Related papers: Updating with incomplete observations
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
Cromwell's rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a…
Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…
Bayesian methods have proven themselves to be successful across a wide range of scientific problems and have many well-documented advantages over competing methods. However, these methods run into difficulties for two major and prevalent…
It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…
This paper proposes an information-based inference method for partially identified parameters in incomplete models that is valid both when the model is correctly specified and when it is misspecified. Key features of the method are: (i) it…
Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. However, they are often overconfident in their predictions, which leads to inaccurate and miscalibrated…
Recent work has discussed the limitations of counterfactual explanations to recommend actions for algorithmic recourse, and argued for the need of taking causal relationships between features into consideration. Unfortunately, in practice,…
We construct a probabilistic coherence measure for information sets which determines a partial coherence ordering. This measure is applied in constructing a criterion for expanding our beliefs in the face of new information. A number of…
The recent success of machine learning models, especially large-scale classifiers and language models, relies heavily on training with massive data. These data are often collected from online sources. This raises serious concerns about the…
In an ideal setting for Bayesian agents, a perfect description of the rules of the environment (i.e., the objective observation model) is available, allowing them to reason through the Bayesian posterior to update their beliefs in an…
Recursive Bayesian inference, in which posterior beliefs are updated in light of accumulating data, is a tool for implementing Bayesian models in applications with streaming and/or very large data sets. As the posterior of one iteration…
Matrix completion tackles the task of predicting missing values in a low-rank matrix based on a sparse set of observed entries. It is often assumed that the observation pattern is generated uniformly at random or has a very specific…
We propose a method for an agent to revise its incomplete probabilistic beliefs when a new piece of propositional information is observed. In this work, an agent's beliefs are represented by a set of probabilistic formulae -- a belief base.…
Bayesian implementation concerns decision making problems when agents have incomplete information. This paper proposes that the traditional sufficient conditions for Bayesian implementation shall be amended by virtue of a quantum Bayesian…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
We give an overview of two approaches to probability theory where lower and upper probabilities, rather than probabilities, are used: Walley's behavioural theory of imprecise probabilities, and Shafer and Vovk's game-theoretic account of…
Boosting has emerged as a useful machine learning technique over the past three decades, attracting increased attention. Most advancements in this area, however, have primarily focused on numerical implementation procedures, often lacking…
Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…