Related papers: From chi-squared to Bayesian model comparison and …
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
In this paper we revisit the weighted likelihood bootstrap, a method that generates samples from an approximate Bayesian posterior of a parametric model. We show that the same method can be derived, without approximation, under a Bayesian…
Several bivariate beta distributions have been proposed in the literature. In particular, Olkin and Liu (2003) proposed a 3 parameter bivariate beta model, which Arnold and Ng (2011) extend to 5 and 8 parameter models. The 3 parameter model…
Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have…
We study inference with a small labeled sample, a large unlabeled sample, and high-quality predictions from an external model. We link prediction-powered inference with empirical likelihood by stacking supervised estimating equations based…
In this paper we develop and study adaptive empirical Bayesian smoothing splines. These are smoothing splines with both smoothing parameter and penalty order determined via the empirical Bayes method from the marginal likelihood of the…
We discuss a Bayesian approach to the analysis of radial velocities in planet searches. We use a combination of exact and approximate analytic and numerical techniques to efficiently evaluate chi-squared for multiple values of orbital…
A hierarchical Bayesian approach that permits simultaneous inference for the regression coefficient matrix and the error precision (inverse covariance) matrix in the multivariate linear model is proposed. Assuming a natural ordering of the…
We develop an empirical Bayes procedure for estimating the cell means in an unbalanced, two-way additive model with fixed effects. We employ a hierarchical model, which reflects exchangeability of the effects within treatment and within…
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…
Bayesian approaches for handling covariate measurement error are well established, and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential…
The Bayesian approach provides powerful methods for variable selection. The ability to incorporate sparsity through prior beliefs and account for parameter uncertainty allows Bayesian variable selection to consistently identify which of the…
Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…
We develop a Bayesian approach for selecting the model which is the most supported by the data within a class of marginal models for categorical variables formulated through equality and/or inequality constraints on generalised logits…
Procedural material models have been gaining traction in many applications thanks to their flexibility, compactness, and easy editability. We explore the inverse rendering problem of procedural material parameter estimation from…
We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…
Bayesian experimental design involves the optimal allocation of resources in an experiment, with the aim of optimising cost and performance. For implicit models, where the likelihood is intractable but sampling from the model is possible,…
Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the…
We put forward an adaptive alpha (Type I Error) that decreases as the information grows, for hypothesis tests in which nested linear models are compared. A less elaborate adaptation was already presented in \citet{PP2014} for comparing…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…