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This book aims to provide a graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC) algorithms, as applied broadly in the Bayesian computational context. Most, if not all of these topics (stochastic gradient MCMC,…
Disease mapping is the field of spatial epidemiology interested in estimating the spatial pattern in disease risk across $n$ areal units. One aim is to identify units exhibiting elevated disease risks, so that public health interventions…
Throughout the different phases of a drug development program, randomized trials are used to establish the tolerability, safety, and efficacy of a candidate drug. At each stage one aims to optimize the design of future studies by…
The Hamiltonian Monte Carlo (HMC) method allows sampling from continuous densities. Favorable scaling with dimension has led to wide adoption of HMC by the statistics community. Modern auto-differentiating software should allow more…
Here, we examine the latest advances in glaucoma detection through Deep Learning (DL) algorithms using Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA). This study focuses on three aspects of DL-based glaucoma…
We consider the analysis of sets of categorical sequences consisting of piecewise homogeneous Markov segments. The sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each…
We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy…
Glaucoma is the leading cause of irreversible but preventable blindness in the world. Its major treatable risk factor is the intra-ocular pressure, although other biomarkers are being explored to improve the understanding of the…
We present a scalable Bayesian framework for the analysis of confocal fluorescence spectroscopy data, addressing key limitations in traditional fluorescence correlation spectroscopy methods. Our framework captures molecular motion,…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…
A plethora of multi-view subspace clustering (MVSC) methods have been proposed over the past few years. Researchers manage to boost clustering accuracy from different points of view. However, many state-of-the-art MVSC algorithms, typically…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…
In recent years, the Hamiltonian Monte Carlo (HMC) algorithm has been found to work more efficiently compared to other popular Markov Chain Monte Carlo (MCMC) methods (such as random walk Metropolis-Hastings) in generating samples from a…
Rich data generating mechanisms are ubiquitous in this age of information and require complex statistical models to draw meaningful inference. While Bayesian analysis has seen enormous development in the last 30 years, benefitting from the…
In this paper, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to…
Collecting multiple longitudinal measurements and time-to-event outcomes is a common practice in clinical and epidemiological studies, often focusing on exploring associations between them. Joint modeling is the standard analytical tool for…
Spatial transcriptomics has revolutionized tissue analysis by simultaneously mapping gene expression, spatial topography, and histological context across consecutive tissue sections, enabling systematic investigation of spatial…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…