Related papers: A Hierarchical Bayesian Model for Frame Representa…
This paper introduces an integer-valued generalized autoregressive conditional heteroskedasticity (INGARCH) model based on the novel geometric distribution and discusses some of its properties. The parameter estimation problem of the models…
Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…
Graphical models are widely used to make inferences concerning interplay in multivariate systems. In many applications, data are collected from multiple related but nonidentical units whose underlying networks may differ but are likely to…
Determining if two histograms are consistent, whether they have been drawn from the same underlying distribution or not, is a common problem in physics. Existing approaches are not only limited in power but also inapplicable to histograms…
Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…
A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…
Recent advances in molecular biology allow the quantification of the transcriptome and scoring transcripts as differentially or equally expressed between two biological conditions. Although these two tasks are closely linked, the available…
In this paper, we explore the class of the Hidden Semi-Markov Model (HSMM), a flexible extension of the popular Hidden Markov Model (HMM) that allows the underlying stochastic process to be a semi-Markov chain. HSMMs are typically used less…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a…
Software is highly contextual. While there are cross-cutting `global' lessons, individual software projects exhibit many `local' properties. This data heterogeneity makes drawing local conclusions from global data dangerous. A key research…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed…
With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over recent years. Stochastic block model constitutes a classical…
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…
Purpose: Machine learning is broadly used for clinical data analysis. Before training a model, a machine learning algorithm must be selected. Also, the values of one or more model parameters termed hyper-parameters must be set. Selecting…
We present a Bayesian approach to estimate the parameters of mathematical models of cardiac electrophysiology with quantified uncertainty. Such models capture the dynamics of the electrical signal that coordinates the muscle cell…
Hierarchical Bayesian methods enable information sharing across multiple related regression problems. While standard practice is to model regression parameters (effects) as (1) exchangeable across datasets and (2) correlated to differing…
Purpose: Tracer-kinetic models can be used for the quantitative assessment of contrast-enhanced MRI data. However, the model-fitting can produce unreliable results due to the limited data acquired and the high noise levels. Such problems…