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Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…

In this paper, the use of the Generalized Beta Mixture (GBM) and Horseshoe distributions as priors in the Bayesian Compressive Sensing framework is proposed. The distributions are considered in a two-layer hierarchical model, making the…

Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual…

The tensor Ising model is a discrete exponential family used for modeling binary data on networks with not just pairwise, but higher-order dependencies. A particularly important class of tensor Ising models are the tensor Curie-Weiss…

Deep neural networks (DNNs) have made significant strides in Natural Language Processing (NLP), yet their interpretability remains elusive, particularly when evaluating their intricate decision-making processes. Traditional methods often…

We consider the problem of Bayesian parameter estimation for deep neural networks, which is important in problem settings where we may have little data, and/ or where we need accurate posterior predictive densities, e.g., for applications…

It is widely acknowledged that the performance of Transformer models is logarithmically related to their number of parameters and computational complexity. While approaches like Mixture of Experts (MoE) decouple parameter count from…

Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…

Simulation-based inference (SBI) with neural posterior estimation (NPE) provides rapid X-ray spectral fitting in both Gaussian and Poisson regimes by learning approximate parameter posteriors from simulations. We investigate auto-encoders…

Neural networks are being extensively used for modelling data, especially in the case where no likelihood can be formulated. Although in the case of X-ray spectral fitting, the likelihood is known, we aim to investigate the neural networks…

While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…

In performing a Bayesian analysis, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multi-modal or exhibit pronounced (curving) degeneracies.…

Diagnosing the internal state of Li-ion batteries is critical for battery research, operation of real-world systems, and prognostic evaluation of remaining lifetime. By using physics-based models to perform probabilistic parameter…

Bayesian neural networks and deep ensembles represent two modern paradigms of uncertainty quantification in deep learning. Yet these approaches struggle to scale mainly due to memory inefficiency issues, since they require parameter storage…

An empirical best linear unbiased prediction (EBLUP) estimator is utilized for efficient inference in small-area estimation. To measure its uncertainty, we need to estimate its mean squared error (MSE) since the true MSE cannot generally be…

A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach…

Solving combinatorial optimization problems involve satisfying a set of hard constraints while optimizing some objectives. In this context, exact or approximate methods can be used. While exact methods guarantee the optimal solution, they…

Markov chain Monte Carlo (MCMC) methods remain the mainstay of Bayesian estimation of structural equation models (SEM), though they often incur a high computational cost. We present a bespoke approximate Bayesian approach to SEM, drawing on…

The linear regression model with a random variable (RV) measurement matrix, where the mean of the random measurement matrix has full column rank, has been extensively studied. In particular, the quasiconvexity of the maximum likelihood…