Related papers: A robust method for reliability updating with equa…

Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…

Advanced AI technologies are serving humankind in a number of ways, from healthcare to manufacturing. Advanced automated machines are quite expensive, but the end output is supposed to be of the highest possible quality. Depending on the…

We consider online prediction of a latent dynamic spatiotemporal process and estimation of the associated model parameters based on noisy data. The problem is motivated by the analysis of spatial data arriving in real-time and the current…

Finite element model updating is challenging because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield responses that are similar with respect to…

Retrieval-Augmented Language Models (RALMs) face significant challenges in reducing factual errors, particularly in document relevance evaluation and knowledge integration. We introduce a framework for structured relevance assessment that…

In reliability engineering, data about failure events is often scarce. To arrive at meaningful estimates for the reliability of a system, it is therefore often necessary to also include expert information in the analysis, which is…

We present a Bayesian nonparametric system reliability model which scales well and provides a great deal of flexibility in modeling. The Bayesian approach naturally handles the disparate amounts of component and subsystem data that may…

In structural health monitoring (SHM) systems, massive amounts of data are often generated that need data compression techniques to reduce the cost of signal transfer and storage. Compressive sensing (CS) is a novel data acquisition method…

Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC…

Efficient information processing is crucial for both living organisms and engineered systems. The mutual information rate, a core concept of information theory, quantifies the amount of information shared between the trajectories of input…

Efficiently sampling from high-dimensional, multi-modal posteriors is a central challenge in Bayesian inference for astrophysics, especially gravitational-wave astronomy. Popular families of methods like Markov-chain Monte Carlo, nested…

Structural reliability analysis is concerned with estimation of the probability of a critical event taking place, described by $P(g(\textbf{X}) \leq 0)$ for some $n$-dimensional random variable $\textbf{X}$ and some real-valued function…

Test-time scaling methods improve the capabilities of large language models (LLMs) by increasing the amount of compute used during inference to make a prediction. Inference-time compute can be scaled in parallel by choosing among multiple…

The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state function, which depends on the solution of a partial…

Quantifying uncertainty and updating reliability are essential for ensuring the safety and performance of engineering systems. This study develops a hierarchical Bayesian modeling (HBM) framework to quantify uncertainty and update…

We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…

In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian…

The Information Bottleneck method is a learning technique that seeks a right balance between accuracy and generalization capability through a suitable tradeoff between compression complexity, measured by minimum description length, and…

Spurious correlations threaten the validity of statistical classifiers. While model accuracy may appear high when the test data is from the same distribution as the training data, it can quickly degrade when the test distribution changes.…

Existing sequential generalized estimating equation methodology for longitudinal and group-correlated data focuses on narrow hypotheses concerning treatment efficacy and often makes modeling assumptions that impede the desirable robustness…