Spectral properties of MCMC algorithms for Bayesian linear regression with generalized hyperbolic errors

Analysis of MCMC algorithms for Bayesian linear regression with Laplace errors

Let π denote the intractable posterior density that results when the standard default prior is placed on the parameters in a linear regression model with iid Laplace errors. We analyze the Markov chains underlying two different Markov chain Monte Carlo algorithms for exploring π. In particular, it is shown that the Markov operators associated with the data augmentation (DA) algorithm and a sand...

Convergence rates and asymptotic standard errors for MCMC algorithms for Bayesian probit regression

Consider a probit regression problem in which Y1, . . . , Yn are independent Bernoulli random variables such that Pr(Yi = 1) = Φ(xi β) where xi is a p-dimensional vector of known covariates associated with Yi, β is a p-dimensional vector of unknown regression coefficients and Φ(·) denotes the standard normal distribution function. We study Markov chain Monte Carlo algorithms for exploring the i...

Algorithms for Generalized Cluster-wise Linear Regression

Cluster-wise linear regression (CLR), a clustering problem intertwined with regression, is to find clusters of entities such that the overall sum of squared errors from regressions performed over these clusters is minimized, where each cluster may have different variances. We generalize the CLR problem by allowing each entity to have more than one observation, and refer to it as generalized CLR...

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...

MCMC algorithms for fitting Bayesian models