Related papers: Population Empirical Bayes
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…
Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…
We propose Bayesian Hierarchical Invariant Prediction (BHIP) reframing Invariant Causal Prediction (ICP) through the lens of Hierarchical Bayes. We leverage the hierarchical structure to explicitly test invariance of causal mechanisms under…
Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification. We propose predictive variational inference…
We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…
Approximate Bayesian inference methods provide a powerful suite of tools for finding approximations to intractable posterior distributions. However, machine learning applications typically involve selecting actions, which -- in a Bayesian…
We introduce a flexible empirical Bayes approach for fitting Bayesian generalized linear models. Specifically, we adopt a novel mean-field variational inference (VI) method and the prior is estimated within the VI algorithm, making the…
The task of quantifying the inherent uncertainty associated with neural network predictions is a key challenge in artificial intelligence. Bayesian neural networks (BNNs) and deep ensembles are among the most prominent approaches to tackle…
Bayesian inference is attractive for its coherence and good frequentist properties. However, it is a common experience that eliciting a honest prior may be difficult and, in practice, people often take an {\em empirical Bayes} approach,…
Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately,…
Group testing is a method of identifying infected patients by performing tests on a pool of specimens collected from patients. For the case in which the test returns a false result with finite probability, we propose Bayesian inference and…
We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…
Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, information spreading or the wisdom of crowds.…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
We propose an approximate hierarchical Bayes approach that uses the Natural Exponential Family with Quadratic Variance Function in combining information from multiple sources to improve traditional survey estimates of finite population…
Bayesian methods have proved powerful in many applications for the inference of model parameters from data. These methods are based on Bayes' theorem, which itself is deceptively simple. However, in practice the computations required are…
Markovian population models are suitable abstractions to describe well-mixed interacting particle systems in situation where stochastic fluctuations are significant due to the involvement of low copy particles. In molecular biology,…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
Modern epidemiological analytics increasingly use machine learning models that offer strong prediction but often lack calibrated uncertainty. Bayesian methods provide principled uncertainty quantification, yet are viewed as difficult to…
Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for…