Related papers: A Novel Bayes' Theorem for Upper Probabilities
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
In this work, we undertake a comprehensive reformulation, modification, and extension of Smith and Spiegelhalter's (1980) and (1982) Bayes Factor work within the evolving subject of Objective Bayes Factors. Our primary focus centers on…
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…
We develop simple methods for constructing likelihoods and parameter priors for learning about the parameters and structure of a Bayesian network. In particular, we introduce several assumptions that permit the construction of likelihoods…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
Probabilities of causation play a crucial role in modern decision-making. Pearl defined three binary probabilities of causation, the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of…
The problem of assigning probabilities when little is known is analized in the case where the quanities of interest are physical observables, i.e. can be measured and their values expressed by numbers. It is pointed out that the assignment…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state…
Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a…
Gyenis and Redei have demonstrated that any prior p on a finite algebra, however chosen, severely restricts the set of posteriors accessible from p by Jeffrey conditioning on a nontrivial partition. Their demonstration involves showing that…
Deep learning has revolutionized the last decade, being at the forefront of extraordinary advances in a wide range of tasks including computer vision, natural language processing, and reinforcement learning, to name but a few. However, it…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
Machine learning algorithms are becoming integrated into more and more high-stakes decision-making processes, such as in social welfare issues. Due to the need of mitigating the potentially disparate impacts from algorithmic predictions,…
A common problem faced in statistical inference is drawing conclusions from paired comparisons, in which two objects compete and one is declared the victor. A probabilistic approach to such a problem is the Bradley-Terry model, first…
We use sets of assignments, a.k.a. teams, and measures on them to define probabilities of first-order formulas in given data. We then axiomatise first-order properties of such probabilities and prove a completeness theorem for our…
Deriving generalization bounds for stable algorithms is a classical question in learning theory taking its roots in the early works by Vapnik and Chervonenkis (1974) and Rogers and Wagner (1978). In a series of recent breakthrough papers by…
When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the…
We consider the problem of estimating the probability of error in multi-hypothesis testing when MAP criterion is used. This probability, which is also known as the Bayes risk is an important measure in many communication and information…