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Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness w.r.t. the prior distribution. Many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of…
In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…
In the context of testing general relativity with gravitational waves, constraints obtained with multiple events are typically combined either through a hierarchical formalism or though a combined multiplicative Bayes factor. We show that…
A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
In a Bayesian inverse problem setting, the solution consists of a posterior measure obtained by combining prior belief, information about the forward operator, and noisy observational data. This measure is most often given in terms of a…
In this expository paper, we consider the problem of causal inference and efficient estimation for the counterfactual survivor function. This problem has previously been considered in the literature in several papers, each relying on the…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
Wilk's theorem, which offers universal chi-squared approximations for likelihood ratio tests, is widely used in many scientific hypothesis testing problems. For modern datasets with increasing dimension, researchers have found that the…
It is a challenge to manage infinite- or high-dimensional data in situations where storage, transmission, or computation resources are constrained. In the simplest scenario when the data consists of a noisy infinite-dimensional signal, we…
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
Estimates of uncertainty or variance in experimental means are central to physics. This is especially the case for `world averages' of fundamental physical parameters in particle physics, which aggregate results from a number of experiments…
The determination of the fundamental parameters of the Standard Model (and its extensions) is often limited by the presence of statistical and theoretical uncertainties. We present several models for the latter uncertainties (random,…
The experimental problem of converting a measured binomial quantity, the fraction of events in a sample that pass a cut, into a physical binomial quantity, the fraction of events originating from a signal source, is described as a system of…
Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. Drawbacks of Bayes factors are their dependence on prior specifications that define null and alternative hypotheses and difficulties…
Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] as a generally applicable method for testing nonparametric hypotheses about nonparametric functions. The likelihood ratio…
Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be…
The concept of wavefunction reduction should be introduced to standard quantum mechanics in any physical processes where effective reduction of wavefunction occurs, as well as in the measurement processes. When the overlap is negligible,…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
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…