Related papers: Why optional stopping can be a problem for Bayesia…

In this work we apply the methodology of integral priors to handle Bayesian model selection in binomial regression models with a general link function. These models are very often used to investigate associations and risks in…

Dropout is one of the key techniques to prevent the learning from overfitting. It is explained that dropout works as a kind of modified L2 regularization. Here, we shed light on the dropout from Bayesian standpoint. Bayesian interpretation…

In the Bayesian literature on model comparison, Bayes factors play the leading role. In the classical statistical literature, model selection criteria are often devised used cross-validation ideas. Amalgamating the ideas of Bayes factor and…

Bayesian optimisation is a powerful tool to solve expensive black-box problems, but fails when the stationary assumption made on the objective function is strongly violated, which is the case in particular for ill-conditioned or…

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…

Before autonomous systems can be deployed in safety-critical applications, we must be able to understand and verify the safety of these systems. For cases where the risk or cost of real-world testing is prohibitive, we propose a…

Order effects occur when judgments about a hypothesis's probability given a sequence of information do not equal the probability of the same hypothesis when the information is reversed. Different experiments have been performed in 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…

Inferences about hypotheses are ubiquitous in the cognitive sciences. Bayes factors provide one general way to compare different hypotheses by their compatibility with the observed data. Those quantifications can then also be used to choose…

Interim analyses are vital in clinical trials for early decision-making. While frequentist implications are well-established, the consequences of repeated Bayesian interim monitoring for efficacy, specifically regarding multiplicity, remain…

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…

Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…

The two key issues of modern Bayesian statistics are: (i) establishing principled approach for distilling statistical prior that is consistent with the given data from an initial believable scientific prior; and (ii) development of a…

In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first…

Is there a way to design powerful AI systems based on machine learning methods that would satisfy probabilistic safety guarantees? With the long-term goal of obtaining a probabilistic guarantee that would apply in every context, we consider…

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…

The measurement of the efficiency of an event selection is always an important part of the analysis of experimental data. The statistical techniques which are needed to determine the efficiency and its uncertainty are reviewed. Frequentist…

In the first part of this paper, we study RBSDEs in the case where the filtration is not quasi-left continuous and the lower obstacle is given by a predictable process. We prove the existence and uniqueness by using some results of optimal…

The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of…

Many Bayesian model selection problems, such as variable selection or cluster analysis, start by setting prior model probabilities on a structured model space. Based on a chosen loss function between models, model selection is often…