相关论文: Overcoming priors anxiety

The plausibility of uncommon events and miracles based on testimony of such an event has been much discussed. When analyzing the probabilities involved, it has mostly been assumed that the common events can be taken as data in the…

Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of…

Cosmological models that invoke a multiverse - a collection of unobservable regions of space where conditions are very different from the region around us - are controversial, on the grounds that unobservable phenomena shouldn't play a…

Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…

Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…

This paper introduces a framework for incorporating prior information into the design of sequential experiments. These sources may include past experiments, expert opinions, or the experimenter's intuition. We model the problem using a…

In this contribution to the proceedings of the 182nd Nobel Symposium, I reflect on the concept of "discovery" as it is used by physicists and astronomers. In particular, I comment on how the scientific community distinguishes discoveries…

A scientific reasoning system makes decisions using objective evidence in the form of independent experimental trials, propositional axioms, and constraints on the probabilities of events. As a first step towards this goal, we propose a…

Some criticisms that have been raised against the Cox approach to probability theory are addressed. Should we use a single real number to measure a degree of rational belief? Can beliefs be compared? Are the Cox axioms obvious? Are there…

In order to study updating rules, we consider the problem of a malevolent principal screening an imperfectly Bayesian agent. We uncover a fundamental dichotomy between underreaction and overreaction to information. If an agent's posterior…

We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…

Following Fisher, it is widely believed that randomization "relieves the experimenter from the anxiety of considering innumerable causes by which the data may be disturbed." In particular, it is said to control for known and unknown…

Common statistical practice has shown that the full power of Bayesian methods is not realized until hierarchical priors are used, as these allow for greater "robustness" and the ability to "share statistical strength." Yet it is an ongoing…

The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from…

Hypothesis testing and model choice are quintessential questions for statistical inference and while the Bayesian paradigm seems ideally suited for answering these questions, it faces difficulties of its own ranging from prior modelling to…

Recent work in cognitive science has uncovered a diversity of explanatory values, or dimensions along which we judge explanations as better or worse. We propose a Bayesian account of how these values fit together to guide explanation. The…

We develop a representation of a decision maker's uncertainty based on e-variables. Like the Bayesian posterior, this *e-posterior* allows for making predictions against arbitrary loss functions that may not be specified ex ante. Unlike the…

The lately developed part of Quantum Bayesianism named QBism has been proclaimed by its authors a powerful interpretation of Quantum Physics. This article presents analysis of some aspects of QBism. The considered examples show…

This paper considers the problem of making statistical inferences about a parameter when a narrow interval centred at a given value of the parameter is considered special, which is interpreted as meaning that there is a substantial degree…

Can multiverse hypotheses ever receive empirical support? Critics argue that multiverse scenarios posit unobservable entities, face severe underdetermination, or fall outside the bounds of science. This chapter challenges that view by…