Related papers: Quantifying Observed Prior Impact
Causal effect estimation from observational data is an important and much studied research topic. The instrumental variable (IV) and local causal discovery (LCD) patterns are canonical examples of settings where a closed-form expression…
Prediction of future observations is a fundamental problem in statistics. Here we present a general approach based on the recently developed inferential model (IM) framework. We employ an IM-based technique to marginalize out the unknown…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
Large-scale black-box models have become ubiquitous across numerous applications. Understanding the influence of individual training data sources on predictions made by these models is crucial for improving their trustworthiness. Current…
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
Statistical analyses of multipopulation studies often use the data to select a particular population as the target of inference. For example, a confidence interval may be constructed for a population only in the event that its sample mean…
We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…
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…
Unlike classification, whose goal is to estimate the class of each data point in a dataset, prevalence estimation or quantification is a task that aims to estimate the distribution of classes in a dataset. The two main tasks in prevalence…
There is growing interest in Bayesian clinical trial designs with informative prior distributions, e.g. for extrapolation of adult data to pediatrics, or use of external controls. While the classical type I error is commonly used to…
While there exists a large amount of literature on the general challenges of and best practices for trustworthy online A/B testing, there are limited studies on sample size estimation, which plays a crucial role in trustworthy and efficient…
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
We address the problem of inferring the causal effect of an exposure on an outcome across space, using observational data. The data is possibly subject to unmeasured confounding variables which, in a standard approach, must be adjusted for…
Many causal models of interest in epidemiology involve longitudinal exposures, confounders and mediators. However, repeated measurements are not always available or used in practice, leading analysts to overlook the time-varying nature of…
The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in…
Importance sampling is used to approximate Bayes' rule in many computational approaches to Bayesian inverse problems, data assimilation and machine learning. This paper reviews and further investigates the required sample size for…
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…
We present a sample path dependent measure of causal influence between two time series. The proposed measure is a random variable whose expected sum is the directed information. A realization of the proposed measure may be used to identify…
Substantial advances in Bayesian methods for causal inference have been developed in recent years. We provide an introduction to Bayesian inference for causal effects for practicing statisticians who have some familiarity with Bayesian…
In Bayesian analysis, the posterior follows from the data and a choice of a prior and a likelihood. One hopes that the posterior is robust to reasonable variation in the choice of prior, since this choice is made by the modeler and is often…