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We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
As large language models (LLMs) gain popularity in conducting prediction tasks in-context, understanding the sources of uncertainty in in-context learning becomes essential to ensuring reliability. The recent hypothesis of in-context…
Modern AI systems are being deployed in complex domains such as medicine, science, and law, where it is important that they not only produce correct answers, but also represent and update uncertain beliefs about the world as new evidence…
Recent advancements in machine learning have emphasized the need for transparency in model predictions, particularly as interpretability diminishes when using increasingly complex architectures. In this paper, we propose leveraging…
We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…
As artificial agents become increasingly capable, what internal structure is *necessary* for an agent to act competently under uncertainty? Classical results show that optimal control can be *implemented* using belief states or world…
Conformal prediction (CP) was developed to provide finite-sample probabilistic prediction guarantees. While CP algorithms are a relatively general-purpose approach to uncertainty quantification, with finite-sample guarantees, they lack…
In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters…
Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking is depends on the inconsistency of the data from which it was created. There are many indices used for…
Analyzing decision problems under uncertainty commonly relies on idealizing assumptions about the describability of the world, with the most prominent examples being the closed world and the small world assumption. Most assumptions are…
Our previous work on classifying complex ship images [1,2] has evolved into an effort to develop software tools for building and solving generic classification problems. Managing the uncertainty associated with feature data and other…
Bayes' rule has enabled innumerable powerful algorithms of statistical signal processing and statistical machine learning. However, when model misspecifications exist in prior and/or data distributions, the direct application of Bayes' rule…
In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit conditions and the implicit conditions of probability assignments `me properly distinguished,…
Causal inference from observational data provides strong evidence for the best action in decision-making without performing expensive randomized trials. The effect of an action is usually not identifiable under unobserved confounding, even…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…
Inverse optimization has been increasingly used to estimate unknown parameters in an optimization model based on decision data. We show that such a point estimation is insufficient in a prescriptive setting where the estimated parameters…
Recovering and distinguishing between the strict-preference, indifference and/or indecisiveness parts of a decision maker's preferences is a challenging task but also important for testing theory and conducting welfare analysis. This paper…
We propose a general solution to the problem of robust Bayesian inference in complex settings where outliers may be present. In practice, the automation of robust Bayesian analyses is important in the many applications involving large and…
One of the most important aspects in any treatment of uncertain information is the rule of combination for updating the degrees of uncertainty. The theory of belief functions uses the Dempster rule to combine two belief functions defined by…
We present locally complete inference rules for probabilistic deduction from taxonomic and probabilistic knowledge-bases over conjunctive events. Crucially, in contrast to similar inference rules in the literature, our inference rules are…