Related papers: Bayesian Inference Methods for Univariate and Mult…
One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the last method. We consider the Poisson and binomial distributions in detail to illustrate a group invariance…
We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
This survey covers state-of-the-art Bayesian techniques for the estimation of mixtures. It complements the earlier Marin, Mengersen and Robert (2005) by studying new types of distributions, the multinomial, latent class and t distributions.…
Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…
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…
Mixture autoregressive (MAR) models provide a flexible way to model time series with predictive distributions which depend on the recent history of the process and are able to accommodate asymmetry and multimodality. Bayesian inference for…
The Bayesian statistical paradigm provides a principled and coherent approach to probabilistic forecasting. Uncertainty about all unknowns that characterize any forecasting problem -- model, parameters, latent states -- is able to be…
Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
Using a collection of simulated an real benchmarks, we compare Bayesian and frequentist regularization approaches under a low informative constraint when the number of variables is almost equal to the number of observations on simulated and…
Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently we estimate the causal effect of a treatment,…
Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…
A key quantity of interest in Bayesian inference are expectations of functions with respect to a posterior distribution. Markov Chain Monte Carlo is a fundamental tool to consistently compute these expectations via averaging samples drawn…
A new empirical Bayes approach to variable selection in the context of generalized linear models is developed. The proposed algorithm scales to situations in which the number of putative explanatory variables is very large, possibly much…
There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…
Stochastic variational inference algorithms are derived for fitting various heteroskedastic time series models. We examine Gaussian, t, and skew-t response GARCH models and fit these using Gaussian variational approximating densities. We…
In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…