Intuitive joint priors for Bayesian linear multilevel models: The R2D2M2 prior

Bayesian Inference for Spatial Beta Generalized Linear Mixed Models

In some applications, the response variable assumes values in the unit interval. The standard linear regression model is not appropriate for modelling this type of data because the normality assumption is not met. Alternatively, the beta regression model has been introduced to analyze such observations. A beta distribution represents a flexible density family on (0, 1) interval that covers symm...

Introducing of Dirichlet process prior in the Nonparametric Bayesian models frame work

Statistical models are utilized to learn about the mechanism that the data are generating from it. Often it is assumed that the random variables y_i,i=1,…,n ,are samples from the probability distribution F which is belong to a parametric distributions class. However, in practice, a parametric model may be inappropriate to describe the data. In this settings, the parametric assumption could be r...

Multilevel Linear Models for the Educational System

During the last eight years, interest in assessing the comparative performance of teachers, schools and educational policies has greatly increased in the USA, the UK and other countries. Particularly in the context of declining budgets for education, a serious concern for accountability and effectiveness of the school systerr1 has led to attempts to rate teachers, schools, education authorities...

Bayesian Inference for Gaussian Semiparametric Multilevel Models

Bayesian inference for complex hierarchical models with smoothing splines is typically intractable, requiring approximate inference methods for use in practice. Markov Chain Monte Carlo (MCMC) is the standard method for generating samples from the posterior distribution. However, for large or complex models, MCMC can be computationally intensive, or even infeasible. Mean Field Variational Bayes...

Extended Linear Models with Gaussian Priors Extended Linear Models with Gaussian Priors