Related papers: A frequentist framework of inductive reasoning
Active inference is a state-of-the-art framework in neuroscience that offers a unified theory of brain function. It is also proposed as a framework for planning in AI. Unfortunately, the complex mathematics required to create new models --…
The analysis of practical probabilistic models on the computer demands a convenient representation for the available knowledge and an efficient algorithm to perform inference. An appealing representation is the influence diagram, a network…
After some general remarks about the interrelation between philosophical and statistical thinking, the discussion centres largely on significance tests. These are defined as the calculation of $p$-values rather than as formal procedures for…
We derive confidence intervals and confidence sequences for causal effects in situations where the back-door or front-door criteria are applicable. Our tightest confidence intervals hold in the standard setting where the training data…
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
We address the problem of uncertainty propagation in the discrete Fourier transform by modeling the fast Fourier transform as a factor graph. Building on this representation, we propose an efficient framework for approximate Bayesian…
Probabilistic prediction aims to compute predictive distributions rather than single point predictions. These distributions enable practitioners to quantify uncertainty, compute risk, and detect outliers. However, most probabilistic methods…
This paper is a review of a particular approach to the method of maximum entropy as a general framework for inference. The discussion emphasizes the pragmatic elements in the derivation. An epistemic notion of information is defined in…
Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference;…
The prediction interval has been increasingly used in meta-analyses as a useful measure for assessing the magnitude of treatment effect and between-studies heterogeneity. In calculations of the prediction interval, although the…
We revisit empirical Bayes in the absence of a tractable likelihood function, as is typical in scientific domains relying on computer simulations. We investigate how the empirical Bayesian can make use of neural density estimators first to…
Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as…
Though the ability of human beings to deal with probabilities has been put into question, the assessment of rarity is a crucial competence underlying much of human decision-making and is pervasive in spontaneous narrative behaviour. This…
Don Fraser has given an interesting account of the agreements and disagreements between Bayesian posterior probabilities and confidence levels. In this comment I discuss some cases where the lack of such agreement is extreme. I then discuss…
Large amounts of evidence suggest that trust levels in a country are an important determinant of its macroeconomic growth. In this paper, we investigate one channel through which trust might support economic performance: through the levels…
Bayesian inference as applied in a legal setting is about belief transfer and involves a plurality of agents and communication protocols. A forensic expert (FE) may communicate to a trier of fact (TOF) first its value of a certain…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
Reasoning about degrees of belief in uncertain dynamic worlds is fundamental to many applications, such as robotics and planning, where actions modify state properties and sensors provide measurements, both of which are prone to noise. With…
Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigorous theory of probability while the latter is not. In this…
Gaussian belief propagation (GBP) is a recursive computation method that is widely used in inference for computing marginal distributions efficiently. Depending on how the factorization of the underlying joint Gaussian distribution is…