Multiple regression is frequently used across the various social sciences to analyze cross-sectional data. However, it can often times be challenging to justify the assumption of common regression coefficients across all respondents. This manuscript presents a heterogeneous Bayesian regression...

This paper proposes a generalized class of univariate skew distributions that are constructed through mixture of two scaled normal distributions. The proposed skew distributions with the skewness parameter defined in the (0,1) interval allow us to have an application on parametric quantile...

In many manuscripts, researchers use multivariable logistic regression to adjust for potential confounding variables when estimating a direct relationship of a treatment or exposure on a binary outcome. After choosing how variables are entered into that model, researchers can calculate an...

In this paper, I propose a tractable approach to Bayesian inference in linear regression models for which the standard exogeneity assumption does not hold. By specifying a beta prior for the squared correlation between an error term and regressor, I demonstrate that the implied prior for a bias...

A central maxim in statistics is that correlation does not imply causation, and a lack of correlation does not imply a lack of causation. However, this does not mean that correlation contains no informational content whatsoever for causality. In this paper, I propose a tractable characterisation...

This paper introduces a new measure of dependence or jointness among explanatory variables. Jointness is based on the joint posterior distribution of variables over the model space, thereby taking model uncertainty into account. By looking beyond marginal measures of variable importance,...

Bayesian regularization, a relatively new method for estimating model parameters, shrinks estimates towards the overall mean by shrinking the parameters. It has been proven to lower estimation and prediction variances from those of MLE for linear models, such as regression or GLM. It has a...

We simplify the implementation of some elliptical copula regression models through the normal representation. Both copula and marginal probability density functions are expressed as the scale mixtures of normals to facilitate the estimation procedure. With the fact that all elliptical...

We present the censored regression model with the error term following the asymmetric exponential power distribution. We propose three Markov chain Monte Carlo (MCMC) algorithms: the first one uses the probability integral transformation; the second one uses a combination of the probability...

Numerous empirical studies employ regression discontinuity designs with multiple cutoffs and heterogeneous treatments. A common practice is to normalize all the cutoffs to zero and estimate one effect. This procedure identifies the average treatment effect (ATE) on the observed distribution of...