Related papers: Bayes, E-values and Testing
In this study, we propose a two-stage procedure for hypothesis testing, where the first stage is conventional hypothesis testing and the second is an equivalence testing procedure using an introduced Empirical Equivalence Bound. In 2016,…
This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…
In this paper, we use evidence-specific value abstraction for speeding Bayesian networks inference. This is done by grouping variable values and treating the combined values as a single entity. As we show, such abstractions can exploit…
Likelihood-free methods, such as approximate Bayesian computation, are powerful tools for practical inference problems with intractable likelihood functions. Markov chain Monte Carlo and sequential Monte Carlo variants of approximate…
Large Language Models (LLMs) are increasingly entering specialized, safety-critical engineering workflows governed by strict quantitative standards and immutable physical laws, making rigorous evaluation of their reasoning capabilities…
We propose a new Bayesian Neural Net formulation that affords variational inference for which the evidence lower bound is analytically tractable subject to a tight approximation. We achieve this tractability by (i) decomposing ReLU…
Test-time scaling improves the reasoning performance of large language models but often results in token-inefficient overthinking, where models continue reasoning beyond what is necessary for a correct answer. Existing dynamic early-exit…
This paper proposes a Sequential Monte Carlo approach for the Bayesian estimation of mixed causal and noncausal models. Unlike previous Bayesian estimation methods developed for these models, Sequential Monte Carlo offers extensive…
In this paper we review the concepts of Bayesian evidence and Bayes factors, also known as log odds ratios, and their application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical…
While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…
We use the martingale construction of Luedtke and van der Laan (2016) to develop tests for the presence of treatment heterogeneity. The resulting sequential validation approach can be instantiated using various validation metrics, such as…
As black box explanations are increasingly being employed to establish model credibility in high-stakes settings, it is important to ensure that these explanations are accurate and reliable. However, prior work demonstrates that…
We introduce a Bayesian solution for the problem in forensic speaker recognition, where there may be very little background material for estimating score calibration parameters. We work within the Bayesian paradigm of evidence reporting and…
Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known…
The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic…
Empirical likelihood is a popular nonparametric statistical tool that does not require any distributional assumptions. In this paper, we explore the possibility of conducting variable selection via Bayesian empirical likelihood. We show…
Stochastic Differential Equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and…
This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches,…
Large language models (LLMs) have demonstrated strong capabilities in complex reasoning tasks, yet their decision-making processes remain difficult to interpret. Existing explanation methods often lack trustworthy structural insight and are…
We introduce a new conservative test for quantifying the consistency of two or more datasets. The test is based on the Bayesian answer to the question, ``How much more probable is it that all my data were generated from the same model…