Related papers: Holes in Bayesian Statistics

A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter was equal or lay close to a specified value, which may, for…

The problem of the priors is well known: it concerns the challenge of identifying norms that govern one's prior credences. I argue that a key to addressing this problem lies in considering what I call the problem of the posteriors -- the…

The goal of causal inference is to understand the outcome of alternative courses of action. However, all causal inference requires assumptions. Such assumptions can be more influential than in typical tasks for probabilistic modeling, and…

Bayesian Deep Learning (BDL) gives access not only to aleatoric uncertainty, as standard neural networks already do, but also to epistemic uncertainty, a measure of confidence a model has in its own predictions. In this article, we show…

Standard statistical theory has arguably proved to be unsuitable as a basis for constructing a satisfactory completely general framework for performing statistical inference. For example, frequentist theory has never come close to providing…

In this manuscript, we discuss the substantial importance of Bayesian reasoning in Social Science research. Particularly, we focus on foundational elements to fit models under the Bayesian paradigm. We aim to offer a frame of reference for…

We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…

Differential privacy has emerged as an significant cornerstone in the realm of scientific hypothesis testing utilizing confidential data. In reporting scientific discoveries, Bayesian tests are widely adopted since they effectively…

The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks. (1) Neural networks are typically…

Is it possible for a large sequence of measurements or observations, which support a hypothesis, to counterintuitively decrease our confidence? Can unanimous support be too good to be true? The assumption of independence is often made in…

Bayesian linear mixed-effects models and Bayesian ANOVA are increasingly being used in the cognitive sciences to perform null hypothesis tests, where a null hypothesis that an effect is zero is compared with an alternative hypothesis that…

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the…

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…

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…

The AI ethics of statistical fairness is an error, the approach should be abandoned, and the accumulated academic work deleted. The argument proceeds by identifying four recurring mistakes within statistical fairness. One conflates fairness…

We consider the Bayesian analysis of a few complex, high-dimensional models and show that intuitive priors, which are not tailored to the fine details of the model and the estimated parameters, produce estimators which perform poorly in…

Many questions in experimental mathematics are fundamentally inductive in nature. Here we demonstrate how Bayesian inference --the logic of partial beliefs-- can be used to quantify the evidence that finite data provide in favor of a…

Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis…

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…

Recently, optional stopping has been a subject of debate in the Bayesian psychology community. Rouder (2014) argues that optional stopping is no problem for Bayesians, and even recommends the use of optional stopping in practice, as do…