Related papers: Evaluating the effect of different non-informative…
A Bayesian inference method for problems with small samples and sparse data is presented in this paper. A general type of prior ($\propto 1/\sigma^{q}$) is proposed to formulate the Bayesian posterior for inference problems under small…
We consider nonparametric inference for event time distributions based on current status data. We show that in this scenario conventional mixture priors, including the popular Dirichlet process mixture prior, lead to biologically…
Nonlinear longitudinal proportional effect models have been proposed to improve power and provide direct estimates of the proportional treatment effect in randomized clinical trials. These models assume a fixed proportional treatment effect…
When constructing a model to estimate the causal effect of a treatment, it is necessary to control for other factors which may have confounding effects. Because the ignorability assumption is not testable, however, it is usually unclear…
Preferential Bayesian optimization allows optimization of objectives that are either expensive or difficult to measure directly, by relying on a minimal number of comparative evaluations done by a human expert. Generating candidate…
We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior…
Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this…
We propose a two-component mixture of a noninformative (diffuse) and an informative prior distribution, weighted through the data in such a way to prefer the first component if a prior-data conflict arises. The data-driven approach for…
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…
Deep Bayesian neural networks (BNNs) are a powerful tool, though computationally demanding, to perform parameter estimation while jointly estimating uncertainty around predictions. BNNs are typically implemented using arbitrary…
Experiments on decision making under uncertainty are known to display a classical pattern of risk aversion and risk seeking referred to as "fourfold pattern" (or "reflection effect") , but recent experiments varying the speed and order of…
Observational healthcare data offer the potential to estimate causal effects of medical products on a large scale. However, the confidence intervals and p-values produced by observational studies only account for random error and fail to…
Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the…
Given the precision of current neutrino data, priors still impact noticeably the constraints on neutrino masses and their hierarchy. To avoid our understanding of neutrinos being driven by prior assumptions, we construct a prior that is…
It is not always clear how to adjust for control data in causal inference, balancing the goals of reducing bias and variance. We show how, in a setting with repeated experiments, Bayesian hierarchical modeling yields an adaptive procedure…
A new general framework is presented for implementing complex a priori knowledge, having in mind especially situations where the number of available training data is small compared to the complexity of the learning task. A priori…
Conditioning on variables affected by treatment can induce post-treatment bias when estimating causal effects. Although this suggests that researchers should measure potential moderators before administering the treatment in an experiment,…
In many randomized clinical trials of therapeutics for COVID-19, the primary outcome is an ordinal categorical variable, and interest focuses on the odds ratio (active agent vs. control) under the assumption of a proportional odds model.…
Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…
We explore the construction of nonsubjective prior distributions in Bayesian statistics via a posterior predictive relative entropy regret criterion. We carry out a minimax analysis based on a derived asymptotic predictive loss function and…