Related papers: Getting Wiser from Multiple Data: Probabilistic Up…
A desired closure property in Bayesian probability is that an updated posterior distribution be in the same class of distributions --- say Gaussians --- as the prior distribution. When the updating takes place via a statistical model, one…
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…
What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore…
We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…
Inference and learning are commonly cast in terms of optimisation, yet the fundamental constraints governing uncertainty reduction remain unclear. This work presents a first-principles framework inherent to Bayesian updating, termed…
A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the…
We present PPCEF, a novel method for generating probabilistically plausible counterfactual explanations (CFs). PPCEF advances beyond existing methods by combining a probabilistic formulation that leverages the data distribution with the…
Bayesian model comparison is often based on the posterior distribution over the set of compared models. This distribution is often observed to concentrate on a single model even when other measures of model fit or forecasting ability…
The objective of Bayesian inference is often to infer, from data, a probability measure for a random variable that can be used as input for Monte Carlo simulation. When datasets for Bayesian inference are small, a principle challenge is…
Consider two forms of sampling from a population: (i) drawing $s$ samples of $n$ elements with replacement and (ii) drawing a single sample of $ns$ elements. In this paper, under the setting where the descending order population frequency…
The human mind is capable of extraordinary achievements, yet it often appears to work against itself. It actively defends its cherished beliefs even in the face of contradictory evidence, conveniently interprets information to conform to…
Probabilistic epistemic argumentation allows for reasoning about argumentation problems in a way that is well founded by probability theory. Epistemic states are represented by probability functions over possible worlds and can be adjusted…
Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and…
This paper reviews the basic ideas behind a Bayesian unfolding published some years ago and improves their implementation. In particular, uncertainties are now treated at all levels by probability density functions and their propagation is…
A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance…
The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…
Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…
Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…
Surprise-based learning allows agents to rapidly adapt to non-stationary stochastic environments characterized by sudden changes. We show that exact Bayesian inference in a hierarchical model gives rise to a surprise-modulated trade-off…