Related papers: Bayesian Inference for Generalized Linear Model wi…

Bayesian Generalized Nonlinear Models (BGNLM) offer a flexible nonlinear alternative to GLM while still providing better interpretability than machine learning techniques such as neural networks. In BGNLM, the methods of Bayesian Variable…

Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…

We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely…

This paper develops a slice sampler for Bayesian linear regression models with arbitrary priors. The new sampler has two advantages over current approaches. One, it is faster than many custom implementations that rely on auxiliary latent…

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…

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…

A connection between the General Linear Model (GLM) in combination with classical statistical inference and the machine learning (MLE)-based inference is described in this paper. Firstly, the estimation of the GLM parameters is expressed as…

The generalized linear mixed model (GLMM) is widely used for analyzing correlated data, particularly in large-scale biomedical and social science applications. Scalable Bayesian inference for GLMMs is challenging because the marginal…

In this letter, we present a unified Bayesian inference framework for generalized linear models (GLM) which iteratively reduces the GLM problem to a sequence of standard linear model (SLM) problems. This framework provides new perspectives…

Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive…

Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and…

Power law scaling models have been used to understand the complexity of systems as diverse as cities, neurological activity, and rainfall and lightning. In the scaling framework, power laws and standard linear regression methods are widely…

We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…

We introduce a new computational framework for estimating parameters in generalized generalized linear models (GGLM), a class of models that extends the popular generalized linear models (GLM) to account for dependencies among observations…

The Gaussian process (GP) is a popular way to specify dependencies between random variables in a probabilistic model. In the Bayesian framework the covariance structure can be specified using unknown hyperparameters. Integrating over these…

Generalized linear models (GLM) are link function based statistical models. Many supervised learning algorithms are extensions of GLMs and have link functions built into the algorithm to model different outcome distributions. There are two…

The recent work `A unified Bayesian inference framework for generalized linear models' \cite{meng1} shows that the GLM can be solved via iterating between the standard linear module (SLM) (running with standard Bayesian algorithm) and the…

Gaussian and discrete non-Gaussian spatial datasets are common across fields like public health, ecology, geosciences, and social sciences. Bayesian spatial generalized linear mixed models (SGLMMs) are a flexible class of models for…

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…