Related papers: Bayes factors with (overly) informative priors

In this work, we investigate causal learning of independent causal mechanisms from a Bayesian perspective. Confirming previous claims from the literature, we show in a didactically accessible manner that unlabeled data (i.e., cause…

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…

Specifying a Bayesian prior is notoriously difficult for complex models such as neural networks. Reasoning about parameters is made challenging by the high-dimensionality and over-parameterization of the space. Priors that seem benign and…

The quality of a Bayes factor crucially depends on the number of regressors, the sample size and the prior on the regression parameters, and hence it has to be established in a case-by-case basis. In this paper we analyze the consistency of…

We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as…

Bayesian analyses require that all variable model parameters are given a prior probability distribution. This can pose a challenge for analyses where multiple experiments are combined if these experiments use different parametrisations for…

Empirical Bayes is a versatile approach to `learn from a lot' in two ways: first, from a large number of variables and second, from a potentially large amount of prior information, e.g. stored in public repositories. We review applications…

Bayes factors are characterized by both the powerful mathematical framework of Bayesian statistics and the useful interpretation as evidence quantification. Former requires a parameter distribution that changes by seeing the data, latter…

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…

Some scientific research questions ask to guide decisions and others do not. By their nature frequentist hypothesis-tests yield a dichotomous test decision as result, rendering them rather inappropriate for latter types of research…

A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative…

Recently, several researchers have claimed that conclusions obtained from a Bayes factor (or the posterior odds) may contradict those obtained from Bayesian posterior estimation. In this short paper, we wish to point out that no such…

Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…

Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…

In quantum Bayesian inference problems, any conclusions drawn from a finite number of measurements depend not only on the outcomes of the measurements but also on a prior. Here we show that, in general, the prior remains important even in…

Preprocessing forms an oft-neglected foundation for a wide range of statistical and scientific analyses. However, it is rife with subtleties and pitfalls. Decisions made in preprocessing constrain all later analyses and are typically…

I review the problem of the choice of the priors from the point of view of a physicist interested in measuring a physical quantity, and I try to show that the reference priors often recommended for the purpose (Jeffreys priors) do not fit…

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…

While the choice of prior is one of the most critical parts of the Bayesian inference workflow, recent Bayesian deep learning models have often fallen back on vague priors, such as standard Gaussians. In this review, we highlight the…

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…