Related papers: Bayes-assisted Confidence Regions: Focal Point Est…

The paper concerns small-area estimation in the Fay-Herriot type area-level model with random dispersions, which models the case that the sampling errors change from area to area. The resulting Bayes estimator shrinks both means and…

We propose a way to construct fiducial distributions for a multidimensional parameter using a step-by-step conditional procedure related to the inferential importance of the components of the parameter. For discrete models, in which the…

One of the key elements of probabilistic seismic risk assessment studies is the fragility curve, which represents the conditional probability of failure of a mechanical structure for a given scalar measure derived from seismic ground…

We investigate the relation between frequentist and Bayesian approaches. Namely, we find the "frequentist" Bayes prior \pi_{f}(\lambda,x_{obs}) = -\frac{\int_{-\infty}^{x_{obs}}\frac{\partial f(x,\lambda)}{\partial…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…

Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…

This article illustrates how indirect or prior information can be optimally used to construct a prediction region that maintains a target frequentist coverage rate. If the indirect information is accurate, the volume of the prediction…

Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of…

Bayesian posterior distributions naturally represent parameter uncertainty informed by data. However, when the parameter space is complex, as in many nonparametric settings where it is infinite-dimensional or combinatorially large, standard…

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

Empirical Bayes small area estimation based on the well-known Fay-Herriot model may produce unreliable estimates when outlying areas exist. Existing robust methods against outliers or model misspecification are generally inefficient when…

Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution. But is this uncertainty quantification valid in the sense that the posterior credible…

Using instruments comprising ordered responses to items are ubiquitous for studying many constructs of interest. However, using such an item response format may lead to items with response categories infrequently endorsed or unendorsed…

Estimating the difference between two binomial proportions will be investigated, where Bayesian, frequentist and fiducial (BFF) methods will be considered. Three vague priors will be used, the Jeffreys prior, a divergence prior and the…

Raking is widely used in categorical data modeling and survey practice but faced with methodological and computational challenges. We develop a Bayesian paradigm for raking by incorporating the marginal constraints as a prior distribution…

Uncertainty quantification is central to many applications of causal machine learning, yet principled Bayesian inference for causal effects remains challenging. Standard Bayesian approaches typically require specifying a probabilistic model…

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area-level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an…

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…