Related papers: Hyper-g Priors for Generalized Linear Models
We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…
This paper considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a…
In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…
Prior sensitivity analysis is a fundamental method to check the effects of prior distributions on the posterior distribution in Bayesian inference. Exploring the posteriors under several alternative priors can be computationally intensive,…
Many inverse problems arising in applications come from continuum models where the unknown parameter is a field. In practice the unknown field is discretized resulting in a problem in $\mathbb{R}^N$, with an understanding that refining the…
Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between…
In this work we discuss a novel model prior probability for variable selection in linear regression. The idea is to determine the prior mass in an objective sense, by considering the worth of each of the possible regression models, given…
We introduce a Bayesian prior distribution, the Logit-Normal continuous analogue of the spike-and-slab (LN-CASS), which enables flexible parameter estimation and variable/model selection in a variety of settings. We demonstrate its use and…
The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…
The recently developed semi-parametric generalized linear model (SPGLM) offers more flexibility as compared to the classical GLM by including the baseline or reference distribution of the response as an additional parameter in the model.…
The training of high-dimensional regression models on comparably sparse data is an important yet complicated topic, especially when there are many more model parameters than observations in the data. From a Bayesian perspective, inference…
Power-expected-posterior (PEP) methodology, which borrows ideas from the literature on power priors, expected-posterior priors and unit information priors, provides a systematic way to construct objective priors. The basic idea is to use…
Inference and estimation are fundamental in statistics, system identification, and machine learning. When prior knowledge about the system is available, Bayesian analysis provides a natural framework for encoding it through a prior…
Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost…
The paper develops Bernstein von Mises Theorem under hierarchical $g$ -priors for linear regression models. The results are obtained both when the error variance is known, and also when it is unknown. An inverse gamma prior is attached to…
We report the application of implicit likelihood inference to the prediction of the macro-parameters of strong lensing systems with neural networks. This allows us to perform deep learning analysis of lensing systems within a well-defined…
Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach…
Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…
Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…