distribution. However, exact inference over the weight space is computationally intractable due to the ultra-high dimensions of the neural…
Multi-parametric magnetic resonance imaging (mpMRI) plays an increasingly important role in the diagnosis of prostate cancer. Various computer-aided detection algorithms have been proposed for automated prostate cancer detection by…
Many modern data sets require inference methods that can estimate the shared and individual-specific components of variability in collections of matrices that change over time. Promising methods have been developed to analyze these types of…
This work introduces a Bayesian methodology for fitting large discrete graphical models with spike-and-slab priors to encode sparsity. We consider a quasi-likelihood approach that enables node-wise parallel computation resulting in reduced…
This paper examines a new parallel computation model called bulk synchronous farm (BSF) that focuses on estimating the scalability of compute-intensive iterative algorithms aimed at cluster computing systems. In the BSF model, a computer is…
Multidimensional scaling (MDS) is widely used to reconstruct a low-dimensional representation of high-dimensional data while preserving pairwise distances. However, Bayesian MDS approaches based on Markov chain Monte Carlo (MCMC) face…
Markov random fields (MRFs) are invaluable tools across diverse fields, and spatiotemporal MRFs (STMRFs) amplify their effectiveness by integrating spatial and temporal dimensions. However, modeling spatiotemporal data introduces additional…
We tackle the problem of multiscale regression for predictors that are spatially or temporally indexed, or with a pre-specified multiscale structure, with a Bayesian modular approach. The regression function at the finest scale is expressed…
Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…
We numerically investigate a mean-field Bayesian approach with the assistance of the Markov chain Monte Carlo method to estimate motion velocity fields and probabilistic models simultaneously in consecutive digital images described by…
Bayesian spatial modeling provides a flexible framework for whole-brain fMRI analysis by explicitly incorporating spatial dependencies, overcoming the limitations of traditional massive univariate approaches that lead to information waste.…
Determining subgroups that respond especially well (or poorly) to specific interventions (medical or policy) requires new supervised learning methods tailored specifically for causal inference. Bayesian Causal Forest (BCF) is a recent…
Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…
This is a course project report with complete methodology, experiments, references and mathematical derivations. Matrix factorization [1] is a widely used technique in recommendation systems. Probabilistic Matrix Factorization (PMF) [2]…