Related papers: Normalized Power Prior Bayesian Analysis

Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…

A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…

Any Bayesian analysis involves combining information represented through different model components, and when different sources of information are in conflict it is important to detect this. Here we consider checking for prior-data conflict…

To get Bayesian neural networks to perform comparably to standard neural networks it is usually necessary to artificially reduce uncertainty using a "tempered" or "cold" posterior. This is extremely concerning: if the prior is accurate,…

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent…

The normalized maximum likelihood (NML) is a recent penalized likelihood that has properties that justify defining the amount of discrimination information (DI) in the data supporting an alternative hypothesis over a null hypothesis as the…

This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

This paper studies the quantization of prior probabilities, drawn from an ensemble, for distributed detection and data fusion. Design and performance equivalences between a team of N agents tied by a fixed fusion rule and a more powerful…

Missing time-series data is a prevalent problem in many prescriptive analytics models in operations management, healthcare and finance. Imputation methods for time-series data are usually applied to the full panel data with the purpose of…

We investigate the use of normalizing flow (NF) models as flexible priors in Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling for iterative Bayesian calibration. Trained on posteriors from previous analyses, these models can…

The power-expected-posterior (PEP) prior is an objective prior for Gaussian linear models, which leads to consistent model selection inference, under the M-closed scenario, and tends to favor parsimonious models. Recently, two new forms of…

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…

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference,…

In many applications in biology, engineering and economics, identifying similarities and differences between distributions of data from complex processes requires comparing finite categorical samples of discrete counts. Statistical…

Historical data about disease outcomes can be integrated into the analysis of clinical trials in many ways. We build on existing literature that uses prognostic scores from a predictive model to increase the efficiency of treatment effect…

Specification of the prior distribution for a Bayesian model is a central part of the Bayesian workflow for data analysis, but it is often difficult even for statistical experts. In principle, prior elicitation transforms domain knowledge…

We present a Bayesian analysis of large-scale structure and cosmic microwave background data to constrain the form of the primordial power spectrum. We have extended the usual presumption of a scale invariant spectrum to include: (i) a…

Uncertainty quantification in reinforcement learning can greatly improve exploration and robustness. Approximate Bayesian approaches have recently been popularized to quantify uncertainty in model-free algorithms. However, so far the focus…

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the…