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An appealing requirement from the well-known diffraction tomography (DT) exists for success reconstruction from few-view and limited-angle data. Inspired by the well-known compressive sensing (CS), the accurate super-resolution…
Standard Markov chain Monte Carlo methods struggle to explore distributions that are concentrated in the neighbourhood of low-dimensional structures. These pathologies naturally occur in a number of situations. For example, they are common…
We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…
Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…
We develop a modular approach to Markov chain Monte Carlo (MCMC) sampling for unnormalized target densities. In this approach, Markov chains are constructed in parallel, each constrained to a subset of the target space. The Monte Carlo…
The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…
Transit timing variations (TTVs) are a valuable tool to determine the masses and orbits of transiting planets in multi-planet systems. TTVs can be readily modeled given knowledge of the interacting planets' orbital configurations and…
We present a Bayesian sampling algorithm called adaptive importance sampling or Population Monte Carlo (PMC), whose computational workload is easily parallelizable and thus has the potential to considerably reduce the wall-clock time…
Bayesian variable selection is a powerful tool for data analysis, as it offers a principled method for variable selection that accounts for prior information and uncertainty. However, wider adoption of Bayesian variable selection has been…
Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…
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…
The Planck satellite, along with several ground based telescopes, have mapped the cosmic microwave background (CMB) at sufficient resolution and signal-to-noise so as to allow a detection of the subtle distortions due to the gravitational…
Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
Computational tools for characterizing electromagnetic scattering from objects with uncertain shapes are needed in various applications ranging from remote sensing at microwave frequencies to Raman spectroscopy at optical frequencies.…
Bayesian estimation methods for sparse blind deconvolution problems conventionally employ Bernoulli-Gaussian (BG) prior for modeling sparse sequences and utilize Markov Chain Monte Carlo (MCMC) methods for the estimation of unknowns.…
Radiological mapping plays a critical role in nuclear emergency response and environmental management activities. A radiation image, representing the spatial and intensity distribution of the radioactivity, is reconstructed from the…
Classic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov Chain Monte Carlo (rjMCMC), it is possible to vary this…
We formally map the problem of sampling from an unknown distribution with a density in $\mathbb{R}^d$ to the problem of learning and sampling a smoother density in $\mathbb{R}^{Md}$ obtained by convolution with a fixed factorial kernel: the…
We present a Bayesian approach to the problem of determining parameters for coalescing binary systems observed with laser interferometric detectors. By applying a Markov Chain Monte Carlo (MCMC) algorithm, specifically the Gibbs sampler, we…