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This article focuses on inference in logistic regression for high-dimensional binary outcomes. A popular approach induces dependence across the outcomes by including latent factors in the linear predictor. Bayesian approaches are useful for…

The label switching problem arises in the Bayesian analysis of models containing multiple indistinguishable parameters with arbitrary ordering. Any permutation of these parameters is equivalent, therefore models with many such parameters…

There are many practical difficulties in the calibration of computer models to experimental data. One such complication is the fact that certain combinations of the calibration inputs can cause the code to output data lacking fundamental…

Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte…

This paper introduces multimodal conformal regression. Traditionally confined to scenarios with solely numerical input features, conformal prediction is now extended to multimodal contexts through our methodology, which harnesses internal…

Optimization constrained by high-fidelity computational models has potential for transformative impact. However, such optimization is frequently unattainable in practice due to the complexity and computational intensity of the model. An…

Bayesian neural network models (BNN) have re-surged in recent years due to the advancement of scalable computations and its utility in solving complex prediction problems in a wide variety of applications. Despite the popularity and…

Federated Bayesian neural networks require fixing a prior on the model parameters together with a likelihood. Eliciting meaningful priors on the weight space of modern overparameterized models is notoriously difficult, and misspecification…

When building a geometric scene understanding system for autonomous vehicles, it is crucial to know when the system might fail. Most contemporary approaches cast the problem as depth regression, whose output is a depth value for each pixel.…

In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…

We consider systems of ordinary differential equations with multiple scales in time. In general, we are interested in the long time horizon of a slow variable that is coupled to solution components that act on a fast scale. Although the…

Anomaly detection is a fundamental problem in data mining field with many real-world applications. A vast majority of existing anomaly detection methods predominately focused on data collected from a single source. In real-world…

Numerical modeling of morphodynamics presents significant challenges in engineering due to uncertainties arising from inaccurate inputs, model errors, and limited computing resources. Accurate results are essential for optimizing strategies…

Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…

Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in…

We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…

Orthogonal matrices play an important role in probability and statistics, particularly in high-dimensional statistical models. Parameterizing these models using orthogonal matrices facilitates dimension reduction and parameter…

A posteriori error estimates are derived in the context of two-dimensional structural elastic shape optimization under the compliance objective. It is known that the optimal shape features are microstructures that can be constructed using…

In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability…