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The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in…

Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…

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,…

Frequentist (classical) and the Bayesian approaches to the construction of confidence limits are compared. Various examples which illustrate specific problems are presented. The Likelihood Principle and the Stopping Rule Paradox are…

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…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…

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…

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…

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…

We revisit and generalize the concept of composite likelihood as a method to make a probabilistic inference by aggregation of multiple Bayesian agents, thereby defining a class of predictive models which we call composite Bayesian. This…

We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a…

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

The author revisits the Blue Bus Problem, a famous thought-experiment in law involving probabilistic proof, and presents simple Bayesian solutions to different versions of the blue bus hypothetical. In addition, the author expresses his…

Standard random-effects meta-analysis methods perform poorly when applied to few studies only. Such settings however are commonly encountered in practice. It is unclear, whether or to what extent small-sample-size behaviour can be improved…

Empirical Bayes methods offer valuable tools for a large class of compound decision problems. In this tutorial we describe some basic principles of the empirical Bayes paradigm stressing their frequentist interpretation. Emphasis is placed…

Within the framework proposed in this paper, we address the issue of extending the certain networks to a fuzzy certain networks in order to cope with a vagueness and limitations of existing models for decision under imprecise and uncertain…

Between Bayesian and frequentist inference, it's commonly believed that the former is for cases where one has a prior and the latter is for cases where one has no prior. But the prior/no-prior classification isn't exhaustive, and most…

In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation…

Given empirical evidence for the dependence of an outcome variable on an exposure variable, we can typically only provide bounds for the "probability of causation" in the case of an individual who has developed the outcome after being…