Related papers: The Fermi's Bayes Theorem

There is a brief description of the probabilistic causal graph model for representing, reasoning with, and learning causal structure using Bayesian networks. It is then argued that this model is closely related to how humans reason with and…

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

In 1957, Lindley published "A statistical paradox" in Biometrika, revealing a fundamental conflict between frequentist and Bayesian inference as sample size approaches infinity. We present a new paradox of a different kind: a conflict…

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…

Bayesian, frequentist and fiducial (BFF) inferences are much more congruous than they have been perceived historically in the scientific community (cf., Reid and Cox 2015; Kass 2011; Efron 1998). Most practitioners are probably more…

In a Perspectives article in Science, Bradley Efron concludes that Bayesian calculations cannot be uncritically accepted when using uninformative priors. We argue that this conclusion is problematic because Efron's example does not use…

The is no other model or hypothesis verification tool in Bayesian statistics that is as widely used as the Bayes factor. We focus on generative models that are likelihood-free and, therefore, render the computation of Bayes factors…

Although propensity scores have been central to the estimation of causal effects for over 30 years, only recently has the statistical literature begun to consider in detail methods for Bayesian estimation of propensity scores and causal…

The aim of this paper is to introduce a field of study that has emerged over the last decade called Bayesian mechanics. Bayesian mechanics is a probabilistic mechanics, comprising tools that enable us to model systems endowed with a…

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…

Typicality has always been in the minds of the founding fathers of probability theory when probabilistic reasoning is applied to the real world. However, the role of typicality is not always appreciated. An example is the paper "Foundations…

After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…

Objective probability in quantum mechanics is often thought to involve a stochastic process whereby an actual future is selected from a range of possibilities. Everett's seminal idea is that all possible definite futures on the pointer…

The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…

We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…

There are two main opposing schools of statistical reasoning, Frequentist and Bayesian approaches. Until recent days, the frequentist or classical approach has dominated the scientific research, but Bayesianism has reappeared with a strong…

We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…

A gem of classical probability, the Berry-Esseen theorem provides a non-asymptotic form of the central limit theorem. This note gives a friendly and intuitive exposition of the classical Fourier-analytic proof of Esseen's smoothing…

The major goal of this paper is to study the second order frequentist properties of the marginal posterior distribution of the parametric component in semiparametric Bayesian models, in particular, a second order semiparametric…